0

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...

We propose a way to base Situation Semantic to a computational ground of concurrency and to linear logic. One of the core ideas of Situation Semantics is ecological realism, the idea that meaning arises from the interaction between a cog-nitive agent and his/her environments. We model both the agent and environments as a process and study the interaction as a system of communicating processes. ...

This paper studies properties of the logic , which is an extension of multiplicative linear logic (MLL) with a self-dual non-commutative operator. is presented in the calculus of structures, a proof theoretic formalism that supports deep inference, in which inference rules can be applied anywhere inside logical expressions. The use of deep inference results in a simple logical system for MLL ex...

The rst mathematical model of the untyped lambda calculus was discovered by DANA SCOTT in the category of algebraic lattices and Scott continuous maps. The question then arises as to which other cartesian closed categories contain a model of the calculus. In this paper we show that any compact Hausdor model of the calculus must satisfy the property that the semantic map from the calculus to the...

The stochastic Euler-Poincaré equations with pseudo-differential/multiplicative noise are considered in this work. We first establish two new cancellation properties on pseudo-differential operators, which considerably extend the previous results for transport type only involving gradient operator. Then, we obtain local solution, blow-up criterion, and global existence. interplay between stabil...