A Hybrid Linear Logic for Constrained Transition Systems

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus

A Hybrid Linear Logic for Constrained Transition Systems with Applications to Molecular Biology

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus. We also present some preliminary experiments of direct encoding of biological systems in the logic

A Hybrid Linear Logic for Constrained Transition Systems

International audienceLinear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus

Temporalized logics and automata for time granularity

Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym: TPLP Category: Paper for Special Issue (Verification and Computational Logic) Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September 200

A method for rigorous design of reconfigurable systems

Reconfigurability, understood as the ability of a system to behave differently in different modes of operation and commute between them along its lifetime, is a cross-cutting concern in modern Software Engineering. This paper introduces a specification method for reconfigurable software based on a global transition structure to capture the system's reconfiguration space, and a local specification of each operation mode in whatever logic (equational, first-order, partial, fuzzy, probabilistic, etc.) is found expressive enough for handling its requirements. In the method these two levels are not only made explicit and juxtaposed, but formally interrelated. The key to achieve such a goal is a systematic process of hybridisation of logics through which the relationship between the local and global levels of a specification becomes internalised in the logic itself.This work is financed by the ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation – COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT – Fundação para a Ciência e a Tecnologia within projects POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013. The first author is further supported by the BPD FCT Grant SFRH/BPD/103004/2014, and R. Neves is sponsored by FCT Grant SFRH/BD/52234/2013. M.A. Martins is also funded by the EU FP7 Marie Curie PIRSESGA-2012-318986 project GeTFun: Generalizing Truth-Functionality

From Quantum Metalanguage to the Logic of Qubits

The main aim of this thesis is to look for a logical deductive calculus (we will adopt sequent calculus, originally introduced in Gentzen, 1935), which could describe quantum information and its properties. More precisely, we intended to describe in logical terms the formation of the qubit (the unit of quantum information) which is a particular linear superposition of the two classical bits 0 and 1. To do so, we had to introduce the new connective "quantum superposition", in the logic of one qubit, Lq, as the classical conjunction cannot describe this quantum link.Comment: 138 pages, PhD thesis in Mathematic