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...

It is now well-established that the so-called focalization property plays a central role in the design of programming languages based on proof search, and more generally in the proof theory of linear logic. We present here a sequent calculus for non-commutative logic (NL) which enjoys the focalization property. In the multiplicative case, we give a focalized sequentialization theorem, and in th...

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...

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...

There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$-rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf Keywords:} multiplic...

background and aims. previous researches, conducted mostly on extracted teeth, have shown that efficacy of calculus removal decreases with increasing pocket depth, but there is still a lack of clinical studies concerning the correlation be-tween residual calculus and varying pocket depths. the objective of the present clinical study was to assess the efficiency of mechanical tooth depuration by...

Multiplicative Linear Logic for Resource Transformation Nets p. 81 The Parameterized Complexity of Some Problems in Logic and Linguistics p. 89 Foundations of Proof Search Strategies Design in Linear Logic p. 101 On Extreme Points of Convex Compact Turing Located Set p. 114 Application of Typed Lambda Calculi in the Untyped Lambda Calculus p. 129 Classes with Pairwise Equivalent Enumerations p....

The agent expressions of the π-calculus can be translated into a theory of linear logic in such a way that the reflective and transitive closure of π-calculus (unlabeled) reduction is identified with “entailed-by”. Under this translation, parallel composition is mapped to the multiplicative disjunct (“par”) and restriction is mapped to universal quantification. Prefixing, non-deterministic choi...

System MV is a simple, propositional linear calculus that deals with the commutative as well as the non-commutative composition of structures. The multiplicative fragment of linear logic is a special case of MV , and the tensor rule does not suffer from unnecessary non-determinism in context partitioning as it does in the sequent calculus of linear logic. System MV is obtained by breaking the s...