Related papers: LangPro: Natural Language Theorem Prover
As the name suggests, type-logical grammars are a grammar formalism based on logic and type theory. From the prespective of grammar design, type-logical grammars develop the syntactic and semantic aspects of linguistic phenomena…
In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but…
We develop combinatorial test generation algorithms for progressively more powerful theorem provers, covering formula languages ranging from the implicational fragment of intuitionistic logic to full intuitionistic propositional logic. Our…
Natural language explanations represent a proxy for evaluating explanation-based and multi-step Natural Language Inference (NLI) models. However, assessing the validity of explanations for NLI is challenging as it typically involves the…
We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original…
We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus. The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP…
This paper describes a neural semantic parser that maps natural language utterances onto logical forms which can be executed against a task-specific environment, such as a knowledge base or a database, to produce a response. The parser…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
Linear logic and the linear {\lambda}-calculus have a long standing tradition in the study of natural language form and meaning. Among the proof calculi of linear logic, proof nets are of particular interest, offering an attractive…
LPTP (Logic Program Theorem Prover) is an interactive natural-deduction-based theorem prover for pure Prolog programs with negation as failure, unification with the occurs check, and a restricted but extensible set of built-in predicates.…
This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was…
We have developed a web-based pedagogical proof assistant, the Proof Tree Builder, that lets you apply rules upwards from the initial goal in sequent calculus and Hoare logic for a simple imperative language. We equipped our tool with a…
Rule-based models are attractive for various tasks because they inherently lead to interpretable and explainable decisions and can easily incorporate prior knowledge. However, such systems are difficult to apply to problems involving…
The combination of verifiable languages and LLMs has significantly influenced both the mathematical and computer science communities because it provides a rigorous foundation for theorem proving. Recent advancements in the field provide…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
Reo is a formal coordination language. In order to assess and evaluate its capabilities, we need a multi-perspective Language Evaluation Framework. Langar (Language Analysis for Reo) is a framework aimed to provide such an evaluation…
Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…
With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…