Related papers: Towards Automated Readable Proofs of Ruler and Com…
Recently, we developed an automated theorem prover for projective incidence geometry. This prover, based on a combinatorial approach using matroids, proceeds by saturation using the matroid rules. It is designed as an independent tool,…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
In the current control design of safety-critical autonomous systems, formal verification techniques are typically applied after the controller is designed to evaluate whether the required properties (e.g., safety) are satisfied. However,…
We present an approach for designing correct-by-construction neural networks (and other machine learning models) that are guaranteed to be consistent with a collection of input-output specifications before, during, and after algorithm…
In this paper we will develop an axiomatic foundation for the geometric study of straight edge, protractor, and compass constructions, which while being related to previous foundations, will be the first to have all axioms written and all…
This survey provides an analysis of current methodologies integrating legal and logical specifications into the perception, prediction, and planning modules of automated driving systems. We systematically explore techniques ranging from…
We present an automated verification of the well-known modal logic cube in Isabelle/HOL, in which we prove the inclusion relations between the cube's logics using automated reasoning tools. Prior work addresses this problem but without…
Humans are black boxes -- we cannot observe their neural processes, yet society functions by evaluating verifiable arguments. AI explainability should follow this principle: stakeholders need verifiable reasoning chains, not mechanistic…
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…
The Handbook of Combinatorial Designs catalogs many types of combinatorial designs, together with lists of open instances for which existence has not yet been determined. We develop a constructive protocol CPro1, which uses Large Language…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
Constructor rewriting systems are said to be cons-free if any constructor term occurring in the rhs of a rule must be a subterm of the lhs of the rule. Roughly, such systems cannot build new data structures during their evaluation. In…
Automated algorithm design is entering a new phase: Large Language Models can now generate full optimisation (meta)heuristics, explore vast design spaces and adapt through iterative feedback. Yet this rapid progress is largely…
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…
Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications. However, their ability to generate…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
In this paper, I describe several approaches to automatic or semi-automatic development of symbolic rules for grammar checkers from the information contained in corpora. The rules obtained this way are an important addition to…
Large Language Models (LLMs) with reasoning are trained to iteratively generate and refine their answers before finalizing them, which can help with applications to mathematics and code generation. We apply code generation with reasoning…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…