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Counterpart Semantics for a Second-Order mu-Calculus

Gadducci, Fabio and Lluch-Lafuente, Alberto and Vandin, Andrea Counterpart Semantics for a Second-Order mu-Calculus. Fundamenta Informaticae, 118 (1-2). pp. 177-205. ISSN 1875-8681 (2012)

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Quantified μ-calculi combine the fix-point and modal operators of temporal logics with (existential and universal) quantifiers, and they allow for reasoning about the possible behaviour of individual components within a software system. In this paper we introduce a novel approach to the semantics of such calculi: we consider a sort of labeled transition systems called counterpart models as semantic domain, where states are algebras and transitions are defined by counterpart relations (a family of partial homomorphisms) between states. Then, formulae are interpreted over sets of state assignments (families of partial substitutions, associating formula variables to state components). Our proposal allows us to model and reason about the creation and deletion of components, as well as the merging of components. Moreover, it avoids the limitations of existing approaches, usually enforcing restrictions of the transition relation: the resulting semantics is a streamlined and intuitively appealing one, yet it is general enough to cover most of the alternative proposals we are aware of. The paper is rounded up with some considerations about expressiveness and decidability aspects.

Item Type: Article
Identification Number: 10.3233/FI-2012-709
Funders: EU FP7-ICT IP ASCEns (IP 257414) , MIUR PRIN SisteR (PRIN 20088HXMYN)
Uncontrolled Keywords: Quantified μ-calculi, counterpart semantics, modal logics, graph transformation
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Users 30 not found.
Date Deposited: 09 Jan 2012 11:57
Last Modified: 13 Jul 2016 10:50
URI: http://eprints.imtlucca.it/id/eprint/1049

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