Higher-order logical inference with compositional semantics

Abstract

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.

Natural Solution to FraCaS Entailment Problems

“…Several problems for adjectives were not proved as they con-Sec (Sing/All) Single-premised (Acc %) Multi-premised (Acc %) Overall (Acc %) BL NL07,08 LS P/G NLI T14a,b M15 LP BL LS P/G T14a,b M15 LP BL LS P/G T14a,b M15 LP (MacCartney and Manning, 2008), LS (Lewis and Steedman, 2013) with Parser and Gold syntax, NLI (Angeli and Manning, 2014), T14a , T14b (Dong et al, 2014) and M15 (Mineshima et al, 2015). BL is a majority (yes) baseline.…”

“…Since the approach heavily hinges on a sequence of edits that relates a premise to a conclusion, it cannot process multi-premised problems properly. Lewis and Steedman (2013) and Mineshima et al (2015) both base on first-order logic representations. While Lewis and Steedman (2013) employs distributional relation clustering to model the semantics of content words, Mineshima et al (2015) extends first-order logic with several higher-order terms (e.g., for most, believe, manage) and augments first-order inference of Coq with additional inference rules for the higher-order terms.…”

“…Lewis and Steedman (2013) and Mineshima et al (2015) both base on first-order logic representations. While Lewis and Steedman (2013) employs distributional relation clustering to model the semantics of content words, Mineshima et al (2015) extends first-order logic with several higher-order terms (e.g., for most, believe, manage) and augments first-order inference of Coq with additional inference rules for the higher-order terms. and Dong et al (2014) build an inference engine that reasons over abstract denotations, formulas of relational algebra or a sort of description logic, obtained from Dependency-based Compositional Semantic trees (Liang et al, 2011).…”

On-demand Injection of Lexical Knowledge for Recognising Textual Entailment

“…However, the construction of their Markov Networks is limited by first-order logic, which may pose problems to represent modality or generalised quantifiers. Instead, our logical representations can also be used in a more expressive, higher-order inference system such as the one in , as it was shown by Mineshima et al (2015) and in a practical application for RTE.…”

Type Theories and Lexical Networks: using Serious Games as the basis for Multi-Sorted Typed Systems

“…These two facts open up the possibility of using Coq for reasoning with NL using MTT semantics. Indeed, earlier work has shown that Coq can be used to perform very elaborate reasoning tasks with very high precision (Mineshima et al;Bernardy and Chatzikyriakidis 2017). To give an example, consider the case of the existential quantifier some.…”