Related papers: Propositions in Linear Multirole Logic as Multipar…
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.…
We study the notion of subtyping for session types in a logical setting, where session types are propositions of multiplicative/additive linear logic extended with least and greatest fixed points. The resulting subtyping relation admits a…
Client-server sessions are based on a variation of the traditional interpretation of linear logic propositions as session types in which non-linear channels (those regulating the interaction between a pool of clients and a single server)…
We apply an idea originated in the theory of programming languages - monadic meta-language with a distinction between values and computations - in the design of a calculus of cut-elimination for classical logic. The cut-elimination calculus…
The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…
We review the close relationship between abstract machines for (call-by-name or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing the…
Session types enable the specification and verification of communicating systems. However, their theory often assumes that processes never fail. To address this limitation, we present a generalised multiparty session type (MPST) theory with…
Session types model structured communication-based programming. In particular, binary session types for the pi-calculus describe communication between exactly two participants in a distributed scenario. Adding sessions to the pi-calculus…
The scenario-based specification of a large distributed system is usually naturally decomposed into various modules. The integration of specification modules contrasts to the parallel composition of program components, and includes various…
We provide a new realisability model based on orthogonality for the multiplicative fragment of linear logic, both in presence of generalised axioms (MLL*) and in the standard case (MLL). The novelty is the definition of cut elimination for…
Differential Linear Logic (DiLL) is a sequent calculus that expresses differentiation via symmetries between linear and non-linear formulas. In this paper, we express categorical models of DiLL as a pair of Grothendieck fibrations equipped…
Real-valued logics have seen a renewed interest in verification for probabilistic and quantitative systems, in particular machine learning models, where they can be used to directly integrate specifications in the training objective. To do…
Traditionally, each party in a (dyadic or multiparty) session implements exactly one role specified in the type of the session. We refer to this kind of session as an individual session (i-session). As a generalization of i-session, a group…
LLMs demonstrate performance comparable to human abilities in complex tasks such as mathematical reasoning, but their robustness in mathematical reasoning under minor input perturbations still lacks systematic investigation. Existing…
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
Many complex scenarios require the coordination of agents possessing unique points of view and distinct semantic commitments. In response, standpoint logic (SL) was introduced in the context of knowledge integration, allowing one to reason…
Large language models (LLMs) have shown an impressive ability to perform tasks believed to require thought processes. When the model does not document an explicit thought process, it becomes difficult to understand the processes occurring…
Large Language Models (LLMs) have shown impressive capabilities in multi-step reasoning and problem-solving.Recent works introduce multi-agent reflection frameworks where multiple LLM agents critique and refine each other's outputs using…
We present the stellar resolution, a "flexible" tile system based on Robinson's first-order resolution. After establishing formal definitions and basic properties of the stellar resolution, we show its Turing-completeness and to illustrate…
The paper presents a cut-elimination procedure for intuitionistic propositional logic in which cut is eliminated directly, without introducing the multiple-cut rule mix, and in which pushing cut above contraction is one of the reduction…