Related papers: Under Lock and Key: A Proof System for a Multimoda…
Under the Curry--Howard isomorphism, the syntactic structure of programs can be modeled using birelational Kripke structures equipped with intuitionistic and modal relations. Intuitionistic relations capture scoping through persistence,…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
In this thesis I lift the Curry--Howard--Lambek correspondence between the simply-typed lambda calculus and cartesian closed categories to the bicategorical setting, then use the resulting type theory to prove a coherence result for…
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
We present an algorithm for deriving a spatial-behavioral type system from a formal presentation of a computational calculus. Given a 2-monad Calc: Catv$\to$ Cat for the free calculus on a category of terms and rewrites and a 2-monad…
Reasoning is central to human intelligence, enabling structured problem-solving across diverse tasks. Recent advances in large language models (LLMs) have greatly enhanced their reasoning abilities in arithmetic, commonsense, and symbolic…
This paper shows how internal models for polymorphic lambda calculi arise in any 2-category with a notion of discreteness. We generalise to a 2-categorical setting the famous theorem of Peter Freyd saying that there are no sufficiently…
In this paper we introduce a term calculus ${\cal B}$ which adds to the affine $\lambda$-calculus with pairing a new construct allowing for a restricted form of contraction. We obtain a Curry-Howard correspondence between ${\cal B}$ and the…
We present a proof-theoretic analysis of the logic NL$\lambda$ (Barker \& Shan 2014, Barker 2019). We notably introduce a novel calculus of proof nets and prove it is sound and complete with respect to the sequent calculus for the logic. We…
In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear…
Proofs of coherence in category theory, starting from Mac Lane's original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what one finds in the lambda calculus, or in term-rewriting…
The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We…
A system of session types is introduced as induced by a Curry Howard correspondence applied to Bounded Linear Logic, and then extending the thus obtained type system with probabilistic choices and ground types. The obtained system satisfies…
This reports introduces a novel sound and complete semantics for first order intuitionistic logic, in the framework of category theory and by the computational interpretation of the logic based on the so-called Curry-Howard isomorphism.…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…
The aim of this paper is to give a precise proof of the completeness of Lamb modes and associated modes. This proof is relatively simple and short but relies on two powerful mathematical theorems. The first one is a theorem on elliptic…
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…