This article defines and studies a natural deduction system for partially commutative intuitionistic multiplicative linear logic, that is a combination of intuitionistic commutative linear logic with the Lambek calculus, which is noncommutative, and was first introduced as a sequent calculus by de Groote. In this logic, the hypotheses are endowed with a series-parallel partial order: the parall...

We give some basic results of the theory of proof nets for multiplicative linear logic and multiplicative exponential linear logic with mix. The relation between proof nets and the lambda-calculus is precisely described. 1 Multiplicative Proof Nets 1.1 Multiplicative Linear Logic We assume given a denumerable set of atoms X, Y , . . . The formulas of multiplicative linear logic (MLL) are define...

This paper focuses on the study of existence a mild solution to time and space-fractional stochastic equation perturbed by multiplicative white noise. The required results are obtained analysis techniques, fractional calculus, semigroup theory Leray-Schauder nonlinear alternative.

This paper is an updated version of the paper \Discrete choice models with multiplicative error terms" by Fosgerau and Bierlaire (2006). We propose a multiplicative speci cation of a discrete choice model that renders choice probabilities independent of the scale of the utility. The scale can thus be random with unspeci ed distribution. The model mostly outperforms the classical additive formul...

The paper develops multiplicative compensation for complex-valued semimartingales and studies some of its consequences. It is shown that the stochastic exponential any semimartingale with independent increments becomes a true martingale after when such meaningful. This generalization L\'evy--Khintchin formula fills an existing gap in literature. allows, example, computation Mellin transform sig...