We refine a model for linear logic based on two well-known ingredients: games and simulations. We have already shown that usual simulation relations form a sound notion of morphism between games; and that we can interpret all linear logic in this way. One particularly interesting point is that we interpret multiplicative connectives by synchronous operations on games. We refine this work by giv...

Proof nets can be seen as a multiple conclusion natural deduction system for Linear Logic (LL) and form a good formalism to analyze some computation mechanisms, for instance in type-theoretic interpretations. This paper presents an algorithm for automated proof nets construction in the non-commutative multiplicative linear logic that is useful for applications including planning, concurrency or...

The proof-theoretic approach to logic programming has benefited from the introduction of focused proof systems, through the non-determinism reduction and control they provide when searching for proofs in the sequent calculus. However, this technique was not available in the calculus of structures, known for inducing even more non-determinism than other logical formalisms. This work in progress ...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

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Proof-search (the basis of logic programming) with multiplicative inference rules, such as linear logic's R and OL, is problematic because of the required non-deterministic splitting of resources. Similarly , searching with additive rules such as NL and R requires a non-deterministic choice between two formulae. Many strategies which resolve such non-determinism, either locally or globally, are...

System BV is an extension of multiplicative linear logic with a non-commutative self-dual operator. We first map derivations of system BV of the calculus of structures to rewritings in a term rewriting system modulo equality, and then express this rewriting system as a Maude system module. This results in an automated proof search implementation for this system, and provides a recipe for implem...

This paper provides a natural deduction system for Partially Commutative Intuitionistic Multiplicative Linear Logic (PCIMLL) and establishes its normalisation and subformula property. Such a system involves both commutative and non commutative connectives and deals with context that are series-parallel multisets of formulæ. This calculus is the extension of the one introduced by de Groote prese...

The logic of bunched implication BI provides a framework for reasoning about resource composition and forms the basis for an assertion language of separation logic which is used to reason about software programs. Propositional BI is obtained by freely combining propositional intuitionistic logic and multiplicative intuitionistic linear logic. It possesses an elegant proof theory: its bunched ca...

This paper re-addresses the old problem of providing a categorical model for Intuitionistic Linear Logic (ILL). In particular we compare the now standard model proposed by Seely to the lesser known one proposed by Benton, Bierman, Hyland and de Paiva. Surprisingly we nd that Seely's model is unsound in that it does not preserve equality of proofs. We shall propose how to adapt Seely's deenition...