Elimination of Quantifiers and Undecidability in Spatial Logics for Concurrency

Caires, Luís; Lozes, Étienne

doi:10.1007/978-3-540-28644-8_16

Cited by 16 publications

(9 citation statements)

References 13 publications

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“…Such a phenomenon was already observed for the spatial logic of CCS [15], where = L coincided with structural congruence up to injective renaming. Non-congruence makes the proof of the converse of Proposition 5.2 much harder than the Howe-like method used e.g.…”

Section: Proposition 52 Let R Be An Intensional Bisimulation Then supporting

confidence: 61%

A Spatial Equational Logic for the Applied π-Calculus

Lozes

Villard

2008

CONCUR 2008 - Concurrency Theory

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Abstract. Spatial logics have been proposed to reason locally and modularly on algebraic models of distributed systems. In this paper we define the spatial equational logic AπLwhose models are processes of the applied π-calculus. This extension of the π-calculus allows term manipulation and records communications as active substitutions in a frame, thus augmenting the underlying predefined equational theory. Our logic allows one to reason locally either on frames or on processes, thanks to static and dynamic spatial operators. We study the logical equivalences induced by various relevant fragments of AπL, and show in particular that the whole logic induces a coarser equivalence than structural congruence. We give characteristic formulae for some of these equivalences and for static equivalence. Going further into the exploration of AπL's expressivity, we also show that it can eliminate standard term quantification.

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Section: Proposition 52 Let R Be An Intensional Bisimulation Then supporting

confidence: 61%

A Spatial Equational Logic for the Applied π-Calculus

Lozes

Villard

2008

CONCUR 2008 - Concurrency Theory

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“…These spatial modalities have an intensional flavor, the properties they express being invariant only for simple spatial rearrangements of the system. Still most of the spatial logics face with decidability problems: it was proved that the basic spatial operators, in combination with temporal operators, generate undecidable logics [11,12,13] even against a finite piece of CCS [14].…”

Section: The Agent Is Nothing More But Its Behaviormentioning

confidence: 99%

Decidable Extensions of Hennessy-Milner Logic

Mardare

Priami

2006

Lecture Notes in Computer Science

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Abstract. We propose a new class of logics for specifying and modelchecking properties of distributed systems -Dynamic Epistemic Spatial Logics. They have been designed as extensions of Hennessy-Milner logic with spatial operators (inspired by Cardelli-Gordon-Caires spatial logic) and epistemic operators (inspired by dynamic-epistemic logics). Our logics focus on observers, agents placed in different locations of the system having access to some subsystems. Treating them as epistemic agents, we develop completely axiomatized and decidable logics that express the information flow between them in a dynamic and distributed environment. The knowledge of an epistemic agent, is understood as the information, locally available to our observer, about the overall-global system.

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“…As for the semantics, the same fragment of CCS yields undecidability for other spatial logics, e.g. with a modality encoding communication-based transitions [5].…”

Section: Introductionmentioning

confidence: 99%

A Complete Axiomatic System for a Process-Based Spatial Logic

Mardare

Policriti

2008

Lecture Notes in Computer Science

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A complete axiomatic system for a process-based spatial logic / R. MARDARE; POLICRITI A. -STAMPA. -5162 (2008) Abstract 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.

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Elimination of Quantifiers and Undecidability in Spatial Logics for Concurrency

Cited by 16 publications

References 13 publications

A Spatial Equational Logic for the Applied π-Calculus

A Spatial Equational Logic for the Applied π-Calculus

Decidable Extensions of Hennessy-Milner Logic

A Complete Axiomatic System for a Process-Based Spatial Logic

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