eprintid: 1049
rev_number: 10
eprint_status: archive
userid: 30
dir: disk0/00/00/10/49
datestamp: 2012-01-09 11:57:49
lastmod: 2016-07-13 10:50:07
status_changed: 2012-01-09 11:57:49
type: article
metadata_visibility: show
creators_name: Gadducci, Fabio
creators_name: Lluch-Lafuente, Alberto
creators_name: Vandin, Andrea
creators_id: 
creators_id: alberto.lluch@imtlucca.it
creators_id: andrea.vandin@imtlucca.it
title: Counterpart Semantics for a Second-Order mu-Calculus
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
keywords: Quantified μ-calculi, counterpart semantics, modal logics, graph transformation 
abstract: 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.
date: 2012
date_type: published
publication: Fundamenta Informaticae
volume: 118
number: 1-2
publisher: IOS Press
pagerange: 177-205
id_number: 10.3233/FI-2012-709
refereed: TRUE
issn: 1875-8681
official_url: http://iospress.metapress.com/content/G154233H0U87Q571
funders: EU FP7-ICT IP ASCEns (IP 257414) 
funders: MIUR PRIN SisteR (PRIN 20088HXMYN)
citation:   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)