SlowGuess/NeurIPS_2023_OCR huggingface dataset:
$$
q _ {i} = q _ {i} + \operatorname {F F N} \left(v _ {i}\right). \tag {7}
$$
3.3 Learning Memory-Enhanced Query Encoding
To train the model, we compute the normalized probability of  $v$  being the correct answer to query  $q$  by applying the softmax function to all similarity scores:
$$
p (q, v) = \frac {e ^ {<   q , e _ {v} >}}{\sum_ {v ^ {\prime} \in V} e ^ {<   q , e _ {v ^ {\prime}} >}}, \tag {8}
$$
where  $<\cdot, \cdot>$  denotes the dot product of two vectors, when  $q$  is the query embedding after the last operation. A cross-entropy loss is used to maximize the log probabilities of all correct answer pairs:
$$
\mathcal {L} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \log p \left(q ^ {(i)}, v ^ {(i)}\right), \tag {9}
$$
where  $(q^{(i)},v^{(i)})$  denotes one of the positive query-answer pairs, and  $N$  is the total number of them.
To ensure a fair comparison of various methods for the CEQA problem, we generated a dataset by sampling from ASER [53], the largest eventuality knowledge graph, which encompasses fourteen types of discourse relations. The division of edges within each knowledge graph into training, validation, and testing sets was performed in an 8:1:1 ratio, as illustrated in Table 5. The training graph  $\mathcal{G}_{train}$ , validation graph  $\mathcal{G}_{val}$ , and test graph  $\mathcal{G}_{test}$  were constructed using the training edges, training+validation edges, and training+validation+testing edges, respectively, following the established configuration outlined in prior research by [37]. Moreover, we conducted evaluations using different reasoning models, consistent with settings in previous studies.
4.1 Query Sampling with Theorem Prover
We employ the sampling algorithm proposed by [37] with the conjunctive query types outlined in [46]. Specifically, for the training dataset, we sample queries that have a maximum of two anchor nodes, while for the validation and test sets, we select queries containing up to three anchor eventualities. The query types in our framework reflect the structure of the computational graph and are represented using a Lisp-like format [46, 7]. Once the query-answer pairs are sampled, we randomly select up to three edges that share common vertices with the reasoning chain of the query-answer pairs. These selected edges are then used as the informational atomics for the corresponding query. Subsequently, we employ the z3 prover [15] to filter the queries. We retain only those queries where the informational atomics incorporate effective implicit constraints, ensuring the presence of meaningful constraints in the data. The detailed query types and their numbers of answer with/without contradictions are shown in Table 6, in which the p is for projection, the i is for intersection, and e is for eventuality.
In detail, for each eventuality present on the reasoning path towards an answer in the complex query, we create a corresponding boolean variable in the z3 prover. We then incorporate the relevant
Table 3: Experiment results of different query encoding models. In this experiment, we compare the performance of the query encoder with or without the memory-enhanced query encoding method.
Models	OccurrenceConstraints	Temporal Constraints	Average
Hit@1	Hit@3	MRR	Hit@1	Hit@3	MRR	Hit@1	Hit@3	MRR
GQE	8.92	14.21	13.09	9.09	14.03	12.94	9.12	14.12	13.02
+ MEQE	10.20	15.54	14.31	10.70	15.67	14.50	10.45	15.60	14.41
Q2P	14.14	19.97	18.84	14.48	19.69	18.68	14.31	19.83	18.76
+ MEQE	15.15	20.67	19.38	16.06	20.82	19.74	15.61	20.74	19.56
Nerual MLP	13.03	19.21	17.75	13.45	19.06	17.68	13.24	19.14	17.71
+ MEQE	15.26	20.69	19.32	15.91	20.63	19.47	15.58	20.66	19.40
FuzzQE	11.68	18.64	17.07	11.68	17.97	16.53	11.68	18.31	16.80
+ MEQE	14.76	21.12	19.45	15.31	21.01	19.49	15.03	21.06	19.47
occurrence constraints based on the relations between these eventualities, as outlined in Table 1, and feed them into the z3 prover. If the result returned by the prover is unsat, it indicates a contradiction in the reasoning process. Regarding temporal constraints, we follow a similar approach. We create corresponding floating variables that represent the timestamps of the occurrence of the eventualities. We then establish constraints on the temporal order by utilizing floating operators such as  $>, =$ , or  $<$  between the variables. By doing so, for each query, we establish a corresponding linear program. Once again, if the prover outputs unsat, it signifies a contradiction, namely, there is no solution for the timestamps of these events. Queries that have no contradictory answers and queries where all the answers are contradictory are discarded. The remaining queries are then categorized into two types: queries with occurrence constraints and queries with temporal constraints. Table 6 presents the average number of contradictory and non-contradictory answers per query.
4.2 Baselines and Metrics
In this section, we introduce several baseline query encoding models that use different neural network architectures to parameterize the operators in the computational graph and recursively encode the query into various embedding structures: (1) GQE [23] uses vectors to encode complex queries; (2) Q2P [5] uses multiple vectors to encode queries; (3) Neural MLP [1] use MLP as the operators; (4) FuzzQE [12] uses fuzzy logic to represent logical operators.
To define the evaluation metrics, we use  $q$  to represent a testing query, and  $\mathcal{G}_{val}$  and  $\mathcal{G}_{test}$  to represent the validation and testing knowledge graphs, respectively. We use  $[q]_{val}$  and  $[q]_{test}$  to represent the answers to query  $q$  on  $\mathcal{G}_{val}$  and  $\mathcal{G}_{test}$ , respectively. Eq. (10) shows how to compute the metrics. When the evaluation metric is Hit@K,  $m(r)$  is defined as  $m(r) = 1[r \leq K]$ , where  $m(r) = 1$  if  $r \leq K$ , and  $m(r) = 0$  otherwise. For mean reciprocal ranking (MRR),  $m(r)$  is defined as  $m(r) = \frac{1}{r}$ .
$$
\operatorname {m e t r i c} (q) = \frac {\sum_ {v \in [ q ] _ {t e s t} / [ q ] _ {v a l}} m (\operatorname {r a n k} (v))}{| [ q ] _ {t e s t} / [ q ] _ {v a l} |}. \tag {10}
$$
During the training process, the testing graph  $\mathcal{G}_{test}$  is unobserved. In the hyper-parameters selection process, we use the same metrics as Eq. (10), but replace the graphs  $\mathcal{G}_{test} / \mathcal{G}_{val}$  with  $\mathcal{G}_{val} / \mathcal{G}_{train}$ .
4.3 Details
To ensure fair comparisons, we replicate all the models under a unified framework. We use the same number of embedding sizes of three hundred for all models and use grid-search to tune the hyperparameters of the learning rate ranging from  $\{0.002, 0.001, 0.0005, 0.0002, 0.0001\}$  and batch size ranging from  $\{128, 256, 512\}$ . All the experiments can be run on NVIDIA RTX3090 GPUs. Experiments are repeated three times, and the averaged results are reported.
Table 4: The Hit@3 and MRR on different query types with a various number of anchor nodes.
#Anc.	Query Type	Metric	GQE	Q2P	Neural MLP	FuzzQE
Base.	MEQE	Base.	MEQE	Base.	MEQE	Base.	MEQE
2	(p,(i,(p,(e)),(p,(e))))	Hit@3	12.97	13.76	17.74	18.88	15.93	17.32	15.23	18.02
MRR	11.86	12.75	16.90	18.35	15.31	16.51	14.38	16.58
(i,(p,(e)),(p,(e)))	Hit@3	33.52	34.48	44.65	39.54	38.39	40.29	43.71	39.77
MRR	30.53	32.80	39.79	34.77	35.02	35.16	36.92	36.53
(i,(p,(e)),(p,(p,(e))))	Hit@3	12.40	12.42	15.22	15.96	15.03	15.69	15.56	16.45
MRR	11.46	11.38	14.36	15.25	14.21	14.74	14.82	15.36
(i,(p,(p,(e)),(p,(p,(e))))	Hit@3	14.16	14.87	17.49	19.86	17.06	19.07	16.58	18.65
MRR	13.16	13.19	16.48	18.89	15.49	18.27	14.69	17.22
3	(p,(i,(i,(p,(e)),(p,(e))), (p,(e))))	Hit@3	14.63	18.02	25.67	26.17	23.93	24.34	18.58	26.31
MRR	13.47	16.95	24.38	25.13	22.63	23.41	17.72	24.92
(i,(p,(e)),(p,(i,(p,(e)),(p,(e))))	Hit@3	17.20	20.63	22.52	22.92	23.22	23.99	22.67	24.53
MRR	15.63	19.61	21.76	21.93	21.73	22.67	21.51	23.01
(i,(i,(p,(e)),(p,(e)),(p,(e)))	Hit@3	24.66	28.11	45.10	44.12	40.28	40.62	47.14	47.56
MRR	22.57	24.22	40.14	37.87	35.71	36.70	40.95	41.65
(i,(i,(p,(e)),(p,(p,(e))), (p,(e)))	Hit@3	13.17	13.31	17.06	16.72	18.04	18.80	16.62	18.31
MRR	11.81	12.38	17.00	16.44	16.86	17.42	15.88	17.24
(i,(i,(p,(p,(e)),(p,(p,(e))), (p,(e)))	Hit@3	16.94	19.63	22.06	22.94	21.66	23.85	19.70	22.65
MRR	15.62	17.59	20.76	21.60	20.45	22.19	17.52	21.70
(i,(p,(i,(p,(e)),(p,(e))), (p,(p,(e))))	Hit@3	16.23	19.75	24.45	25.59	23.39	25.45	22.33	25.63
MRR	15.05	18.36	23.30	24.15	21.60	24.26	20.87	24.00
(i,(i,(p,(e)),(p,(e))), (p,(p,(e))))	Hit@3	20.43	23.08	34.52	36.44	36.56	42.00	35.88	41.80
MRR	19.26	21.74	31.91	33.45	32.46	37.41	33.74	36.65
(i,(i,(p,(e)),(p,(p,(e))), (p,(p,(e))))	Hit@3	13.29	15.05	20.08	20.87	21.79	22.94	19.65	22.81
MRR	12.34	14.04	19.31	19.81	19.57	21.65	17.85	21.37
(i,(i,(p,(p,(e)),(p,(p,(e))), (p,(p,(e))))	Hit@3	15.64	17.67	22.63	25.10	22.97	24.50	20.22	25.44
MRR	14.54	16.39	21.08	23.13	20.70	23.04	21.93	23.22
4.4 Experiment Results
Table 3 presents the results of the main experiment, which compares different query encoding models with and without MEQE. The table includes the performance metrics of Hit@1, Hit@3, and MRR for both occurrence constraints and temporal constraints, along with the average scores across all categories. The experimental results demonstrate that our proposed memory-enhanced query encoding (MEQE) model consistently improves the performance of existing query encoders in complex eventuality query answering. We conduct experiments on four commonly used query encoders, and the MEQE model, leveraging the memory model depicted in Figure 4, outperforms the baselines. The MEQE models differ structurally from the baseline models by incorporating a memory module that contains informational atomics. By reading this memory module, MEQE effectively incorporates implicit constraints from these atomics, leading to improved performance.
Additionally, we observed that combining MEQE with the Q2P [5] model yields the best average performance across three metrics: Hit@1, Hit@3, and MRR. Furthermore, on average, MEQE enhances the Hit@1 metric by  $17.53\%$  and the Hit@3 metric by  $9.53\%$ . The greater improvement in the Hit@1 metric suggests that the model's ability to accurately predict the top-ranked answer has improved more significantly compared to predicting answers within the top three rankings. Moreover, MEQE demonstrates a  $13.85\%$  improvement in performance on queries with temporal constraints and an  $11.15\%$  improvement on occurrence constraints. This indicates that MEQE is particularly effective in handling temporal constraints compared to occurrence constraints.
Table 4 displays the Hit@3 and MRR results of various types of complex queries. The table demonstrates the superiority of MEQE over the baseline models across different query types. Furthermore, the table indicates that, on average, MEQE achieves an improvement of  $8.1\%$  and  $11.6\%$  respectively. This suggests that MEQE is particularly adept at handling queries with multiple eventualities.
Complex query answering is a task in deductive knowledge graph reasoning, where a system or model is required to answer a logical query on an incomplete knowledge graph. Query encoding [23] is a fast and robust method for addressing complex query answering. Various query embedding methods
utilize different structures to encode logical KG queries, enabling them to handle different types of logical queries. The GQE method, introduced by Hamilton et al. [23], represents queries as vector representations to answer conjunctive queries. Ren et al. [37] employed hyper-rectangles to encode and answer existential positive first-order (EPFO) queries. Simultaneously, Sun et al. [42] proposed the use of centroid-sketch representations to enhance the faithfulness of the query embedding method for EPFO queries. Both conjunctive queries and EPFO queries are subsets of first-order logic (FOL) queries. The Beta Embedding [36] is the first query embedding method that supports a comprehensive set of operations in FOL by encoding entities and queries into probabilistic Beta distributions. Moreover, Zhang et al. [55] utilized cone embeddings to encode FOL queries. Meanwhile, there are also neural-symbolic methods for query encoding. Xu et al. [49] proposes an entangled neural-symbolic method, ENeSy, for query encoding. Wang et al. [47] propose using pre-trained knowledge graph embeddings and one-hop message passing to conduct complex query answering. Additionally, Yang et al. [50] propose using Gamma Embeddings to encode complex logical queries. Finally, Liu et al. [27] propose pre-training on the knowledge graph with kg-transformer and then fine-tuning on the complex query answering. Recently, Bai et al. [7] proposes to use sequence encoders to encode the linearized computational graph of complex queries. Galkin et al. [20] propose to conduct inductive logical reasoning on KG, and Zhu et al. [56] proposes GNN-QE to conduct reasoning on KG with message passing on the knowledge graph. Meanwhile, Bai et al. [6] formulate the problem of numerical CQA and propose the corresponding query encoding method of NRN.
Another approach to addressing complex knowledge graph queries is query decomposition [2]. In this research direction, the probabilities of these atomic queries are modeled using link predictors, and then an inference time optimization is used to find the answers. In addition, an alternative to query encoding and query decomposition is proposed by Wang et al. [47]. They employ message passing on one-hop atomic queries to perform complex query answering. A recent neural search-based method called QTO is introduced by Bai et al. [8], which has shown impressive performance in complex question answering (CQA). Theorem proving is another deductive reasoning task applied to knowledge graphs. Neural theorem proving methods [39, 31, 32] have been proposed to tackle the incompleteness of KGs by using embeddings to conduct inference on missing information.
Although our experiments demonstrate that MEQE improves the performance of existing models on the CEQA task, the evaluation is conducted on specific benchmark datasets constructed with theorem provers from the largest general-domain eventuality graph ASER [53]. The generalizability of the proposed approach to specific or professional fields may require further investigation and evaluation.
In this paper, we introduced complex eventuality query answering (CEQA) as a more rigorous definition of complex query answering (CQA) for eventuality knowledge graphs (EVKGs). We addressed the issue of implicit logical constraints on the occurrence and temporal order of eventualities, which had not been adequately considered in the existing definition of CQA. To ensure consistent reasoning, we leveraged theorem provers to construct benchmark datasets that enforce implicit logical constraints on the answers. Furthermore, we proposed constraint memory-enhanced query encoding with (MEQE) to enhance the performance of state-of-the-art neural query encoders on the CEQA task. Our experiments showed that MEQE significantly improved the performance of existing models on the CEQA task. Overall, our work provides a more comprehensive and effective solution to the complex query-answering problem on eventuality knowledge graphs.
The authors of this paper were supported by the NSFC Fund (U20B2053) from the NSFC of China, the RIF (R6020-19 and R6021-20) and the GRF (16211520 and 16205322) from RGC of Hong Kong. We also thank the support from the UGC Research Matching Grants (RMGS20EG01-D, RMGS20CR11, RMGS20CR12, RMGS20EG19, RMGS20EG21, RMGS23CR05, RMGS23EG08).
A Broader Impact
This paper is the first work discussing how to conduct logical reasoning over knowledge graphs that describe events, states, and actions, known as eventualities. The proposed method, MEQE, is capable of effectively and efficiently answering logical queries over eventuality knowledge graphs.
The experiments were conducted on publicly available knowledge graphs, eliminating any data privacy concerns. However, one possible concern is that our proposed reasoning method is susceptible to adversarial attacks [14, 57, 9] and data poisoning [51] on knowledge graph reasoning systems, which may result in unintended outcomes for users.
B Logical Constraints from Discourse Relations
In this paper, we utilize discourse structures based on the early work by Asher [3], where discourse relations are considered as predicates that involve two abstract objects, such as events, states, and propositions [48]. We have adopted the discourse relation definitions from the Penn Discourse Treebank (PDTB) [34], which consist of four general classes: Temporal, Comparison, Contingency, and Expansion. Each general class comprises various types, and the logical constraints are derived based on the semantic meaning of these discourse types.
The Temporal class is used when there is a temporal relationship between the described situations in the arguments. It includes Precedence(A,B), Succession(A,B), and Synchronous(A,B). In Temporal relations, we employ the temporal logic expressions  $\succ$ ,  $\prec$ , and = to represent the temporal order between two eventualities [22]. A  $\prec$  B denotes that A occurs before B, A = B implies that they happen simultaneously, and A  $\succ$  B indicates that A occurs after B.
The Contingency class is used when one of the described situations in  $A$  and  $B$  causally influences the other. It encompasses Reason, Result, and Condition. Reason describes a cause-and-effect relationship between two eventualities. We use the conditional operator  $>$  [21] to represent conditional and causal relations. Reason(B,A), Result(A,B), and Condition(B,A) can all implies  $A > B$ , indicating that A causes B [21]. Moreover, Reason and Result also imply they both occur.
The Comparison class depicts a discourse relation between  $A$  and  $B$  to highlight significant differences between the two situations. Semantically, it indicates that the underlying values of  $A$  and  $B$  are independent of the connective [35]. Therefore, we simply use  $A \wedge B$  to represent both sub-types of  $\operatorname{Contrast}(A, B)$  and  $\operatorname{Concession}(A, B)$ , signifying that both eventualities indeed occur.
Expansion class describes those relations that expand the discourse and move its narratives or exposition forward. The Conjunction  $(A, B)$  is used to indicate new situations that provide new information in  $B$  that is related to the situation described in  $A$ . The logical formulation from the conjunction can be expressed as  $A \wedge B$ . Meanwhile, the Instantiation  $(A, B)$  relation also requires both arguments to hold [35]. Thus it can also be described by the expression  $A \wedge B$ . Exception  $(A, B)$  indicates that  $B$  specifies an exception to the generalization specified by  $A$ . In other words,  $A$  is false because  $B$  is true, but if  $B$  were false,  $A$  would be true. The semantics of an exception is expressed in  $\neg A \wedge B \wedge (\neg B \rightarrow A)$ . Restatement  $(A, B)$  describes the relationship that the semantics of  $B$  restates the semantics of  $A$ . So the  $A$  and  $B$  hold true at the same time  $A \leftrightarrow B$ . Alternative  $(A, B)$  relationship applies when two eventualities describe alternative situations. The semantics of Alternative  $(A, B)$  is  $A \lor B$ . ChosenAlternative  $(A, B)$  means that two alternatives  $A$  and  $B$  are given, but the first one  $A$  is not chosen. Its semantic meaning is represented as  $(A \lor B) \wedge \neg A$ .
The Expansion class encompasses relations that expand the discourse and advance its narratives or exposition [35]. Conjunction  $(A, B)$  is used to indicate new situations in  $B$  that provide related information to the situation described in  $A$ . The logical formulation from conjunction can be expressed as  $A \wedge B$ . Similarly, Instantiation  $(A, B)$  also requires both arguments to hold [35] and can be described by the expression  $A \wedge B$ . Exception  $(A, B)$  indicates that  $B$  specifies an exception to the generalization specified by  $A$ . In other words,  $A$  is false because  $B$  is true, but if  $B$  were false,  $A$  would be true. The semantics of an exception can be expressed as  $\neg A \wedge B \wedge (\neg B \rightarrow A)$ . Restatement  $(A, B)$  describes a relationship where the semantics of  $B$  restates the semantics of  $A$ . Therefore,  $A$  and  $B$  hold true simultaneously, represented as  $A \leftrightarrow B$ . Alternatively  $(A, B)$  applies
Table 5: The basic information about the ASER-50K used for the experiments, and its standard training, validation, and testing edges separations.
Dataset	Relation Types	Entities	Training	Validation	Testing	All Edges
ASER50K	14	54,557	113,608	13,860	13,784	141,252
Table 6: A breakdown of the detailed query types is provided in the training, validation, and testing sets, along with corresponding statistics. Specifically, we report the number of samples, the number of non-contradictory answers, and the number of answers that satisfy the relational constraints but are contradictory due to occurrence or temporal constraints.
Split	#Anc.	Type	Depths	OccurrenceConstantint	TemporalConstraints
# Queries	# Ans.	# Contr. Ans.	# Queries	# Ans.	# Contr. Ans.
Trn.	1	(p,(e))(p,(p,(e)))	1	4,231	2.29	1.15	112	3.41	1.06
2	21,010	6.03	2.09	1,876	6.16	1.36
2	(p,(i,(p,(e),(p,(e))))	2	40,728	7.59	1.63	15,941	7.44	1.20
(i,(p,(e),(p,(e)))	1	3,048	1.78	1.07	84	1.60	1.00
(i,(p,(e),(p,(p,(e))))	2	18,088	4.93	1.38	1,940	4.10	1.10
(i,(p,(p,(e),(p,(p,(e))))	2	37,661	7.50	1.87	16,009	7.43	1.19
Val.	1	(p,(e))(p,(p,(e)))	1	1,023	4.47	1.36	69	4.77	1.22
2	2,317	12.82	3.33	965	13.57	1.81
2	(p,(i,(p,(e),(p,(e))))	2	2,482	10.77	2.02	2,357	13.80	1.65
(i,(p,(e),(p,(p,(e))))	2	2,130	8.01	1.59	877	8.07	1.37
(i,(p,(e),(p,(e)))	1	821	2.85	1.19	71	2.08	1.21
(i,(p,(p,(e),(p,(p,(e))))	2	2,391	10.13	2.32	2,338	12.50	1.50
3	(p,(i,(i,(p,(e),(p,(e)),p,(e))))	2	2,452	10.02	1.73	2,618	12.57	1.57
(i,(p,(e),(p,(i,(p,(e),(p,(e))))	2	2,428	9.08	1.57	2,394	10.68	1.37
(i,(i,(p,(e),(p,(e))),p,(e))	1	1,026	2.43	1.15	281	2.20	1.23
(i,(i,(p,(e),(p,(p,(e))),p,(e))	2	1,952	7.64	1.52	977	8.19	1.43
(i,(i,(p,(e),(p,(p,(e))),p,(e))	2	2,327	7.89	1.59	2,368	10.86	1.39
(i,(i,(i,(p,(e),(p,(e))),p,(p,(e))))	2	2,399	9.12	1.90	2,555	11.64	1.46
(i,(i,(p,(e),(p,(e))),p,(p,(e))))	2	1,862	3.10	1.30	1,068	3.67	1.44
(i,(i,(p,(e),(p,(p,(e))),p,(p,(e))))	2	2,329	7.73	1.61	2,399	10.73	1.42
(i,(i,(p,(e),(p,(p,(e))),p,(p,(e))))	2	2,333	9.20	2.07	2,568	12.19	1.45
Tst.	1	(p,(e))(p,(p,(e)))	1	1,091	4.83	1.38	50	6.78	1.18
2	2,261	14.19	3.39	954	16.50	1.85
2	(p,(i,(p,(e),(p,(e))))	2	2,425	11.77	2.20	2,434	17.13	1.95
(i,(p,(e),(p,(e)))	1	899	3.29	1.23	91	2.88	1.29
(i,(p,(e),(p,(p,(e))))	2	2,093	8.53	1.65	845	10.30	1.38
(i,(p,(p,(e),(p,(p,(e))))	2	2,402	10.89	2.30	2,315	15.11	1.53
3	(p,(i,(i,(p,(e),(p,(e)),p,(e))))	2	2,386	11.26	1.81	2,648	15.95	1.77
(i,(p,(e),(p,(i,(p,(e),(p,(e))))	2	2,368	9.67	1.62	2,470	13.00	1.47
(i,(i,(p,(e),(p,(e)),p,(e))	1	1,234	2.67	1.18	310	2.97	1.27
(i,(i,(p,(e),(p,(p,(e))),p,(e))	2	1,928	7.76	1.55	1,049	10.24	1.45
(i,(i,(p,(p,(e),(p,(p,(e))),p,(e))	2	2,282	9.13	1.72	2,420	12.97	1.40
(i,(i,(i,(p,(e),(p,(e))),p,(p,(e))))	2	2,346	10.09	1.93	2,607	13.89	1.64
(i,(i,(p,(e),(p,(e))),p,(p,(e))))	2	1,910	3.44	1.42	1,052	5.94	1.41
(i,(i,(p,(e),(p,(p,(e))),p,(p,(e))))	2	2,297	8.33	1.63	2,423	12.68	1.39
(i,(i,(p,(p,(e),(p,(p,(e))),p,(p,(e))))	2	2,321	10.13	2.17	2,558	14.66	1.57
when two eventualities describe alternative situations. The semantics of Alternative(A, B) is A  $\vee$  B. ChosenAlternative(A, B) means that two alternatives,  $A$  and  $B$ , are given, but only the first one  $A$  is chosen. Its semantic meaning is represented as  $(A \lor B) \land \neg B$ .
C Differences Between Commonsense Reasoning and Eventuality Reasoning