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Common programming tools, like compilers, debuggers, and IDEs, crucially rely on the ability to analyse program code to reason about its behaviour and properties. There has been a great deal of work on verifying compilers and static…
One challenge in fact checking is the ability to improve the transparency of the decision. We present a fact checking method that uses reference information in knowledge graphs (KGs) to assess claims and explain its decisions. KGs contain a…
Highly automated theorem provers like Dafny allow users to prove simple properties with little effort, making it easy to quickly sketch proofs. The drawback is that such provers leave users with little control about the proof search,…
Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
We introduce pseudo-deterministic interactive proofs (psdAM): interactive proof systems for search problems where the verifier is guaranteed with high probability to output the same output on different executions. As in the case with…
"Theorem proving is similar to the game of Go. So, we can probably improve our provers using deep learning, like DeepMind built the super-human computer Go program, AlphaGo." Such optimism has been observed among participants of AITP2017.…
Recent advances in automated theorem proving leverages language models to explore expanded search spaces by step-by-step proof generation. However, such approaches are usually based on short-sighted heuristics (e.g., log probability or…
Symbolic regression is emerging as a promising machine learning method for learning succinct underlying interpretable mathematical expressions directly from data. Whereas it has been traditionally tackled with genetic programming, it has…
This paper describes a new method for Symbolic Regression that allows to find mathematical expressions from a dataset. This method has a strong mathematical basis. As opposed to other methods such as Genetic Programming, this method is…
Formal methods for verification of programs are extended to testing of programs. Their combination is intended to lead to benefits in reliable program development, testing, and evolution. Our geometric theory of testing is intended to serve…
We describe how we connected three programs that compute Groebner bases to Coq, to do automated proofs on algebraic, geometrical and arithmetical expressions. The result is a set of Coq tactics and a certificate mechanism (downloadable at…
In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each…
We have developed an alternative approach to teaching computer science students how to prove. First, students are taught how to prove theorems with the Coq proof assistant. In a second, more difficult, step students will transfer their…
Large language model pipelines have improved automated fact-checking for complex claims, yet many approaches rely on few-shot in-context learning with demonstrations that require substantial human effort and domain expertise. Among these,…
We present ML4PG - a machine learning extension for Proof General. It allows users to gather proof statistics related to shapes of goals, sequences of applied tactics, and proof tree structures from the libraries of interactive higher-order…
In recent years, deep metric learning and its probabilistic extensions claimed state-of-the-art results in the face verification task. Despite improvements in face verification, probabilistic methods received little attention in the…
Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise…
This paper addresses a significant gap in explainable AI: the necessity of interpreting epistemic uncertainty in model explanations. Although current methods mainly focus on explaining predictions, with some including uncertainty, they fail…
A key component of mathematical reasoning is the ability to formulate interesting conjectures about a problem domain at hand. In this paper, we give a brief overview of a theory exploration system called QuickSpec, which is able to…