Denote the free group on 2 letters by F2 and the SL(2,C)-representation variety of F2 by R = Hom(F2, SL(2,C)). The group SL(2,C) acts on R by conjugation. We construct an isomorphism between the coordinate ring C[SL(2,C)] and the ring of matrix coefficients, providing an additive basis of C[R]SL(2,C) in terms of spin networks. Using a graphical calculus, we determine the symmetries and multipli...

We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms à la De Mo...

In this paper, we deal with the bounded real lemma for stochastic singular systems with multiplicative noises. Based on the adaptation of Itô calculus, the admissibility for this class of systems is defined and the bounded real lemma is derived using the mean square exponential stability. This lemma is then used to synthetize a H∞ output feedback controller for the considered class of systems t...

In this article, we consider the two-dimensional stochastic Navier-Stokes equation (SNSE) on a smooth bounded domain, driven by affine-linear multiplicative white noise and with random initial conditions and Dirichlet boundary conditions. The random initial condition is allowed to anticipate the forcing noise. Our main objective is to prove the existence and uniqueness of the solution to the SN...

The present report is a, somewhat lengthy, addendum to Danos et al.(1997), where the elimination of cuts from derivations in sequent calculus for classical logic was studied`from the point of view of linear logic'. To that purpose a formulation of classical logic was used, that-as in linear logic-distinguishes between multiplicative and additive versions of the binary connectives. The main nove...

J. Dix, F. L. Del Cerro, U. Furbach eds., 6 European Workshop on Logics in Artificial Intelligence, European Workshop, JELIA ’98, LNAI 1489, pp. 169–183, c ©Springer Verlag, 1998. Abstract. We present a matrix characterization of logical validity in the multiplicative fragment of linear logic with exponentials. In the process we elaborate a methodology for proving matrix characterizations corre...

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...

We present a geometrical analysis of the principles that lay at the basis of Categorial Grammar and of the Lambek Calculus. In Abrusci (On residuation, 2014) it is shown that the basic properties known as Residuation laws can be characterized in the framework of Cyclic Multiplicative Linear Logic, a purely non-commutative fragment of Linear Logic. We present a summary of this result and, pursui...

Using the method of steps, we describe stochastic processes with delays in terms of Markov diffusion processes. Thus, multivariate Langevin equations and Fokker-Planck equations are derived for stochastic delay differential equations. Natural, periodic, and reflective boundary conditions are discussed. Both Ito and Stratonovich calculus are used. In particular, our Fokker-Planck approach recove...

Permutative logic (PL) is a noncommutative variant of multiplicative linear logic (MLL) arising from recent investigations concerning the topology of linear proofs. Permutative sequents are structured as oriented surfaces with boundary whose topological complexity is able to encode some information about the exchange in sequential proofs. In this paper we provide a complete permutative sequent ...