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...

In this paper we describe the form of those continuous multiplicative maps on B(H) (H being a separable complex Hilbert space of dimension not less than 3) which preserve the rank, or the corank. Furthermore, we characterize those continuous *-semigroup endomorphisms of B(H) which are spectrum non-increasing.

Duration Calculus (DC) is a real-time logic with measurement of duration of propositions in observation intervals. It is a highly expressive logic with continuous time behaviours (also called signals) as its models. Validity checking of DC is undecidable. We propose a method for validity checking of Duration Calculus by reduction to a sampled time version of this logic called well sampled Inter...

In this paper we present a syntactical approach for the design of real-time embedded systems. The requirement of the system is specified as Duration Calculus formula over continuous state variables. We model discretization at the state level and approximate continuous state variables by discrete ones. The discrete design is formulated as Duration Calculus formula over discrete state variables. ...

semilinear stochastic evolution equations with multiplicative l'evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollarie...

The Event Calculus of Kowalski and Sergot only deals with discrete change. This paper introduces a simplified version of the Event Calculus and extends it to deal with continuous change, as in the height of a falling object or the level of liquid in a filling vessel. The idea of autotermination is introduced. A period of continuous change autoterminates if it brings about the event which termin...