Related papers: On the Relational Translation Method for Propositi…
This paper presents a proof-theoretic analysis of the modal $\mu$-calculus. More precisely, we prove a syntactic cut-elimination for the non-wellfounded modal $\mu$-calculus, using methods from linear logic and its exponential modalities.…
In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the…
We describe here a simple application of rational trees to the implementation of an interpreter for a procedural language written in a logic programming language. This is possible in languages designed to support rational trees (such as…
In this paper, we introduce a semantics of realisability for the classical propositional natural deduction and we prove a correctness theorem. This allows to characterize the operational behaviour of some typed terms.
Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…
This paper continues the investigation of the logic of competing theories, be they scientific, social, political etc. We introduce a many-valued, multi-type modal language which we endow with relational semantics based on enriched reflexive…
This paper presents a many-sorted polyadic modal logic that generalizes some of the existing approaches. The algebraic semantics has led us to a many-sorted generalization of boolean algebras with operators, for which we prove the analogue…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
Despite the increasing effectiveness of language models, their reasoning capabilities remain underdeveloped. In particular, causal reasoning through counterfactual question answering is lacking. This work aims to bridge this gap. We first…
In a previous paper, a tableau calculus has been presented, which constitute a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work extends such a calculus to multi-modal…
Semantic typing has become a powerful tool for program verification, applying the technique of logical relations as not only a proof method, but also a device for prescribing program behavior. In recent work, Yao et al. scaled semantic…
We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…
I deal with two approaches to proof-theoretic semantics: one based on argument structures and justifications, which I call reducibility semantics, and one based on consequence among (sets of) formulas over atomic bases, called base…
Formal theorem provers based on large language models (LLMs) are highly sensitive to superficial variations in problem representation: semantically equivalent statements can exhibit drastically different proof success rates, revealing a…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
Until recently, First-Order Temporal Logic (FOTL) has been little understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However,…
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 establish a natural translation from word rewriting systems to strictly positive polymodal logics. Thereby, the latter can be considered as a generalization of the former. As a corollary we obtain examples of undecidable strictly…
We find a translation with particularly nice properties from intuitionistic propositional logic in countably many variables to intuitionistic propositional logic in two variables. In addition, the existence of a possibly-not-as-nice…
As the development of formal proofs is a time-consuming task, it is important to devise ways of sharing the already written proofs to prevent wasting time redoing them. One of the challenges in this domain is to translate proofs written in…