Using curated tables with TupleInf	For each question, we select the 7 best matching tables using the tf-idf score of the table w.r.t. the question tokens and top 20 rows from each table using the Jaccard similarity of the row with the question. (same as  tableilp2016). We then convert the table rows into the tuple structure using the relations defined by TableILP. For every pair of cells connected by a relation, we create a tuple with the two cells as the subject and primary object with the relation as the predicate. The other cells of the table are used as additional objects to provide context to the solver. We pick top-scoring 50 tuples using the Jaccard score.

Experiment Details	We use the SCIP ILP optimization engine  to optimize our ILP model. To get the score for each answer choice $a_i$ , we force the active variable for that choice $x_{a_i}$ to be one and use the objective function value of the ILP model as the score. For evaluations, we use a 2-core 2.5 GHz Amazon EC2 linux machine with 16 GB RAM. To evaluate TableILP and TupleInf on curated tables and tuples, we converted them into the expected format of each solver as follows.

Tuple KB	We use the text corpora (S) from  aristo2016:combining to build our tuple KB. For each test set, we use the corresponding training questions $Q_\mathit {tr}$ to retrieve domain-relevant sentences from S. Specifically, for each multiple-choice question $(q,A) \in Q_\mathit {tr}$ and each choice $a \in A$ , we use all non-stopword tokens in $q$ and $a$ as an ElasticSearch query against S. We take the top 200 hits, run Open IE v4, and aggregate the resulting tuples over all $a \in A$ and over all questions in $Q_\mathit {tr}$ to create the tuple KB (T).

Using Open IE tuples with TableILP	We create an additional table in TableILP with all the tuples in $T$ . Since TableILP uses fixed-length $(subject; predicate; object)$ triples, we need to map tuples with multiple objects to this format. For each object, $O_i$ in the input Open IE tuple $(S; P; O_1; O_2 \ldots )$ , we add a triple $(S; P; O_i)$ to this table.

Answering Complex Questions Using Open Information Extraction	While there has been substantial progress in factoid question-answering (QA), answering complex questions remains challenging, typically requiring both a large body of knowledge and inference techniques. Open Information Extraction (Open IE) provides a way to generate semi-structured knowledge for QA, but to date such knowledge has only been used to answer simple questions with retrieval-based methods. We overcome this limitation by presenting a method for reasoning with Open IE knowledge, allowing more complex questions to be handled. Using a recently proposed support graph optimization framework for QA, we develop a new inference model for Open IE, in particular one that can work effectively with multiple short facts, noise, and the relational structure of tuples. Our model significantly outperforms a state-of-the-art structured solver on complex questions of varying difficulty, while also removing the reliance on manually curated knowledge.

Experiments	Comparing our method with two state-of-the-art systems for 4th and 8th grade science exams, we demonstrate that (a) TupleInf with only automatically extracted tuples significantly outperforms TableILP with its original curated knowledge as well as with additional tuples, and (b) TupleInf's complementary approach to IR leads to an improved ensemble. Numbers in bold indicate statistical significance based on the Binomial exact test  at $p=0.05$ . We consider two question sets. (1) 4th Grade set (1220 train, 1304 test) is a 10x larger superset of the NY Regents questions  , and includes professionally written licensed questions. (2) 8th Grade set (293 train, 282 test) contains 8th grade questions from various states. We consider two knowledge sources. The Sentence corpus (S) consists of domain-targeted $~$ 80K sentences and 280 GB of plain text extracted from web pages used by  aristo2016:combining. This corpus is used by the IR solver and also used to create the tuple KB T and on-the-fly tuples $T^{\prime }_{qa}$ .

Appendix: ILP Model Details	To build the ILP model, we first need to get the questions terms (qterm) from the question by chunking the question using an in-house chunker based on the postagger from FACTORIE.

Tuple Inference Solver	We first describe the tuples used by our solver. We define a tuple as (subject; predicate; objects) with zero or more objects. We refer to the subject, predicate, and objects as the fields of the tuple.

We discovered (see empirical evaluation) that this simple model can achieve the same score as TableILP on the Regents test (target test set used by TableILP) and generalizes better to different grade levels. We define active vertices and edges using ILP constraints: an active edge must connect two active vertices and an active vertex must have at least one active edge. To avoid positive edge coefficients in the objective function resulting in spurious edges in the support graph, we limit the number of active edges from an active tuple, question choice, tuple fields, and qterms (first group of constraints in Table 1 ). Our model is also capable of using multiple tuples to support different parts of the question as illustrated in Figure 1 . To avoid spurious tuples that only connect with the question (or choice) or ignore the relation being expressed in the tuple, we add constraints that require each tuple to connect a qterm with an answer choice (second group of constraints in Table 1 ). We also define new constraints based on the Open IE tuple structure. Since an Open IE tuple expresses a fact about the tuple's subject, we require the subject to be active in the support graph.

Additionally, TableILP uses $\sim $ 70 Curated tables (C) designed for 4th grade NY Regents exams. We compare TupleInf with two state-of-the-art baselines. IR is a simple yet powerful information-retrieval baseline  that selects the answer option with the best matching sentence in a corpus. TableILP is the state-of-the-art structured inference baseline  developed for science questions.

Similar to TableILP, we score the support graph based on the weight of the active nodes and edges. Each edge $e(t, h)$ is weighted based on a word-overlap score. While TableILP used WordNet  paths to compute the weight, this measure results in unreliable scores when faced with longer phrases found in Open IE tuples. Compared to a curated KB, it is easy to find Open IE tuples that match irrelevant parts of the questions. To mitigate this issue, we improve the scoring of qterms in our ILP objective to focus on important terms. Since the later terms in a question tend to provide the most critical information, we scale qterm coefficients based on their position. Also, qterms that appear in almost all of the selected tuples tend not to be discriminative as any tuple would support such a qterm. Hence we scale the coefficients by the inverse frequency of the tokens in the selected tuples. Since Open IE tuples do not come with schema and join rules, we can define a substantially simpler model compared to TableILP. This reduces the reasoning capability but also eliminates the reliance on hand-authored join rules and regular expressions used in TableILP.

Error Analysis	We describe four classes of failures that we observed, and the future work they suggest. Missing Important Words: Which material will spread out to completely fill a larger container? (A)air (B)ice (C)sand (D)water In this question, we have tuples that support water will spread out and fill a larger container but miss the critical word “completely”. An approach capable of detecting salient question words could help avoid that. Lossy IE: Which action is the best method to separate a mixture of salt and water? ... The IR solver correctly answers this question by using the sentence: Separate the salt and water mixture by evaporating the water. However, TupleInf is not able to answer this question as Open IE is unable to extract tuples from this imperative sentence. While the additional structure from Open IE is useful for more robust matching, converting sentences to Open IE tuples may lose important bits of information. Bad Alignment: Which of the following gases is necessary for humans to breathe in order to live?(A) Oxygen(B) Carbon dioxide(C) Helium(D) Water vapor TupleInf returns “Carbon dioxide” as the answer because of the tuple (humans; breathe out; carbon dioxide).

Introduction	Effective question answering (QA) systems have been a long-standing quest of AI research. Structured curated KBs have been used successfully for this task  ,  . However, these KBs are expensive to build and typically domain-specific. Automatically constructed open vocabulary (subject; predicate; object) style tuples have broader coverage, but have only been used for simple questions where a single tuple suffices  ,  . Our goal in this work is to develop a QA system that can perform reasoning with Open IE  tuples for complex multiple-choice questions that require tuples from multiple sentences. Such a system can answer complex questions in resource-poor domains where curated knowledge is unavailable. Elementary-level science exams is one such domain, requiring complex reasoning  . Due to the lack of a large-scale structured KB, state-of-the-art systems for this task either rely on shallow reasoning with large text corpora  ,  or deeper, structured reasoning with a small amount of automatically acquired  or manually curated  knowledge. Consider the following question from an Alaska state 4th grade science test: Which object in our solar system reflects light and is a satellite that orbits around one planet?

To avoid issues such as (Planet; orbit; Sun) matching the sample question in the introduction (“Which object $\ldots $ orbits around a planet”), we also add an ordering constraint (third group in Table 1 ). Its worth mentioning that TupleInf only combines parallel evidence i.e. each tuple must connect words in the question to the answer choice. For reliable multi-hop reasoning using OpenIE tuples, we can add inter-tuple connections to the support graph search, controlled by a small number of rules over the OpenIE predicates. Learning such rules for the Science domain is an open problem and potential avenue of future work.

(A) Earth (B) Mercury (C) the Sun (D) the Moon This question is challenging for QA systems because of its complex structure and the need for multi-fact reasoning. A natural way to answer it is by combining facts such as (Moon; is; in the solar system), (Moon; reflects; light), (Moon; is; satellite), and (Moon; orbits; around one planet). A candidate system for such reasoning, and which we draw inspiration from, is the TableILP system of  . TableILP treats QA as a search for an optimal subgraph that connects terms in the question and answer via rows in a set of curated tables, and solves the optimization problem using Integer Linear Programming (ILP). We similarly want to search for an optimal subgraph.

Tuple Selection	Given a multiple-choice question $qa$ with question text $q$ and answer choices A= $\lbrace a_i\rbrace $ , we select the most relevant tuples from $T$ and $S$ as follows. Selecting from Tuple KB: We use an inverted index to find the 1,000 tuples that have the most overlapping tokens with question tokens $tok(qa).$ . We also filter out any tuples that overlap only with $tok(q)$ as they do not support any answer. We compute the normalized TF-IDF score treating the question, $q$ as a query and each tuple, $t$ as a document: $
&\textit {tf}(x, q)=1\; \textmd {if x} \in q ; \textit {idf}(x) = log(1 + N/n_x) \\
&\textit {tf-idf}(t, q)=\sum _{x \in t\cap q} idf(x)
$   where $N$ is the number of tuples in the KB and $n_x$ are the number of tuples containing $x$ .

We normalize the tf-idf score by the number of tokens in $t$ and $q$ . We finally take the 50 top-scoring tuples $T_{qa}$ . On-the-fly tuples from text: To handle questions from new domains not covered by the training set, we extract additional tuples on the fly from S (similar to  knowlhunting). We perform the same ElasticSearch query described earlier for building T. We ignore sentences that cover none or all answer choices as they are not discriminative. We also ignore long sentences ( $>$ 300 characters) and sentences with negation as they tend to lead to noisy inference. We then run Open IE on these sentences and re-score the resulting tuples using the Jaccard score due to the lossy nature of Open IE, and finally take the 50 top-scoring tuples $T^{\prime }_{qa}$ .

Support Graph Search	Similar to TableILP, we view the QA task as searching for a graph that best connects the terms in the question (qterms) with an answer choice via the knowledge; see Figure 1 for a simple illustrative example. Unlike standard alignment models used for tasks such as Recognizing Textual Entailment (RTE)  , however, we must score alignments between a set $T_{qa} \cup T^{\prime }_{qa}$ of structured tuples and a (potentially multi-sentence) multiple-choice question $qa$ . The qterms, answer choices, and tuples fields form the set of possible vertices, $\mathcal {V}$ , of the support graph. Edges connecting qterms to tuple fields and tuple fields to answer choices form the set of possible edges, $\mathcal {E}$ . The support graph, $G(V, E)$ , is a subgraph of $\mathcal {G}(\mathcal {V}, \mathcal {E})$ where $V$ and $E$ denote “active” nodes and edges, resp. We define the desired behavior of an optimal support graph via an ILP model as follows.

However, a large, automatically extracted tuple KB makes the reasoning context different on three fronts: (a) unlike reasoning with tables, chaining tuples is less important and reliable as join rules aren't available; (b) conjunctive evidence becomes paramount, as, unlike a long table row, a single tuple is less likely to cover the entire question; and (c) again, unlike table rows, tuples are noisy, making combining redundant evidence essential. Consequently, a table-knowledge centered inference model isn't the best fit for noisy tuples. To address this challenge, we present a new ILP-based model of inference with tuples, implemented in a reasoner called TupleInf. We demonstrate that TupleInf significantly outperforms TableILP by 11.8% on a broad set of over 1,300 science questions, without requiring manually curated tables, using a substantially simpler ILP formulation, and generalizing well to higher grade levels. The gains persist even when both solvers are provided identical knowledge. This demonstrates for the first time how Open IE based QA can be extended from simple lookup questions to an effective system for complex questions.

Results	Table 2 shows that TupleInf, with no curated knowledge, outperforms TableILP on both question sets by more than 11%. The lower half of the table shows that even when both solvers are given the same knowledge (C+T), the improved selection and simplified model of TupleInf results in a statistically significant improvement. Our simple model, TupleInf(C + T), also achieves scores comparable to TableILP on the latter's target Regents questions (61.4% vs TableILP's reported 61.5%) without any specialized rules. Table 3 shows that while TupleInf achieves similar scores as the IR solver, the approaches are complementary (structured lossy knowledge reasoning vs. lossless sentence retrieval). The two solvers, in fact, differ on 47.3% of the training questions. To exploit this complementarity, we train an ensemble system  which, as shown in the table, provides a substantial boost over the individual solvers. Further, IR + TupleInf is consistently better than IR + TableILP.

Finally, in combination with IR and the statistical association based PMI solver (that scores 54.1% by itself) of  aristo2016:combining, TupleInf achieves a score of 58.2% as compared to TableILP's ensemble score of 56.7% on the 4th grade set, again attesting to TupleInf's strength.

The chunk “to breathe” in the question has a high alignment score to the “breathe out” relation in the tuple even though they have completely different meanings. Improving the phrase alignment can mitigate this issue. Out of scope: Deer live in forest for shelter. If the forest was cut down, which situation would most likely happen?... Such questions that require modeling a state presented in the question and reasoning over the state are out of scope of our solver.

Conclusion	We presented a new QA system, TupleInf, that can reason over a large, potentially noisy tuple KB to answer complex questions. Our results show that TupleInf is a new state-of-the-art structured solver for elementary-level science that does not rely on curated knowledge and generalizes to higher grades. Errors due to lossy IE and misalignments suggest future work in incorporating context and distributional measures.

Related Work	We discuss two classes of related work: retrieval-based web question-answering (simple reasoning with large scale KB) and science question-answering (complex reasoning with small KB).

Question: Is an entity linking process used?
Answer: No