Weakly Supervised Explainable Phrasal Reasoning with Neural Fuzzy Logic
Authors: Zijun Wu
Zi Xuan Zhang
Atharva Naik
Zhijian Mei
Mauajama Firdaus
Lili Mou
Venue: ICLR 2023 poster (2023)
Keywords: Neural Fuzzy Logic
Weakly Supervised Reasoning
Natural Language Inference
Explainability and Interpretability

Abstract: Natural language inference (NLI) aims to determine the logical relationship between two sentences, such as Entailment, Contradiction, and Neutral. In recent years, deep learning models have become a prevailing approach to NLI, but they lack interpretability and explainability. In this work, we address the explainability of NLI by weakly supervised logical reasoning, and propose an Explainable Phrasal Reasoning (EPR) approach. Our model first detects phrases as the semantic unit and aligns corresponding phrases in the two sentences. Then, the model predicts the NLI label for the aligned phrases, and induces the sentence label by fuzzy logic formulas. Our EPR is almost everywhere differentiable and thus the system can be trained end to end. In this way, we are able to provide explicit explanations of phrasal logical relationships in a weakly supervised manner. We further show that such reasoning results help textual explanation generation.

Published as a conference paper at ICLR 2023
WEAKLY SUPERVISED EXPLAINABLE PHRASAL REASONING WITH NEURAL FUZZY LOGIC
Zijun Wu"!, Xuan Zhang* Atharva Naik Zhijian Mei', Mauajama Firdaus' Lili Mou Deptt. Computing Science & Alberta Machine Intelligence Institute (Ami), University of Alberta Carnegie Mellon University
{zijun4, zixuan7, zimei 1 /uuabberra. ca, (mauzama. .0, doublepower peepowerrmouus mouu@gmmil........ coom
arnaikēcs. cmu. edu,
"Equal contribution, "Wrk done during the internship at UofA/Amii
ABSTRACT
Natural language inference (NLI) aims to determine the logical relationship be- tween two sentences, such as Entailment, Contradiction, and Neutral. In recent years, deep learning models have become prevailing approach NLI, but they lack interpretability and explainability. In this work, we address the explainability of NLI by weakly supervised logical reasoning, and propose an Explainable Phrasal Reasoning (EPR) approach. Our model first detects phrases the semantic unit and aligns corresponding phrases the two sentences. Then, the model predicts the NLI label for the aligned phrases, and induces the sentence label by fuzzy logic formulas. Our EPR almost everywhere differentiable and thus the system can be trained end to end. In this way, we are able to provide explicit explanations of phrasal logical relationships in weakly supervised manner, We further show that such reasoning results help textual explanation generation
INTRODUCTION
Natural language inference (NLI) aims to determine the logical relationship between two sentences (called a premise and a hypothesis), and target labels include Entailment, Contradiction, and Neutral (Bowman et al., 2015 MacCartney & Manning 2008). Figure gives example, where the hypothesis contradicts the premise. NLI is important to natural language processing, because involves logical reasoning and is key problem in artificial intelligence. Previous work shows that
NLI can be used in various downstream tasks, such as information retrieval (Krpukhin et al. 2020
and text summarization (Liu & Lapata| 2019).
In recent years, deep learning has become a prevailing approach to NLI (Bowman et al., 2015 Mou al., [016]] Wang Jiang, 2016: Yoon et al. 2018). Especially, pretrained language models with the Transformer architecture (Vaswani et al. (017) achieve oftt-oof-theart performance for the NLI task (Radford et al. 2018: Zhang et al. 2020). However, such deep learning models are black-box machinery and lack interpretability. In real applications, it is important to understand how these models make decisions (Rudin (019)).
Several studies have addressed the explainability of NLI models. Camburu et al. (0118) generate textual explanation by sequence-to-scquenc supervised learning, in addition to NLI classification; such approach is multi-task learning of text classification and generation, which does not perform reasoning itself. MacCartney et al. (2008) propose a scoring model to align related phrases; Parikh et al.] (2166) and Diang et al. (2021) propose obtain alignment by attention mechanisms. However, they only provide correlation information, instead of logical reasoning. Other work incorporates upward and downward monotonicity entailment reasoning for NLI (Hu et al.) 2020 Chen al.
202I). but these approaches are based on hand-crafted rules (e.g., every downward entailing some) and are restricted Entai 1ment only; they cannot handle Contradictio or Neutral.
In this work, we address the explainability for NLI by weakly supervised phrasal logical reasoning. Our goal is to explain NLI predictions with phrasal logical relationships between the premise and
Cooe and resources available at htttts::///giii httpss///ggtubb.cco////a----- wtt.:/.////N--UOO///EEEEEE

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hypothesis. Intuitively, an NLI system with explainable reasoning mechanism should be equipped with the following functionalities:
1. The system should be able to detect corresponding phrases and tell their logical relationship. c.g.. several men contradicting one man, but pull in a fishing net entailing holding the net (Figure [.]
2. The system should be able to induce sentence labels from phrasal reasoning. In the example, the two sentences are contradictory because there exists one contradictory phrase pair.
3. More importantly, such reasoning should be trained in a weakly supervised manner, i.e., the phrase- level predictions are trained from sentence labels only. Otherwise, the reasoning mechanism degrades to multi-task learning, which requires massive fine- ane-grained human annotations.
To this end, we propose an Explainable Phrasal Reasoning (EPR) approach to the NLI task. Our model obtains phrases as semantic units, and aligns corresponding phrases by embedding sim- ilarity. Then, predict the NLI labels (namely, Entailment, Contradiction, and Neutral) for the aligned phrases. Finally, we propose to induce the sentence-level label from phrasal labels in fuzzy logic manner (Zadeh 1988 1996). Our model is differentiable, and the phrasal reasoning component with the weak supervision of sentence NLI labels. In this way, our EPR approach satisfies all the desired properties mentioned above.
Input:
Premise: Several men helping eoch other pull in a fishing net.
Hypothesis: There
holding the net.
Sentence-Level Prediction:
Entailment
Contradiction
C Neutral
Phrase-Level Reasoning:
Entailment
Contradiction
Neutral
Unaligned
Figure 1:
The natural language inference (NL.)
task and desired phrasal reasoning.
be trained
In our experiments, we developed a comprehensive methodology (data annotation and evaluation metrics) to quantitatively evaluate phrasal reasoning performance, which has not been accomplished in previous work. We extend previous studies and obtain plausible baseline models. Results show that our EPR yields much more meaningful explanation regarding F scores against human annotation.
To further demonstrate the quality of extracted phrasal relationships, we feed them to a textual explanation model. Results show that our EPR reasoning leads to an improvement of 2 points in BLEU scores, achieving new state of the art on the e-SNLI dataset (Camburu et al. 2018).
Our contributions are summarized follows:
1. We formulate a phrasal reasoning task for natural language inference (NLI), addressing the interpretability neural models.
2. We propose an EPR model that induces sentence-level NLI labels from explicit phrasal logical labels by neural fuzzy logic. EPR able to perform reasoning a weakly supervised way.
3. We annotated phrasal logical labels and designed set of metrics to evaluate phrasal reasoning. We further use our reasoning results to improve textual explanation generation. Our code and annotated data released for future studies.
To the best of our knowledge, we are the first to develop a weakly supervised phrasal reasoning model for the NLI task.
RELATED WORK
Natural Language Inference. MacCartney & Manning 2009) propose seven natural logic relations in addition to Entailment. Contradiction, and Neutral, MacCartney & Manning (2007) also distinguish upward entailment (every mammal upward entailing some mummall and downward entailment (every mammal downward entailing every dog) as different categories. Manually designed lexicons and rules are used to interpret Entai 1ment in finer-graing manner, such as downward and upward entailment (Hu et al. 2020; Chen et al. 2021). Feng et al. (2020) apply such natural logic to NLI reasoning at the word level; however, experiments will show that their word-level treatment is not an appropriate granularity, and they fail to achieve meaningful reasoning performance.
The above reasoning schema focuses more the quantifiers of first-order logic (Beltagy al. 2016). However, the SNLI dataset (Bowman et al., 2015) we use only contains less than 5 5% samples with explicit quantifiers, and the seven-category schema complicates reasoning in the weakly supervised
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setting. Instead, adopt three- category NLI labels following the SNLI dataset. Our focus is entity-based reasoning, and the treatment of quantifiers is absorbed into phrases.
We also notice that previous work lacks explicit evaluation the reasoning performance for NLL For example, the SNLI dataset only provides sentence-level labels. The HELP Yanaka et al.) 2019a) and MED (Yanaka et al. 2019b) datasets concern monotonicity inference problems, where the label is also at the sentence level; they only consider Entailment, ignoring cntradiction and Neutral.
Thus, we propose comprehensive framework for the evaluation of NLI reasoning.
e-SNLI. Camburu et al. (2018) propose the e-SNLI task of textual explanation generation and LSTT as a baseline. Kumar & Talukdar (2020) propose the NILE approach, using multiple
decoders to generate explanations for all E, C, and N Jabels, and then predicting which to be selected.
Zhao & Vydiswaran (202T) propose the LIREx approach, using additionally annotated rationales for explanation generation. Narang et al. (2020) finetune T5 with multiple explanation generation tasks. Although these systems can generate explanations, the nature of such finetuning approaches renders the explanation generator per unexplainable. By contrast, we design textual explanation generation model that utilizes our EPR's 's phrasal reasoning, obtained in a weakly supervised manner.
Neuro-Symbolic Approaches. In recent years, neuro-symbolic approaches have attracted increasing interest in the and NI.P communities for interpreting deep learning models. Typically, these approaches are trained by reinforcement learning its relaxation, such as attention and Gumbel- softmax (Jang et al. 2017), to reason about certain latent structures in a downstream task.
For example, Lei et al. (2016) and Liu et al. (018)) extract key phrases or sentences for text classification task. Lu et al. (2018) extract entities and relations for document understanding. Liang et al. (2017) and Mou et al. (2017) perform SQL-like execution based on input text for semantic parsing. Xiong et al. (2017) hop over a knowledge graph for reasoning the relationships between entities. Li et al.] (2019) and Deshmukh et al. (202T) model symbolic actions for unsupervised syntactic structure induction. In the vision domain, Mao et al. (2019) propose a neuro-symbolic approach learn visual concepts. Our work addresses logical reasoning for the NLI task, which is not tackled in previous neuro-symbolic studies.
1996) models an assertion and performs logic calculation with probability. For example, a quantifier (e.g., "most") and assertion (e.g., "ill") are modeled by score in (0, 1); the score of a conjunction s(x1 A 222 is the product of s(x) ) and s(22). In old-school fuzzy logic studies, the mapping from language to the score is usually given by human-defined heuristies (Zadeh] 1988; Nozaki et al., 1997), and may not be suited to the task of interest. By contrast, we train neural networks predict the probability of phrasal logical relations, and induce the sentence NLI label by fuzzy logic formulas. Thus, our approach takes advantage of both worlds of symbolism and connectionism. Mahabadii multi-layer perceptrons for NLI. But they are unable to provide expressive reasoning because their fuzzy logic works sentence features. Our work is inspired by Mahabadi et al. (2020). However, propose to apply fuzzy logic to the detected and aligned phrases, enabling our approach to provide reasoning in symbolic (i.e., expressive) way. We develop own fuzzy logic formulas, which also different from Mahabadi et al. (2020).
Fuzzy Logic. Fuzzy logic (Zadeh] 1988
al. (020) apply fuzzy logic formulas replace
3 OUR EPR APPROACH
In this section, describe our EPR approach in detail, also shown in Figure It has three main components: phrase detection and alignment, phrasal NLI prediction, and sentence label induction.
Phrase Detection and Alignment. In NLI, data point consists of two sentences, a premise and hypothesis. We first extract content phrases from both input sentences by rules and heuristics. For example, "[AUX] + [NOT] VERB + [RP]" is treated as verb phrase. Full details presented in Appendix A. Compared with the word level (Parikh et al. 2016 Feng et al. 2020), a phrase is a more meaningful semantic unit for logical reasoning.
We then align corresponding phrases in the two sentences based on cosine similarity. Let P (pi.... . PPM) and H = (h,, ... hx) be the premise and hypothesis. respectively, where Pm and h, are extracted phrases. We apply Sentence-BERT (Reimers & Gurevych] 2019) to each individual
phrase and obtain the local phrase embeddings by pm SBERT(Pm). h SBERT(h,,)) We
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Phrase Detection and Alignment
cc) Sentence Induction
Scores
Sentence Label
Premise
There is
Several men
helping
each other
pull in
fishing net
Phrass
Normalize
Sentence-BERT
Local similarity matrix
Phrasal Prediction
Hypothesis
Sentence-Bre BERT
Alignment Se Reblection
Feed forward Network
holding
Local Transformer Encoder
Globel Transformer Encoder
Alighments
helping
pull
fishing net
Global similarity matrix
One man
<EMPTY>
holding
the net
Figure 2: An overview of our Explainable Phrasal Reasoning (EPR) model.
Table 1: An example showing the importance of handling unaligned phrases (in highlight).
Premise
People shopping for fruit.
People are shopping for fruit in the market
Hypothesis
People are shopping for fruit in the market
People are shopping for fruit.
Sentence NL.
[] Fntailment [] Contradiction [V] Neutral
[v] Fintallment
[] Contradiction [] Neutral
also apply Sentence-BERG to the entire premise and hypothesis sentences to obtain the global phrase embeddings p!=)) and h!!?) by mean-pooling the features of the words in the phrase. The phrase similarity is given by
sim hn.) = 7 cos(p... (,,,,,,,,)))) (. (1-7) cos(p! (
where y is a hyperparameter balancing the lexical and contextual representations of a phrase (Hewitt) & Manning 2019). is noted that Sentence- BERT is finetuned on paraphrase datasets, and thus is more suitable for phrasal similarity matching than pretrained language models (Devlin et al. 2019).
We obtain phrase alignment between the premise and hypothesis in a heuristic way. For every phrase Pm in the premise, we look for the most similar phrase h, from the hypothesis by
argmax,, sim h,
(2)
Likewise, for every phrase hn in the hypothesis, we look for the most similar phrase pm from the premise. A phrase pair (Pm: h2) is considered to be aligned if h, is selected as the closest phrase to Pm, and Pm is the closest to h, Such hard alignment differs from commonly used soft attention-bart based approaches (Parikh et al. 2016). Our aligmment method can ensure the quality of
phrase alignment, and more importantly, leave other phrases unaligned (e.g., helping each other in Figure D. which are common in the NLJ task. The process is illustrated in Figure
Phrasal NLI Prediction. Our model then predicts the logical relationship of aligned phrase pair (p. h) among three target labels: Entailment, Contradiction and Neutral. While previous work (Feng et al. 2020) identifies finer-grained labels for NLI, we do follow their categorization, because it complicates the reasoning process and makes weakly supervised training more difficult. Instead, we adopt three-way phrasal classification, which is consistent with sentence NLI labels.
We represent a phrase, say, in the premise. by a vector embedding, and we consider two types of features: a local feature p(4) and a global feature p!C), re-used from the phrase alignment component. They are concatenated as the phrase representation p = (p( phrase representation for hypothesis phrase h is obtained in similar way. Intuitively, local features force the model to perform reasoning in a serious manner, but global features are important to sentence-level prediction. Such intuition is also verified in ablation study ($ 4.2..
Likewise, the
Then, we use a neural network to predict the phrasal NLI label (Entailment, Contradiction, and Neutral). This given by the standard heuristic matching (Mou et al. 2016) based on phrase embeddings, followed by multi-layer perceptron (MLP) and three-way softmax layer:
[Pprrase (Elp, h); P Pphrase (Clp, h); Pphrass (N]p, h)] = softmax h; Ip h):po))) hl))
(3)
where o is the element-wine product, and the semicolon refers to column vector concatenation. E, C, and N refer the Entailment Contradiction and Neutral labels, respectively.
should be mentioned that a phrase may be unaligned, but plays an important role in sentence-leve ILI prediction, shown in Table T Thus, would like predict phrasal NI.I labels for unaligned
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phrases well, but pair them with a special token (P(EmPyy) h(EMPTY)), ) whose embedding is randomly initialized and learned by back pack-propagation.
Sentence Label Induction. We observe the sentence NLI label can be logically induced from phrasal NLI labels. Based on the definition of the NLI task, we develop the following induction rules.
Entailment Rule:
According Bowman et al. 2015), premise entailing hypothesis means that, if the premise is true, then the hypothesis must be true. We find that this can be oftentimes transformed into phrasal relationships:
premise entails the hypothesis if all paired phrases have the label
Entailment.
Let ((DE; he) U[(k) hx)) K= be all phrase pairs. For k 1, K, they aligned phrases; for k K 1, ................ K', they unaligned phrases paired with the special token, i.e., Pk = P(EMPTY) or h2 = HEMPPYY. Then, we induce a sentence-level Entailment score by
K'
Senttence [E|P, H)
parass (Elps, R
(4)
This works in a fuzzy logic fashion (Zadeh] 1988 1996), deciding whether the sentence-level label should be Entai Iment considering the average of phrasal predictions Here, we use the geometric mean, because it is biased towards low scores, i.e., if there exists one phrase pair with a low Entai Iment score, then the chance of sentence label being Entai Iment is also low. Unaligned pairs should be considered in Eq. 4.. because an unaligned phrase may indicate Entailment, shown in the second example of Table ! Notice that the resulting value Sseneene (E) P, H) is not normalized with respect to Contrade contradicn cnttraitiioonn and Neutral; thus, we call it a score (instead of probability). which will be normalized afterwards.
Contradiction Rule: Two sentences are contradictory there exists (at least) one paired phrase labeled Contradiction. The fuzzy logic version of this induction rule is given by
Syentence (c|P,, H) max .K phraase Caarase(Clpp) (Clpa h2)
(5)
Here, the max operator is used the induction, because the contradiction rule an existential statement, i.e., there exist(s) .... Also, unaligned phrases excluded in calculating the sentence- level Contradiction score, because an unaligned phrase indicates the corresponding information is missing in the other sentence and it cannot be Contradi ction (recall examples in Table
Rule for Neutral: Two sentences are neutral if there exists (at least) one neutral phrase pair, but there does not exist any contradictory phrase pair. The fuzzy logic formula is
Seeteenee (N/P, H) max .K' Pphrsse (N|ps, hR]]
Syentence (C/P, H))
(6)
The first factor determines whether there exists a Neutral phrase pair (including unaligned phrases, illustrated in the first example in Table TT. The second factor evaluates the negation of "at least one contradictory phrase," as suggested in the second clause of the Rule for Neutral.
Finally, normalize the scores into probabilities by dividing the sum, since all the scores already positive. This is given by
P Psentence (L|-) Sventence (L|-)
where L E (E, and 7 = Syentence (EI-) + Spentence (Cl-) + Ssentene (N)-) is the normalizing factor.
Training and Inference. We use cross-entropy loss to train our EPR model by minimizing log Psentence (t).), where E (E, C, is the groundtruth sentence-level label.
Our underlying logical reasoning component can be trained end-to-end by back-propagatio in weakly supervised manner, because the fuzzy logic rules almost everywhere differentiable. Although the max operators in Eqs. (5) and (6) may not be differentiable at certain points, they are common max-margin learning and the rectified linear unit (ReLU) activation functions, and do not cause trouble in pack-propagation
Once our EPR model is trained, we can obtain both phrasal and sentence-level labels. This is accomplished by performing argmax on the predicted probabilities and (7) respectively.
"In traditional fuzzy logic, the conjunction is given by probability product (Zaeeh 1988 We find that this gives too small Iment score compared with Contradiction and Neutral scores, causing difficulties in end-to-end training. Thus, take the geometric mean and maintain all the scores the magnitude.
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Improving Textual Explanation. Camburu et al. (2018) annotated dataset to address NLI in- terpretability by generating an explanation sentence. For the example in Figure [ the reference explanation is "There cannot be man and several men at same time."
In this part, we apply the predicted phrasal logical relationships to textual explanation generation and examine whether our EPR's output can help downstream task. Figure B shows the overview of our textual explanation generator. We concatenate the premise and hypothesis in the form of " "Premise Hypothesis :...." and feed
standard Transformer encoder (Vaswani et al.) 2017).
We utilize the phrase pairs and our predicted phrasal labels as factual knowledge to enhance the decoder. Specifically, our EPR model yields set of tuples { hg, 1s)) k== for sample, where l E {E,N, C} is the predicted phrasal label for the aligned phrases, P& and hg. We embed phrases by Sentence-BERT: p(4) and (4;;; the phrasal label is represented by a one-hot vector 4 (1e)ot(lz); They are concatenated
vector m - [p&; hy; 4... We compose the vectors as factual memory matrix M = [ : mmx] K E R xd where d is the dimension of m.g
Our decoder follows standard Transformer archi- tecture (Vaswani et al. 2017). but is equipped with additional attention mechanisms to the factual mem- ory. Consider the ith decoding step. We feed the
Next word
Factual Memory
Softmex
Phrases
Phrases in
Label
Feed-forward Network
the
running marathon
running her backyard
factual memory to MLP as M ML)(M). We
N-
Transformer Decader
in park
compute attention a over M with the embedding of
the input y1-1, and aggregate factual information c for the rows m; in M:
N-
Transformer Encoder
MLP
Factual Memory Attention
a = -oftmax(MMM M yi-1), c= c=ΣE
Premise co Hypothesis
N
k=1 agm:
Figure 3: Overview of the model for textual explanation generation.
where dg is the kth element of the vector a and m, is the kth row of the matrix M. The factual information e is fed to another layer g. = MLP(((. 11-1)) cc.
Our Transformer decoder layer starts with self-attention q. SelfAttn(g:). Then, residual connec- tion and layer normalization are applied as q: = LayerNormm + g:). A cross-attention mechanism obtains input information by v; - CrossAtint encoder. v, is fed to the Transformer's 's residual connection and layer normalization sub-layer. Multi- ple Transformer layers as mentioned above are stacked to form a deep architecture. The model is trained by standard cross-entropy loss against the reference explanation as in previous work (Kumar & Talukdar 2020; Zhho & Vydiswaran 2021 Narang et al.) (020).
H), where is the representation given by the
In this way, the model is enhanced with factual information given by our EPR weakly supervised reasoning. Experiments will show that it largely improves the BLEU score by 2 points ($) ($ being a new state of the art. This further verifies that our EPR indeed yields meaningful phrasal explanations.
4 EXPERIMENTS
4.1 DATASETS AND EVALUATION METRICS
The main dataset we used in our experiments is the Stanford Natural Language Inference (SNLI) dataset (Bowman
2015). which consists of 550K training samples, 10K validation samples, and another IOK test samples. Each data sample consists of two sentences (premise and hypothesis) and a sentence-level groundtruth label For sentence-level NLI prediction, we still use accuracy to evaluate
our approach, following previous work (Parikh et al. 2016 [Cen et al. 2017: Radford et al. 2018).
To evaluate the phrasal reasoning performance, we need additional human annotation and evaluation metrics, because most previous work only considers sentence-level performance (Feng et al. 2020)
and has not performed quantitative phrasal reasoning evaluation. Although Camburu et al. (2018) 8)
annotated phrase highlights in their e-SNLI dataset, they incomplete and do not provide logical relationships. Our annotators selected relevant phrases from two sentences and tagged them with phrasal NLI labels; they also selected and tagged unaligned phrases.
A groundtruth label is for data point, which consists of two sentences. We call it sentence-level label instead of phrasal labels.

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Table 2: Main results the SNLI dataset. 'Quoted from respective papers. 'Obtained from the checkpoint sent by the authors. Other results are obtained by our experiments. GM and AM are the geometric and arithmetic means of the F scores.
Reasoning Performance
Model
Scot Acc
F
Fc
F
Fi
Fun
GM
AM
Human
84.71
71.01
55.12
82.46
61.00
70.07
71.02
Non-ressoning
Mahabadi et
20201t
85.1
LSTM Wang & Jiang 2016
86.
Transformer RKarrrrd an 2018
89.9
SBERT Reeihers & Gurevyelz yeln 2019
91.4
Baselines
NNI. (Feng 2020
79.91
1,50
29.59
STP
85.76
62.40
34.76
37.04
76.61
51.80
50,20
52.52
Divvinii Brown al. 2020
53.75
58.00
52.04
31.08
42.24
Ours
EPR (Local, LM unfinetuned)
-6.33_no4
83,1
38.73
44.63_os:
76.61
51.80
56.39 26.39
58.98-034
EPR (Local, LM finetuned)
79.36
82.44
44.10
44.69_37
76.61
51,80
57.77
59.93_m07
EPR
(Concat, 1. unfinetuned)
84.53_am
73.29
37.95
40.56_1110
76.61
51.80
53.73g039
26.04
EPR (Concar, LM finetuned)
87.56-am
69.91
39.97
-3.31
76.61
51.80
54,46.1.35
56.32a118
We further propose set of F-scores, which are balanced measure of precision and recall between human annotation and model output for Entailment, Contradiction Neutral, and Unaligned in terms of word indexes. Details of human annotation and evaluation metrics are shown in Appendix B
The anter-annotator agreement is presented in Table iin comparison with model performance (detailed in the next part). Here, we compute the agreement by treating one annotator the ground truth and another as the system output; the score is averaged among all annotator pairs. As seen, humans generally achieve high agreement with each other, whereas model performance is relatively low. This shows that our task and metrics are well-defined, yet phrasal logical reasoning is a challenging task for machine learning models.
Textual explanation generation was evaluated on the e-SNLI dataset (Camburu et al. 2018 which extends the SNLI dataset with one reference explanation for each training sample, and three reference explanations for each validation or test sample. Each reference explanation comes with highlighted rationales, a set of annotated words the premise or hypothesis considered as the reason for the explanation annotation. We do not use these highlighted rationales, but enhance the neural model with EPR output for textual explanation generation. We follow previous work (Camburu et al. 2018 Narang et al. 2020), adopting BLEU (Papineni et al. 2002) and SacreBLEU (Post] 2018 scores as the evaluation metrics; they mainly differ in the tokenizer. Camburu et al. (2018) also report low consistency of the third annotated reference, and thus use only two references for evaluation. In
our study, we consider both two-reference and three-refereee rreerreference BLEUU/ScreBLEUU Attp///eeeBLEUUApppeniiiiii A.2 provides additional implementation details of textual explanation generation.
4.2 RESULTS
Phrasal Reasoning Performance. To the best of our knowledge, phrasal reasoning for NLI was not explicitly evaluated in previous literature. Therefore. we propose plausible extensions to previous studies baselines. We consider the study of Neural Natural Logic (NNL., [Fnn et al. 2020) as the first baseline. It applies an attention mechanism (Parikh et al.) 2016). so that each word in the hypothesis is softly aligned with the words in the premise. Then, each word in the hypothesis is predicted with one of the seven natural logic relations proposed by MacCartney & Manning (2009). We consider the maximum attention score as the alignment, and map their seven natural logic relations to our categoyy NLI labels: Equivalence, ForwardEntailmest + Entailment: Negation, Alternation + Contradiction; and ReverseEntaillmmnt Cover, Independence + Neutral.
Table 2 shows that the word-level NNL approach cannot perform meaningful phrasal reasoning, although our metries have already excluded explicit evaluation of phrases. The low performance is because their soft attention leads to many misalignments, whereas their seven-category logical relations are too fine-grained and cause complications weakly supervised reasoning. In addition, NNL does not allow unaligned words in the hypothesis, showing that such model is inadequate for NLI reasoning. By contrast, our EPR model extracts phrases of meaningful semantic units, being an appropriate granularity of logical reasoning. Moreover, work with three-categon NLI labels following the sentence-level NLI task formulation. This actually restricts the model's 's capacity, forcing the model perform serious phrasal reasoning.
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Table 3: Results of ablation studies on SNLI.
Model
Features
Sent Acc
Fr
Fr.
Reasoning Performance
Fir
Fai
GM
AM
Local
76.33
83,11 10:
38,73
44.63.005
76.61
51.80
56.39
58,98.014
Full model
Global
24.03
20.0
35.12_m00
36.37
76.61
51.80
51.41
24.15
Concat
84.53+a19
73.29
37.95
40.56+1.10
76.61
51.80
53.73
56.04
Local
72.44
63.21
22.65
32.04
65.94
36.13
40.53
43.99
Random chunker
Global
82.81
58.09
30.64
27.49
65.94
36.13
41.05
43.66
Concat
83.09
32.41
31.14
65.94
36.
42.66
44.87
Local
71.10
73.79
29.39
28.99
70.19
43.11
45.27
49.09
Semantic role laheling
Global
82.81
60:14
32.07
30.48
70.19
43.11
44.67
47.20
Concat
83.11
61.64
31.76
28.33
70.19
43.11
44.15
47.01
Local
68.52
59.32
21.79
26.20
51,43
16.50
31,02
35.05
Random alignment
Global
81 .999
53.85
35.10
31.39
51.43
16.50
34.71
37.66
Concat
82.49
57.22
34,83
30.91
51.43
16.50
34.97
38.18
Local
79.61
77.38
37.14
36.13
76.61
$1.80
52.84
55,81
Mean induction
Global
83.82
55.08
29.92
24.70
76.61
51.80
43.82
47.62
Concat
84,96
57.12
31,93
31.41
76.61
51.80
46.92
49.77
In addition, we include another intuitive SBERT-based competing model for comparison. We first apply our own heuristics of phrase detection and alignment (thus, the model will have the same FuP and Fis scores); then, we directly train the phrasal NLI predictor by sentence-level labels. We obtain the sentence NLI prediction by taking argmax over Eq. (7). We call this STP (Sentence label Training Phrases). As seen, STP provides some meaningful phrasal reasoning results, because the training can smooth out the noise of phrasal labels, which are directly set as the sentence-level labels. But still, its performance is significantly lower than our EPR model.
We experimented with baseline of few-shot prompting with GPT-3 (Brown et al. 2020). and the implementation detail shown in Appendix A.2 We see that GPT-3 is able to provide more or less meaningful reasoning, and surprisingly the contradiction F-score is higher than all competing methods. However, the overall mean F scores are much lower. The results show that phrasal reasoning is challenging for pretrained language models, highlighting the importance of our task formulation and the proposed EPR approach even in the prompting era.
Among EPR variants, reasoning performance, and that EPR with concatenated features achieves a good balance between sentence-level accuracy and reasoning. Our EPR variants were run 5 times with different initialization, and standard deviations are also reported in Table As seen, our improvement compared with the best baseline is around 9. 9.1-10.7 times the standard deviation in mean F scores, which is large margin. Suppose the I' scores are Gaussian distributed 4] the improvement is also statistically significant (p-value <4.5e-20 comparing our worse variant with the best competing model by one-sided test).
that EPR with local phrase embeddings achieves the highest
We further compare our EPR with non-reasoning models (Wang & Jiang, 2016; Radford et al., 2018). which are unable to provide phrasal explanations but may or may not achieve high sentence accuracy. The results show that our phrasal EPR model hurts the sentence-level accuracy by 2-4 points, when the model architecture is controlled. This resonates with traditional symbolic Al approaches (MacCartney & Manning 2008), where interpretable models may not outperform black- box neural networks. Nevertheless, our sentence-level accuracy still decent, outperforming a few classic neural models, including fuzzy logic applied to sentence embeddings (Mahabadi et al. 2020).
Analysis. We consider several ablated models to verify the effect of every component in our EPR model. (1) Random chunker, which splits the sentence randomly based on the number of chunks detected by our system. (2) Random aligner, which randomly aligns phrases but keeps the number of aligned phrases unchanged. (3) Semantic role labeling, which uses the semantic roles, detected by AlIenNLP (Gardner et al. 2018), as the reasoning unit. (4) Mean induction, which induces the sentence NLI label by the geometric mean of phrasal NLI prediction. In addition, we consider local phrase embedding features, global features, and their concatenation for the above model variants. Due to large number of settings, each variant was run only once; do not view this as concern because Table 2 shows low variance of our approach. Also, the underlying language model is un-finetuned our ablation study, as yields slightly lower performance but much more efficient.
As seen in Table 3 the random chunker and aligner yield poor phrasal reasoning performance, showing that working with meaningful semantic units and their alignments important to logical reasoning. This also verifies that our word index-based metrics are able to evaluate phrase detection
'When the score has low standard deviation, a Gaussian distribution is reasonable assumption because the probability of exceeding the range of F' scores is extremely low.
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and alignment in an implicit manner. We further applied semantic role labeling as reasoning unit. We find its performance is higher than the random chunker but lower than our method. This is because semantic role labeling is verb-centric, and the extracted spans may be incomplete.
Interestingyy, local features yield higher reasoning performance, but global and concatenated features yield higher sentence accuracy. This is because global features provide aggregated information of the entire sentence and allow the model to bypass meaningful reasoning. In the variant of the mean induction, for example, the phrasal predictor can simply learn to predict the sentence-level label with global sentence information; then, the mean induction is an ensemble of multiple predictors. In this way, it achieves the highest sentence accuracy (0.43 points higher than our full model with concatenated features), but is 6 points lower in reasoning performance.
This reminds us of the debate between old schools of AI (Chandrasekaran al. 1988 Boucher & Dienes, 2003 Goel, 2022). Recent deep learning models take the connectionists' view, and generally outperform symbolists' approaches in terms of the ultimate prediction, but they lack expressible explanations. Combining neural and symbolic methods becomes a hot direction in recent Al research (Liang et al. [017]] Dong et al., 2018 Yi et al. 2018). In general, our EPR model with global features achieves high performance in both reasoning and ultimate prediction for the NLI task.
Results of Textual Explanation Gen- eration. In this part, we apply EPR's s predicted output-phrasal log- factual knowl- edge to textual explanation genera- tion. Most previous studies use the groundtruth sentence-level NLI label and/or highlighted rationales. This re- quires human annotations, which are consuumin to obtain. By contrast, we require no extra human- annotated resources; our factual knowl- edge is based on our weakly super- vised reasoning approach.
Table 4: Textual explanation results on e-SNLI. Previous work uses auxiliary information (L: the groundtruth NLI label; H: human-annotated highlights), but we use neither. Quoted from respective papers. *Evaluated by checkpoints. Our replication with provided code.
ical relationships-
Model
Info
BLBU reeff
SacreBLEU refs
nofs
Cambura al. 2018/1
27.58
NILE Kumar Talukdar NILE Kumar& & Talukdar 2010
20100
28.57
37.73
32.51
41.78
28.67
37,84
32.74
42.06
Finetuned W 1yyay Narang
2020
32.40
FinetunedWTS... nn
Karang et al.
2120
33.70
(Zhoo Vydiswaran
17.22
21.24
26.68
Finetune 159mt
27.75
36.78
31.74
40.89
Annotated Highlightssa
27.91
36.90
32:20
41.21
EPR Outputisoou (ours)
29.91
38.30
33.96
42.63
Table 4 shows our explanation generation performance e-SNLI. Since evaluation metrics are not consistently used for cxplanation generation in previous studies, we replicate the approaches when the code checkpoint is available. For large pretrained models, quote results from the previous paper (Narang et al. 2020). Their model is called WT5, having 220M or 11B parameters depending on the underlying 15 model. Profoundly, we achieve higher performance with 60M-parameter T5-small, which is 3.3x and 170x smaller in model size than the two WT5 variants.
In addition, conducted a controlled experiment using the rationale highlights annotated by Camburu et al. (2018) for e-SNLI. It achieves a relatively small increase of 0.2-0.5 BLEU points, whereas our EPR's outputs yield 2-point improvement. The difference in the performance gains shows that our EPR's phrasal logical relationships provide more valuable information than human- annotated highlights. In general, we achieve a new state of the art on e-SNLI with small language model, demonstrating the importance of phrasal reasoning in textual explanations.
Additional Results. We show additional results as appendices. $ C.I Reasoning performance on the MNLI dataset; $ C Error analysis; $ C.3 Case studies of our EPR model; and S C.4 Case studies
of textual explanation generation.
Conclusion. The paper proposes an explainable phrasal reasoning (EPR) model for NLI with neural fuzzy logic, trained including data annotation, evaluation metrics, and plausible baselines. Results show that phrasal reasoning for NLI is a meaningfully defined task, as humans can achieve high agreement. Our EPR achieves decent sentence-level accuracy, but much higher reasoning performance than all competing models. We also achieve a new state-of oftte-o-thhe-rr performance on e-SNLI textual explanation generation by applying EPR's 's phrasal logical relationships.
weakly supervised manner. We further propose an experimental design,

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A IMPLEMENTATION DETAILS
A.1 PHRASE DETECTION
We present more details about our phrase detection. We use SpaCy to obtain the part-of-speecl (POS) tage) of every word. SpaCy also tags noun phrases. However, a noun phrase follows preposition (with fine-grained POS tag being IN), we remove it from noun phrases but tag it as prepositional phrase.
In addition, extract verbs by the POS tag VERB. A verb may be followed by particle with the fine-grained POS tag being RP (e.g., show off). treated as a verb phrase. In order to handle negation, allow optional AUX NOT before verb, (e.g.. could not help). This, however, only counts less than 1% in the dataset, and does not affect our model much.
To capture other potential semantic units, treat remaining open class word as individual phrases. Finally, the remaining non-content words (in the categories of closed words and others) are discarded (e.g., "there is"). This is appropriate, because they do not represent meaningful semantics play
'nttps://spacy. 10 'See in htt.///chhciiiii/o///////o/o///a
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Table Our rules for phrase detection. "I"" means the item is optional.
Example: The woman showing off her blue dog the playground.
Number
Phrase type
Rule
Extracted phrase(s)
Prepositional phrase
IN + NP NP
at the playground
2
Noun phrase
The womanl her blue dog showing off
3
Verb phrase
[AUX] + [NOT] + VERB [RP]
4
Others
Other open class words
(a) Sentence-level accuracy
(b) Phrasal reasoning F-score
89.0
SNLI
Accuracy
60.3
88.0
54
07.5
$7.0
T-score
0.0
0.2
0.4
0.0
38
1.0
50
81.0
MNLI
Accuracy
80.0
SNUI (GMF)
SNIUI (AMF)
19.
MNLI (AMF)
785
0.4
38
0.4
34
Coefficient global reatures
Coefficient global
Figure 4: Results of tuning the coefficient of global features.
role in reasoning. T summarrzzs all the rules used in our approach. They executed in order and extracted phrases are exclusive. For example, the playground in the phrase at the playground will not be treated as standalone noun phrase, as is already part prepositional phrase.
Empirically, our rule-based approach works well for the NLI dataset, and our logical reasoning is at the gramularity of the extracted phrases.
A.2 SETTINGS
Details of the EPR Model. We chose the pretrained model all-mpnet-base-v22 from the Sentence- BERT study (Reimers & Gurevych] 2019) and obtained 768-dimensional local and global phrase embeddings. Our MLP had the same dimension as the embeddings. i.e., 768D for the local and global variants, or 1536D for the concatenation variant. We chose the coefficient for the global feature in Eq. 1 from a candidate set of {0.0, 0.2, 0.4, 0.6, 0.8, 1.0). Figure 4 shows the hyperparameter tuning results SNLI (mentioned in $ 4.2) and MNLI (to be discussed in $ C.I. We find that 0.4 yields the best sentence accuracy SNLI, and that 1.0 the best for MNLI. As our focus is on reasoning, we set the coefficient to be 0.6, because yields the highest phrasal reasoning performance and decent sentence-leve performance for both experiments and in terms of both geometric mean and arithmetic mean of F scores. The pretrained language model (LM) un-finetuned during training. Finetuning yields higher performance (Table whereas un-finetuned
either finetuned or
LM is more efficient for in-depth analyses (Table 3). We trained the model with batch size of 256. We used Adam (Kinmma & Ba 2015) with learning rate of 5e-5, =,,0,9 ,3=0,999,, learning rate warm up over the first 10 percent of the total steps, and linear decay of the learning rate. The model was trained up to 3 epochs, following the common practice (Dodge et al. 2020). Our main model variants were trained times with different parameter initializations, and we report the mean and standard deviation.
Details of Textual Explanation Generation. We used the pretrained T5-small model for finetuning with a batch size of 32. The optimizer was Adam with an initial learning rate of 3e-4, ,3 =099., 8,=0.999, learning rate warm-up for the first 2 epochs, and linear decay of the learning rate up to 10
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The phrasal logical reasoning between two sentences: "Several men helping each other pull in fishing net." and "There is one man holding the net." is:
1. Entailment: "pull in fishing net" vs. "holding the net".
2. Contradiction: "Several
vs. "one man".
3. Neutral: None.
4. Unaligned premise: "helping each other".
5. Unaligned hypothesis: None.
The phrasal logical reasoning between two sentences: "An elderly couple are looking at black and white photos displayed on a wall." and "Octogenarians in heavy coats admiring the old photographs that decorated the wall. is:
1. Entailment: "An elderly couple" vs. "Octogenarians", "displayed on wall" vs. "decorated the wall".
2. Contradiction: None.
3. Neutral: "looking black white photos" vs. "admiring old photographs".
4. Unaligned premise: None.
5. Unaligned hypothesis:" "in heavy coats".
The phrasal logical reasoning between sentences: "[PREMISE]" and "[HYPOTHESIS]" is:
Figure 5: The prompt for phrasal reasoning.
epochs; then we decreased the learning rate to 3e-6 and trained the model until the validation BLEU score did not increase for epochs.
Details of the Prompting Baseline. We adopted the GPT-3 (the text-davinch -003 version with 175B parameters) [Brown et al. 2020) as a prompting baseline to demonstrate large language models (LLMs)' phrasal reasoning ability.
We consider exemplar- based prompting, because it is unlikely for an LLM to output structured reasoning results in zero-shot manner. Moreover, our examples are chosen cover all reasoning cases. We also set the temperature of decoding to to obtain deterministic reasoning, following CoT prompting (Wei et al.) 2022). Rule-based post-processing was applied to extract slot values. Figure presents the prompt used for phrasal reasoning.
B DATA ANNOTATION AND REASONING EVALUATION METRICS
Previous studies have not explicitly evaluated reasoning performance. Typically, they resort to sentence-level classification accuracy (Wang & Jiang, 2016 Mahabadi et al., 2020) or case stud- ies (Parikh al.) 2016 Feng et al. (0200) demonstrate the effectiveness of their alleged interpretable models, which we believe is inadequate.
Therefore, annotated model-agnostic corpus about phrasal logical relationships and developed set of metrics to evaluate the phrasal reasoning performance quantitatively. The resources are released on website (Footnote 1) to facilitate future research.
B. DATA ANNOTATION
We annotated the phrases and their logical relationships a data sample. The annotators were asked select corresponding phrases from both premise and hypothesis, and label them as either Entai Ietaillmen meett, Contradictt radiction, or Neutral, with the sentence-level NLI label being given. Annotators could also select phrase from either a premise or hypothesis and label it as Unalig repeated until all phrases are labeled for data sample. Figure shows a screenshot of our annotation page. In the left panel, the annotator could select phrases in the two sentences and mark them with NLI labels. The annotator can view sample's s annotated phrases in the right panel and navigate through different samples.
The process can be
The annotation was performed by three in-lab researchers who are familiar with the NLI task. Our preliminary study shows low agreement when the annotators are unfamiliar with the task; thus is inappropriate to recruit Mechanical Turks for annotation. We randomly selected 100 samples for annotation, following previous work on the textual explanation for SNLI (Camburu et al. 2018).
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Collaas
Annotate the Sentence Below i
Switch Uper
Premt
A man eearing inn a weldiing mask working g on ducl.
SNLJ 546
Gold Label soatrddctioe
Label
Presise
Rypoltenis
hypothesis The working underneath vehicle
underneth
on OxC
Unaligned
muskk
weiding
Clear
Clear
Clear All
Clear
E: Eetallant Castrodiciie,
Meaning
Bookmark
Navigate
View Annotations
Prev
Save
Next
Page 10
Boskmarked
Figure 6: screenshot of the annotation page.
Table Examples illustrating the proposed metrics, where we consider the Entai Iment category. "I" refers to phrase segmentation.
Example annolation entailment (in highlight):
Premise: kid in red is playing gurden.
Hypothesis: A child in red is watching TV in the bedroom,
Example Output
p!
p(
P
R[")
RE
Rig
Fe Explanation
P in a garden
Although in occurs in the annotation, the word indexes are different. The reasoning is wrong. Mis-matched phruses in hypothesis.
H
in the bedroom
0
0
P
kid
0
0
1
0
0
0
H
watching TV
The reasoning is wrong. All word indexes match the annotation. The reasoning is correct.
P
kid in red
H child in red
which is adequate show statistical significance. Since our annotation only concerns data samples, it is agnostic to any machine learning model.
B.2 EVALUATION METRICS FOR PHRASAL REASONING
We propose set of F-scores in Entai Iment, contradiction Neutral, and Unal Unaligned to quantita- tively evaluate the phrasal reasoning performance. We first introduce our metric for one data sample and then explain the extension corpus.
Consider the Entailment category as an example. We first count the number of "hits" (true positives) between the word indexes of model output and annotation. Using word indexes (instead of words) rules out hitting the words in misaligned phrases (Example 1, Table 6). Then, we calculate precision scores for the premise and hypothesis, denoted by p!P) and p( respectively. Their geometric mean PE = (P!!") ( is considered as the precision for Entailment. Here, the geometric mean rules out incorrect reasoning that hits either the premise hypothesis, but not both (Example Table 6). Further, we compute the recall score R& in similar way, and finally obtain the F-score by F = 2P. Rt. Likewise, Fe and Fg are calculated for Contradiction and Neutral. In addition, Rt+R:
we compute the f'scorr for unaligned phrases in premise and hypothesis, denoted by Fie and Fin. respectively.
When calculating our F-scores for corpus, we use aveeree, i.e., the precision and recall ratios calculated in the corpus level. This is more stable, especially considering the varying lengths of sentences. Moreover, we compare model output against three annotators and perform an arithmetic average, further reducing the variance caused by ambiguity.
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Table Results on MNLI. 'Quoted from respective papers. *Our replication.
Reasoning Performance
Model
Sent Ace
Fs
Fc
Fup
Fin
GM
AM
Human
85.15
73.44
73.18
46.31
67.85
69.52
Non-reasoning methods
Mahabadi et al. 22020
73.8
LSTM (Wang el al. 2019
72.2
Transformer (Radiont of al. 2018
82.1
Reasoning melhods
NNL (Feng et al. 2020
61.28
50.33
32.00
49.78
0.00
0.00
33.03
STP
75.15
55,47
51.72
64.32
37,57
51.31
52.27
EPR (Concat, LM finetuned)
79.65_0.1
61.76_0032
52.09
64.32
37.57
52.80
53.931007
It should be emphasized that our metrics evaluate phrase detection and alignment in implicit manner. poor phrase detector and aligner will result in a low reasoning score (shown in our ablation study), but do not explicitly calculate phrase detection and alignment accuracy. This helps cope with the ambiguity of the phrase granularity (Example 3, Table 6).
To summarize, propose evaluation framework including data annotation B.1 and evaluation metries ($ B.2 These are our contributions in formulating the phrasal reasoning task for NLI.
C ADDITIONAL RESULTS
C.I RESULTS ON MNLI
In this appendix, provide additional results the matched section of the MNLI dataset (Williams) et al. (018), which consists of 393K training samples, 10K validation samples, and another 10K test samples. It has the same format as the SNLI dataset, but samples come from multiple domains and are more diverse. We follow & [.]] and use the same protocol to create the phrasal reasoning annotation for the MNLI dataset based on 100 randomly selected samples. However, we found that MNLI is much noisier than SNLI; particularly, the sentences labeled as Neutral in MNLI share few related phrases. For example, the two sentences not have much in common in the sample Premise: If you still want to join, it might be worked." and "Hypothesis: Your membership is the only way that this could work". Moreover, the inter-human agreement is low the Neutral category. Therefore, we believe the corpus quality is less satisfactory for Neutral. To ensure meaningful evaluation, we ignored the evaluation of Neutral this experiment, although our reasoning approach is not changed. The remaining 60 samples containing Entailment and contradiction serve the MNLI phrasal reasoning corpus.
We consider the EPR variant with concatenated local and global features, since the SNLI experiment shows it achieves a good balance between sentence-level accuracy and reasoning. Our models were run 5 times with different initializations.
As seen in Table 7 our EPR approach is again worse than humans, but largely improves the reasoning performance compared with NNL. and STP baselines. Its sentence-level prediction is comparable to (although slightly lower than) finetuning Transformers. The results are highly consistent with SNLI experiments, showing the robustness of our approach.
It is important to notice that the EPR model here is trained on MNLI sentence labels, and is not transferred from the SNLI dataset. our preliminary experiments, tried transfer learning from SNLI to MNLI and failed to obtain satisfactory performance. We found that our EPR is more prone to the out-of- vocabuuuyy issue (i.e., does not predict well for the phrases in the new domain), whereas black-box neural network may learn biased sentence patterns and achieve higher performance in transfer learning.
C.2 ERROR ANALYSIS
To show how phrasal reasoning affects sentence-level prediction, we perform analysis in T Specifically, we examine the reasoning performance (arithmetic mean F F-scores) when the sentence label is correctly and incorrectly predicted the SNLI dataset. As shown, EPR models
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Table 8: Sentence-level prediction count and arithmetic average reasoning performance (F-score) when the sentence label is correctly and incorrectly predicted on the SNLI dataset.
Count (in percentage)
Reasoning performance (AMF)
Sentence-level prediction
Local finetuned Concat finetuned
Local finetuned
Concat finetuned
Correct
1.36
87.8
65.7 6
58.68_0.67
Wrong
24.6 1136
12.2
40.74
37.55 37.58_3.28
Overall
100.0+0.00
100.0
59.93
56.32=1113
Three young borss enjoving a day at the beach.
Aman playing tesch with two brown dogi-
(a)
Seccial
The boys are the beach
The dogs are asleep
Groundrruth: Feutzal Prodiction: Sheutzel
Crnundrnute Taxt wi iment:
Predetion: Neutra!
Walkers on a concrete boardwalk under blue sky.
An elderly couple heavy looking black and white photos displayed on a well.
(c)
blue
beach.
Octegenarians admining the old photographs that decorated the wall
Figure 7: Examples of explainable phrasal reasoning predicted by our EPR model. Words in one color block are detected phrases, dotted line shows the alignment of two phrases, and the color represents the predicted phrasal NLI label. In Example (d), EPR's prediction suggests the provided label in SNLI is incorrect.
with both local and concatenated features have much higher reasoning performance when sentence labels are correctly predicted than incorrectly predicted. The positive correlation between phrasal reasoning performance and sentence-level accuracy shows our fuzzy logic induction rules indeed make sense.
We also find that the model with local features has a higher reasoning performance than with concatenated features, even when the sentence-level prediction is wrong. This is because the local model is unaware of the context of the sentences. Thus, it must perform strict phrasal reasoning based the induction rules, even if in this case the reasoning process is imperfect and leads to sentence-level errors.
C.3 CASE STUDY OF EPR
We present case studies of EPR in Figure Our EPR performs impressive reasoning for the NLI task, which is learned in weakly supervised manner with only sentence-level labels.
In Example (a), the two sentences are predicted Entai Iment because three young boys entails the boys and at the beach entails in the beach, whereas unaligned phrases enjoying and day allowed In Example (b), playing contradicts asleep, and the two sentences
the premise for also predicted Contr Contradiction. Likewise, Example (c) is predicted Neutral because the aligned phrases on a concrete boardwalk and near the beach are neutral.
In our study, also find several interesting examples where EPR's reasoning provides clues suggest- ing that the target labels may be incorrect in the SNLI dataset. In Example (d), our model predicts Neutral for looking and admiring, well as for at black and white photos and the old photographs. Thus, the two sentences are predicted Neutral instead of the provided label Entai Iment. We be- lieve our model's reasoning and prediction correct, because people looking at something may or may not admire it; a black-and-white photo may or may not be an old photo (as it could be black-and- white artistic photo).
C.4 CASE STUDY OF THE TEXTUAL EXPLANATION GENERATION
We conduct another case study to show how EPR's reasoning is used in the textual explanation generation task. As seen Figure g our EPR reasoning yields structured factual tuples: on a deserted beach entailing the beach, Some dogs contradicting only one dog. and running unaligned (matched with a special token [EMPTY]). Our explanation generation model attends to these factual tuples, and the heat map shows that model gives the most attention weights (with average of
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Input Premise Some dogs running on deserted beach.
Hypothesis: There is only one dog beach.
Label Contradict (not used during our explanation generation)
Reasoning Output
Premise phrase
Hypothesis phrase
EPR label
Attention score
on a deserted beach
at the beach
23.16
Some dogs
only dog [EMPTY]
61.22
running
15.62
Output explanation Some dogs is mare than one dog.
Reference explanations:
(1) Some is more than one, therefore there can't be only one dog.
(2) Some indicates more than one dog. One dog not some dogs.
(3) Some dogs are not one dog.
Average
attention
some
dogs
is
than
dog
[EOS]
score
1.0
deserted beach at the beach
0.30
0.30
Same dogs only one dog
0.57
0.66
0.5
running [EMPTT]
0.33
0.15
0.22
0.16
0.11
0.22
0.04
0.02
0.10
0.16
Figure 8: Case study of the textual explanation generation. The heat map shows the step-by-step and average attention weights the factual tuples (vertical axis).
0.61) to the tuple, Some dogs contradicting only one dog, to generate the explanation "Some dogs is more than one dog." This example illustrates that the factual tuples given by our EPR model provide meaningful information and improve textual explanation generation.
D LIMITATION AND FUTURE WORK
This paper performs phrase detection and alignment by heuristics. They work well empirically in our experiments, although further improvement possible (for example, by considering syntactic structures). However, main focus is neural fuzzy logic for weakly supervised reasoning. This largely differs from previous work based on manually designed lexicons and rules (Hu et al. 2020 Chen et al.) 2021).
Our long-term goal to develop a weakly supervised, end-to-end trained neuro-symbolic system that can extract semantic units and perform reasoning for given downstream NLP task. This paper an important milestone toward the long-term goal.
E ETHICAL STATEMENTS
Our work involves human annotation of the phrasal logical relationships. Since the research subject here is logic (rather than humans), there are minimal ethical concerns. We nevertheless followed a standard protocol of human evaluation (involving identity protection, and proper compensation). approved by our institional ethics board.
ACKNOWLEDGMENTS
We thank all reviewers and chairs for their valuable comments. The research is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) under Grant No. RGPIN2020-04466 the Amii Fellow Program, the Canada CIFAR AI Chair Program, UAHJIC project, donation from DeepMind, and the Digital Research Alliance of Canada (alliancecan.cam Atharva Naik contributed to the research as an intern the University of Alberta through the Mitacs Globalink program.
19


Reviews:
[{"review_id": "uzscxuYOb_", "reviewer": "Reviewer_VdSJ", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes an interpretable method for Natural Language Inference: first, the premise and hypothesis sentences are splitted into “phrases” (or sub-sentences) with a custom heuristic method, then a pre-trained sentence-BERT is used with cosine-similarity to align phrases from the premise to phrases from the hypothesis, then a Transformer network predicts a NLI label (Entailment / Contradiction / Neutral) for each pair of aligned phrases. Finally, a set of fuzzy logical rules combine those predictions to infer the overall sentence pair NLI label.\n\nExperiments show that the phrase alignments and their NLI labels agree with human judgment. However it seems like the overall NLI prediction is not beating a simpler Transformer baseline.\n", "summary_of_the_review": "This paper represents a lot of work but its motivation is not clearly presented. It is interesting to analyze sub-phrases NLI alignment but results do not show a strong improvement over a transformer baseline on the NLI task. The motivation of this work should be clearly mentioned at the beginning of the paper.\n", "strength_and_weaknesses": "**Strengths**:\n\nThis work proposes a novel technique to do NLI at a sub-sentence level. It is interesting to analyze this behavior in order to better understand how the model behaves. \n\nIn addition, this work proposes a heuristic approach relying on SpaCy tagger to create the sub-sentence chunks.\n\nEventually, the set of fuzzy logical rules is also a contribution of this work.\n\n**question** :  can the authors report how the quality of the phrase definition influences the performance of the sentence-BERT alignment which in turn influences the overall NLI accuracy?\n\n**Weaknesses**:\n\nFrom table 2 it looks like the proposed method is not better than the Transformer baseline on the overall sentence accuracy. It should be mentioned that this work proposes an interpretable way of performing the task of NLI by essentially doing NLI on sub-phrases but this is at the cost of a weaker overall performance.\n\nIt is not clear if this work proposes a new task (sub-phrases NLI) or a new method for doing NLI. In both cases it is not clearly shown that predicting “phrases” NLI labels is beneficial for the NLI task. Maybe the set of fuzzy logical rules are not optimally designed for the model to take advantage of the “phrases” labels? It is very possible that large models rely on other statistical features not captured by our human judgment of what may or may not help performing NLI.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "atEe6BMmyE6", "reviewer": "Reviewer_72Kh", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes a new method for sentence-level natural language inference, which uses intermediate phrase-level entailment annotations to reach to a sentence-level conclusion. First, content phrases are extracted based on a set of heuristics. Secondly, an alignment is found between phrases from the premise and phrases from the hypothesis according to their similarity given by a pretrained text-embedding model. Third, a classification layer predicts class probabilities for each of the alignment pairs. This classification layer is not trained directly from alignment-pair labels, but instead, the predicted probabilities are combined into sentence-level entailment class probabilities, for which labels are available. Hence, phrase-level classification is trained implicitly in a weakly supervised way through sentence-level training.\nThe model is evaluated on three main tasks: Sentence-level entailment, phrase-level entailment (for which a dataset is created), and explanation generation.\nWhile the proposed model achieves competitive results at the sentence-level, it is the only model capable of phrase-level entailment. For explanation generation, it is demonstrated that inclusion of phrase-level annotations obtained from the model helps to generate better explanations.\n", "summary_of_the_review": "The paper makes a number of valuable contributions and has no major weaknesses. I recommend acceptance.", "strength_and_weaknesses": "Strengths:\n* many contributions: a model capable of phrase-level entailment classification, a dataset for evaluation, ablations, multiple use cases\n* the paper is well written\n* significant interest to the NLP community\n\nWeaknesses:\n**Update:** The following weaknesses have been resolved during rebuttal.\n* some ablations are missing or too unclear to fully support all claims:\n    * You claim that EPR achieves a good balance between sentence-level and phrase-level performance. However, it is not clear in how far the provided non-reasoning baselines are comparable, as they are trained with different underlying pretrained models. If I understand correctly, you are missing a controlled experiment where you use the same underlying LM as your model but finetune it in the \"conventional\" way, i.e., by plugging a heuristic matching feature layer on top of a siamese encoder, or by training it BERT-style.\n    * What is the purpose of your baseline called \"Sentence label Training Phrases\"? In my understanding it is proposed to show that directly using the sentence-level labels for phrase-level predictions is not suitable. But it doesn't appear to be a controlled experiment, because it uses a different underlying language model? Moreover, how do you obtain sentence-level classification for this model if it is only trained on phrase-level classification?", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "X2O602RiR6t", "reviewer": "Reviewer_vyjc", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes a phrase-level NLI model that outperforms previous baselines for NLI on SNLI dataset. The proposed model also has improved interpretability thanks to the phrase-level similarity matrix. ", "summary_of_the_review": "The paper proposes a NLI model that has improved explainability. Evaluation is through, even though results are still not on-par with general purpose transformer models. The proposed method also may have trouble for uncurated data.", "strength_and_weaknesses": "Strength:\n1. The proposed model achieves significant improvement in sentence level accuracy when compared to the previous reasoning model baselines, namely NNL and STP, on the SNLI dataset.\n2. Good amount of ablation studies were performed to understand the contributions of each component (e.g. phrase chunking, phrase alignment, fine-tuning etc) .\n3. The model is interpretable to some degree in that it can utilize the phrase-level similarity matrix to generate phrase pairs that contribute to the inference results.\n\nWeakness:\n1. Even with the sophisticated design, the model performance still lacks behind a non ad-hoc transformer model (Transformer model in Table 2). While the added inductive-bias does add more interpretability, this seems to suggest that training universal large LM is still the best performant choice, as demonstrated by various big LM papers.  \n2. The proposed phrasal alignment only works when the dataset are well curated and don't use synonyms, I wonder how much it will be applicable in the wild. Specifically, 1) How well does sentence BERT produced embeddings deal with synonyms and different phrasing of the same content? Is there any analysis on this. 2) Real world NL texts are not as concise as in SNLI, there can be added redudant adjectives, disfluencies,  reversed sentence structure. I wonder if alignment will fail for some of these cases.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "VylQNsPZgI", "reviewer": "Reviewer_K5wq", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper studies the problem of the explainability of NLI tasks. To address the problem, this paper presents a phrase-based reasoning approach by first detecting the phrases in the given two sentences and aligning those phrases between the sentences. Then, the model is trained to predict the NLI label for the aligned phrases and induce the sentence label by fuzzy logic formulas. With such settings, the model is able to interpret the relationships between the phrases, thus contributing to the explainability of the NLI model. ", "summary_of_the_review": "Overall, this work is interesting in the scope of the NLI field. But the technique is heavily customized to the NLI task, it might have less impact to general audiences. The presentation could also be improved.", "strength_and_weaknesses": "Strength:\n\n1. The setting of phrase-level NLI is interesting, and is intuitively beneficial for improving the interpretability of neural models.\n\n2. The technical design is sound, and the effectiveness is verified on several datasets.\n\n3. The annotated phrasal logical labels and designed metrics would be useful resources to the community.\n\nWeakness:\n\n1. The presentation of the experimental part is not quite smooth. Both SNLI and e-SNLI datasets are used in the experiments, but it is not clear which datasets the results in Tables 2-3 are based on. A clear indication in the table captions would be better. Besides, as SNLI is mentioned as the main dataset used in the experiments (Section 4.1), my curiosity is raised about how the model will perform in the standard setting of SNLI (i.e., only considering the sentence-level accuracy). I went through the experiments but did find such results. In my understanding, the technique is supposed to be not only useful for the explanation but also generally effective in the standard settings of NLI. \n\n2. Definition of \"semantic units\" is controversial. Extracting the phrases is the foundation part of this work. According to the details in Appendix A.1, the phrases are extracted based on POS tags. It would be controversial to call those POS-based phrases as \"semantic units\". In the research line of NLI, there are studies that use semantic roles, which are more likely to be \"semantic units\". Clarification about this definition would be beneficial.\n\nIn addition, as implied in Section 4.2, using different \"semantic units\" influences the results dramatically. It would also be helpful to see an ablation study by comparing different kinds of language units (e.g., semantic role labels, fact units, etc.), as those units have been more commonly used as fine-grained units in existing studies.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster