Research Perspectives for Logic and Deduction

The article is meant to be kind of the author's manifesto for the role of logic and deduction within Intellectics. Based on a brief analysis of this role the paper presents a number of proposals for future scientic research along the various di-mensions in the space of logical explorations. These dimensions include the range of possible applications including modelling intelligent behavior, the grounding of logic in some semantic context, the choice of an appropriate logic from the great variety of alternatives, then the choice of an appropriate formal system for repre-senting the chosen logic, and nally the issue of developing the most ecient search strategies. Among the proposals is a conjecture concerning the treatment of cuts in proof search. Often a key advance is a matter of applying a small change to a single formula. Ray Kurzweil [Kur05, p.5]

Stochastic Mechanisms of Growth and Branching in Mediterranean Coral Colonies

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A local system for intuitionistic logic

Abstract. This paper presents systems for first-order intuitionistic logic and several of its extensions in which all the propositional rules are local, in the sense that, in applying the rules of the system, one needs only a fixed amount of information about the logical expressions involved. The main source of non-locality is the contraction rules. We show that the contraction rules can be restricted to the atomic ones, provided we employ deep-inference, i.e., to allow rules to apply anywhere inside logical expressions. We further show that the use of deep inference allows for modular extensions of intuitionistic logic to Dummett’s intermediate logic LC, Gödel logic and classical logic. We present the systems in the calculus of structures, a proof theoretic formalism which supports deep-inference. Cut elimination for these systems are proved indirectly by simulating the cut-free sequent systems, or the hypersequent systems in the cases of Dummett’s LC and Gödel logic, in the cut free systems in the calculus of structures

A Logical Basis for Quantum Evolution and Entanglement

International audienceWe reconsider discrete quantum causal dynamics where quan-tum systems are viewed as discrete structures, namely directed acyclic graphs. In such a graph, events are considered as vertices and edges de-pict propagation between events. Evolution is described as happening between a special family of spacelike slices, which were referred to as locative slices. Such slices are not so large as to result in acausal influ-ences, but large enough to capture nonlocal correlations. In our logical interpretation, edges are assigned logical formulas in a spe-cial logical system, called BV, an instance of a deep inference system. We demonstrate that BV, with its mix of commutative and noncommutative connectives, is precisely the right logic for such analysis. We show that the commutative tensor encodes (possible) entanglement, and the non-commutative seq encodes causal precedence. With this interpretation, the locative slices are precisely the derivable strings of formulas. Several new technical results about BV are developed as part of this analysis

Attributed probabilistic P systems and their application to the modelling of social interactions in primates

We propose a variant of probabilistic P Systems, Attributed Probabilistic P systems (APP systems), in which objects are annotated with attributes. We use APP systems for modelling social behaviours of some species of primates. In this context attributes can represent position of the animals in the environment, age of the animal, dominance level, aggressiveness, etc. As in standard P systems, the dynamics of the system is described by multiset rewrite rules that are applied in a maximally parallel way. Probabilities of rule application, in a maximal step, are computed according to weight functions associated to rules. As an application, we develop models to compare despotic and egalitarian behaviours on different species of primates