An Algebraic Correctness Criterion for Intuitionistic Multiplicative Proof-Nets

An Algebraic Correctness Criterion for Intuitionistic Proof-Nets

Correctness of Multiplicative (and Exponential) Proof Structures is NL -Complete

We provide a new correctness criterion for unit-free MLL proof structures and MELL proof structures with units. We prove that deciding the correctness of a MLL and of a MELL proof structure is NL-complete. We also prove that deciding the correctness of an intuitionistic multiplicative essential net is NL-complete.

Constructive Logics Part II: Linear Logic and Proof Nets

The purpose of this paper is to give an exposition of material dealing with constructive logics, typed -calculi, and linear logic. The first part of this paper gives an exposition of background material (with the exception of the Girard-translation of classical logic into intuitionistic logic, which is new). This second part is devoted to linear logic and proof nets. Particular attention is giv...

Retractile Proof Nets of the Purely Multiplicative and Additive Fragment of Linear Logic

Proof nets are a parallel syntax for sequential proofs of linear logic, firstly introduced by Girard in 1987. Here we present and intrinsic (geometrical) characterization of proof nets, that is a correctness criterion (an algorithm) for checking those proof structures which correspond to proofs of the purely multiplicative and additive fragment of linear logic. This criterion is formulated in t...

Geometry of Interaction for MALL via Hughes-vanGlabbeek Proof-Nets

This paper presents, for the first time, a Geometry of Interaction (GoI) interpretation using Hughes-vanGlabbeek (HvG) proof-nets for multiplicative additive linear logic (MALL). Our GoI captures dynamically HvG’s geometric correctness criterion–the toggling cycle condition–in terms of algebraic operators. Our new ingredient is a scalar extension of the *-algebra in Girard’s *-ring of partial i...