Natural Language Reasoning
with a Natural Theorem Prover
Lecturer: Lasha Abzianidze
Venue: ESSLLI 2022 in Galway, Ireland. ESSLLI course entry

Natural language reasoning is a complex task that requires understanding the meanings of natural language expressions and recognizing semantic relations between them. The course is built around this highly interdisciplinary task. It introduces a computational theory of reasoning, called Natural Tableau, that combines the idea of a Natural Logic (logic using natural language as its vehicle of reasoning) with the semantic tableau method (a proof calculus that searches for certain situations).

The course not only introduces the theory of Natural Tableau but also shows its practical applications. In particular, we will show how an automated theorem prover, called LangPro, based on Natural Tableau, is used for Recognizing Textual Entailment (RTE) benchmarks. To overcome the knowledge sparsity and boost its performance, LangPro uses abductive reasoning to learn lexical relations from RTE training data.

Moreover, it will be also demonstrated how the prover can be extended for other languages than English, namely, for Dutch. During the course, attendees will also have the opportunity to run LangPro on RTE problems and examine human-readable proofs.

Day 1
The task of Recognizing Textual Entailment/Natural Language Inference; why to care about logic-based NLI systems; monotonicity reasoning; and the NatLog system.
[Handouts] [Slides]
Day 2
Tableau methods for propositional and first-order logics; simple type theory; tableau method for natural logic.
[Handouts] [Slides]
Day 3
Making tableau more natural, i.e. Natural Tableau; extending the type system; generating LLFs from CCG papsers; add more linguistically motivated rules
[Handouts] [Slides]
Day 4
Tableau-based theorem proving for natural logic and natural language; results on FraCaS dataset.
[Handouts] [Slides] [Colab notebook]
Day 5
Evaluation on SICK; learning as abduction; going beyond English (Dutch NLI)
[Handouts-1] [Slides-1] [Slides-2]