Related papers: Towards Intuitive Reasoning in Axiomatic Geometry
Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either…
Applying automated reasoning tools for decision support and analysis in law has the potential to make court decisions more transparent and objective. Since there is often uncertainty about the accuracy and relevance of evidence,…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
This position paper argues that AI-assisted software engineering requires explicit mechanisms for tracking the epistemic status and temporal validity of architectural decisions. LLM coding assistants generate decisions faster than teams can…
Interactive theorem provers, like Isabelle/HOL, Coq and Lean, have expressive languages that allow the formalization of general mathematical objects and proofs. In this context, an important goal is to reduce the time and effort needed to…
We present Ax-Prover, a multi-agent system for automated theorem proving in Lean that can solve problems across diverse scientific domains and operate either autonomously or collaboratively with human experts. To achieve this, Ax-Prover…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…
A subclass of nondeterministic Finite Automata generated by means of regular Grammars (GFAs, for short) is introduced. A process algebra is proposed, whose semantics maps a term to a GFA. We prove a representability theorem: for each GFA…
Artificial Intelligence for Theorem Proving has given rise to a plethora of benchmarks and methodologies, particularly in Interactive Theorem Proving (ITP). Research in the area is fragmented, with a diverse set of approaches being spread…
We introduce Prove-It, a Python-based general-purpose interactive theorem-proving assistant designed with the goal of making formal theorem proving as easy and natural as informal theorem proving (with moderate training). Prove-It uses a…
This study presents the first examination of the ability of Large Language Models (LLMs) to follow reasoning strategies that are used to guide Automated Theorem Provers (ATPs). We evaluate the performance of GPT4, GPT3.5 Turbo and Google's…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
Integrating textual graphs into Large Language Models (LLMs) is promising for complex graph-based QA. However, a key bottleneck is retrieving informative yet compact subgraphs that fit the LLM context. Existing retrievers often struggle,…
Prompt engineering is an iterative procedure often requiring extensive manual effort to formulate suitable instructions for effectively directing large language models (LLMs) in specific tasks. Incorporating few-shot examples is a vital and…
Local grammars can be represented in a very convenient way by automata. This paper describes and illustrates an efficient algorithm for the application of local grammars put in this form to lemmatized texts.
Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check…
Despite the recent progress in automatic theorem provers, proof engineers are still suffering from the lack of powerful proof automation. In this position paper we first report our proof strategy language based on a meta-tool approach.…
Understanding geometric relationships with little mathematical knowledge can be challenging for today's students and teachers. A new toolset is introduced that is able to create a proof without words by combining the benefits of the…