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The connection method has earned good reputation in the area of automated theorem proving, due to its simplicity, efficiency and rational use of memory. This method has been applied recently in automatic provers that reason over ontologies…

Cut-introduction is a technique for structuring and compressing formal proofs. In this paper we generalize our cut-introduction method for the introduction of quantified lemmas of the form $\forall x.A$ (for quantifier-free $A$) to a method…

The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…

Scientific computing programs often undergo aggressive compiler optimization to achieve high performance and efficient resource utilization. While performance is critical, we also need to ensure that these optimizations are correct. In this…

Computability logic (CoL) is a formal theory of interactive computation. It understands computational problems as games played by two players: a machine and its environment, uses logical formalism to describe valid principles of…

Good tools can bring mechanical verification to programs written in mainstream functional languages. We use hs-to-coq to translate significant portions of Haskell's containers library into Coq, and verify it against specifications that we…

Should the final right bracket in a record declaration be on a separate line? Should arguments to the rewrite tactic be separated by a single space? Coq code tends to be written in distinct manners by different people and teams. The…

We present a method for learning multi-stage tasks from demonstrations by learning the logical structure and atomic propositions of a consistent linear temporal logic (LTL) formula. The learner is given successful but potentially suboptimal…

Deductive coding is a widely used qualitative research method for determining the prevalence of themes across documents. While useful, deductive coding is often burdensome and time consuming since it requires researchers to read, interpret,…

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,…

We explain the use of quantum process calculus to describe and analyse linear optical quantum computing (LOQC). The main idea is to define two processes, one modelling a linear optical system and the other expressing a specification, and…

Static analyzers based on abstract interpretation are complex pieces of software implementing delicate algorithms. Even if static analysis techniques are well understood, their implementation on real languages is still error-prone. This…

Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…

This paper presents an ongoing work that is part of a more wide-ranging project whose final scope is to define a method to validate LTL formulas w.r.t. a program written in the timed concurrent constraint language tccp, which is a logic…

What provides the highest level of assurance for correctness of execution within a programming language? One answer, and our solution in particular, to this problem is to provide a formalization for, if it exists, the denotational semantics…

The use of temporal logics has long been recognised as a fundamental approach to the formal specification and verification of reactive systems. In this paper, we take on the problem of automatically verifying a temporal property, given by a…

We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In…

We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a…

With the advancement of large language models (LLMs), diverse time series analysis tasks are reformulated as time series question answering (TSQA) through a unified natural language interface. However, existing LLM-based approaches largely…

Recent advances in Large Language Model (LLM) based Generative AI techniques have made it feasible to translate enterprise-level code from legacy languages such as COBOL to modern languages such as Java or Python. While the results of…