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"Systems that Explain Themselves" appears a provocative wording, in particular in the context of mathematics education -- it is as provocative as the idea of building educational software upon technology from computer theorem proving. In…
Interactive-proof games model the scenario where an honest party interacts with powerful but strategic provers, to elicit from them the correct answer to a computational question. Interactive proofs are increasingly used as a framework to…
In this paper, we demonstrate how to do automated theorem proving in the presence of a large knowledge base of potential premises without learning from human proofs. We suggest an exploration mechanism that mixes in additional premises…
The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects.…
Video game playing is an extremely structured domain where algorithmic decision-making can be tested without adverse real-world consequences. While prevailing methods rely on image inputs to avoid the problem of hand-crafting state space…
Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further…
A step-by-step presentation of the code for a small theorem prover introduces theorem-proving techniques. The programming language used is Standard ML. The prover operates on a sequent calculus formulation of first-order logic, which is…
We advocate here the use of computational logic for systems biology, as a \emph{unified and safe} framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Formal, automated theorem proving has long been viewed as a challenge to artificial intelligence. We introduce here a new approach to computer theorem proving, one that employs specialized language models for Lean4 proof generation combined…
This work presents an exploration and imitation-learning-based agent capable of state-of-the-art performance in playing text-based computer games. Text-based computer games describe their world to the player through natural language and…
Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…
Quantum computers are on the verge of becoming a commercially available reality. They represent a paradigm shift in computing, with a steep learning gradient. The creation of games is a way to ease the transition for beginners. We present a…
Automated theorem proving is essential for the formal verification of safety-critical systems. As the corpus of formal proofs grows, a natural paradigm is to learn from existing proofs. However, current learning-based approaches…
In a case study we investigate whether off the shelf higher-order theorem provers and model generators can be employed to automate reasoning in and about quantified multimodal logics. In our experiments we exploit the new TPTP…
Induction lies at the heart of mathematics and computer science. However, automated theorem proving of inductive problems is still limited in its power. In this abstract, we first summarize our progress in automating inductive theorem…
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human…
Automatically generated code is gaining traction recently, owing to the prevalence of Large Language Models (LLMs). Further, the AlphaProof initiative has demonstrated the possibility of using AI for general mathematical reasoning.…
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…
Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the…