The agent expressions of the -calculus can be translated into a theory of linear logic in such a way that the re ective and transitive closure of -calculus (unlabeled) reduction is identi ed with \entailed-by". Under this translation, parallel composition is mapped to the multiplicative disjunct (\par") and restriction is mapped to universal quanti cation. Pre xing, non-deterministic choice (+)...

We consider a linear stochastic differential equation with drift and multiplicative noise. study the problem of approximating its solution process that solves where possibly is replaced by deterministic function. To do this, we use combination Pontryagin’s maximum principle approach direct methods calculus variations. find necessary sufficient conditions for function $$u \in L^1(0, T)$$ to be m...

In this paper, we establish integral inequalities of Hermite-Hadamard type for multiplicativelys-preinvex functions. We also obtain some new inequalities involving multiplicative integralsby using some properties of multiplicatively s-preinvex and preinvex functions.

We prove a completeness result for Multiplicative Exponential Linear Logic (MELL): we show that the relational model is injective for MELL proof-nets, i.e. the equality between MELL proof-nets in the relational model is exactly axiomatized by cut-elimination. In the seminal paper by Harvey Friedman [11], it has been shown that equality between simply-typed lambda terms in the full typed structu...

In this paper the NP-completeness of the system LP (associative-commutative Lambek calculus) will be shown. The complexity of LP has been known for some time, it is a corollary of a result for multiplicative intuitionistic linear logic (MILL)1 from (Kanovich, 1991) and (Kanovich, 1992). We show that this result can be strengthened: LP remains NP-complete under certain restrictions. The proof do...

We present a matrix characterization of logical validity in the multiplicative fragment of linear logic. On this basis we develop a matrix-based proof search procedure for this fragment and a procedure which translates the machine-found proofs back into the usual sequent calculus for linear logic. Both procedures are straightforward extensions of methods which were developed for a uniform treat...

We present a matrix characterization of logical validity in the multiplicative fragment of linear logic. On this basis we develop a matrix-based proof search procedure for this fragment and a procedure which translates the machine-found proofs back into the usual sequent calculus for linear logic. Both procedures are straightforward extensions of methods which originally were developed for a un...

This work deals with semantics of programming languages (or equivalently, thanks to Curry-Howard isomorphism, with semantics of proofs). We introduce a framework in which both static semantics (Ehrhard’s hypercoherences) and dynamic semantics (Hyland-Ong’s games), can be presented. The work is carried in a multiplicative subsystem of Laurent’s polarized linear logic with weakening. Like Böhm tr...

The notion of isomorphisms of types has many theoretical as well as practical consequences, and isomorphisms of types have been investigated at length over the past years. Isomorphisms in weak system (like linear lambda calculus) have recently been investigated due to their practical interest in library search. In this paper we give a remarkably simple and elegant characterization of linear iso...

Graphical calculi provide an intuitive, compositional way to express and manipulate quantum states and processes. They also provide a bridge to automated techniques for reasoning and computation via graph rewriting. The power of these calculi stems from the fact that they subsume a wide range of symmetries in the structure of quantum operations such as the Choi-Jamiolkowski isomorphism. One suc...