Towards a Complete Axiomatization for Spatial Logic

Mardare, Radu and Policriti, Alberto (2008) Towards a Complete Axiomatization for Spatial Logic. UNSPECIFIED.

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    The process-based Spatial Logics are multi-modal logics developed for semantics on Process Algebras and designed to specify concurrent properties of dynamic systems. On the syntactic level, they combine modal operators similar to operators of Hennessy-Milner logic, dynamic logic, arrow logic, relevant logic, or linear logic. This combination generates expressive logics, sometimes undecidable, for which a wide range of applications have been proposed. In the literature, there exist some sound proof systems for spatial logics, but the problem of completeness against process-algebraic semantics is still open. The main goal of this paper is to identify a sound-complete axiomatization for such a logic. We focus on a particular spatial logic that combines the basic spatial operators with dynamic and classical operators. The semantics is based on a fragment of CCS calculus that embodies the core features of concurrent behaviors. We prove the logic decidable both for satisfiability/validity and mode-checking, and we propose a sound-complete Hilbert-style axiomatic system for it. This is the preliminary version of a paper that was published in Proc. of the International Symposium on Mathematical Foundations of Computer Science, MFCS 2008

    Item Type: Departmental Technical Report
    Department or Research center: CoSBi (Center for Computational and Systems Biology)
    Subjects: Q Science > QA Mathematics > QA076 Computer software > QA076.7 Programming Languages - Semantics
    Report Number: TR-21-2008
    Repository staff approval on: 01 Dec 2009

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