We present a higher-order inference system based on a formal compositional semantics and the wide-coverage CCG parser. We develop an improved method to bridge between the parser and semantic composition. The system is evaluated on the FraCaS test suite. In contrast to the widely held view that higher-order logic is unsuitable for efficient logical inferences, the results show that a system based on a reasonably-sized semantic lexicon and a manageable number of non-first-order axioms enables efficient logical inferences, including those concerned with generalized quantifiers and intensional operators, and outperforms the state-of-the-art firstorder inference system.

Monotonicity reasoning is one of the important reasoning skills for any intelligent natural language inference (NLI) model in that it requires the ability to capture the interaction between lexical and syntactic structures. Since no test set has been developed for monotonicity reasoning with wide coverage, it is still unclear whether neural models can perform monotonicity reasoning in a proper way. To investigate this issue, we introduce the Monotonicity Entailment Dataset (MED). Performance by state-of-the-art NLI models on the new test set is substantially worse, under 55%, especially on downward reasoning. In addition, analysis using a monotonicity-driven data augmentation method showed that these models might be limited in their generalization ability in upward and downward reasoning.1 The dataset will be made publicly available at

Large crowdsourced datasets are widely used for training and evaluating neural models on natural language inference (NLI). Despite these efforts, neural models have a hard time capturing logical inferences, including those licensed by phrase replacements, socalled monotonicity reasoning. Since no large dataset has been developed for monotonicity reasoning, it is still unclear whether the main obstacle is the size of datasets or the model architectures themselves. To investigate this issue, we introduce a new dataset, called HELP, for handling entailments with lexical and logical phenomena. We add it to training data for the state-of-the-art neural models and evaluate them on test sets for monotonicity phenomena. The results showed that our data augmentation improved the overall accuracy. We also find that the improvement is better on monotonicity inferences with lexical replacements than on downward inferences with disjunction and modification. This suggests that some types of inferences can be improved by our data augmentation while others are immune to it.

Despite the success of language models using neural networks, it remains unclear to what extent neural models have the generalization ability to perform inferences. In this paper, we introduce a method for evaluating whether neural models can learn systematicity of monotonicity inference in natural language, namely, the regularity for performing arbitrary inferences with generalization on composition. We consider four aspects of monotonicity inferences and test whether the models can systematically interpret lexical and logical phenomena on different training/test splits. A series of experiments show that three neural models systematically draw inferences on unseen combinations of lexical and logical phenomena when the syntactic structures of the sentences are similar between the training and test sets. However, the performance of the models significantly decreases when the structures are slightly changed in the test set while retaining all vocabularies and constituents already appearing in the training set. This indicates that the generalization ability of neural models is limited to cases where the syntactic structures are nearly the same as those in the training set.

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