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Characteristic formulae for fixed-point semantics: a general framework

Published online by Cambridge University Press:  28 February 2012

LUCA ACETO ,
ANNA INGOLFSDOTTIR ,
PAUL BLAIN LEVY  and
JOSHUA SACK
LUCA ACETO
Affiliation:
School of Computer Science, Reykjavik University, IS-101 Reykjavík, Iceland Email: luca@ru.is, annai@ru.is, joshua@ru.is
ANNA INGOLFSDOTTIR
Affiliation:
School of Computer Science, Reykjavik University, IS-101 Reykjavík, Iceland Email: luca@ru.is, annai@ru.is, joshua@ru.is
PAUL BLAIN LEVY
Affiliation:
University of Birmingham, Birmingham B15 2TT, UK Email: pbl@cs.bham.ac.uk
JOSHUA SACK
Affiliation:
School of Computer Science, Reykjavik University, IS-101 Reykjavík, Iceland Email: luca@ru.is, annai@ru.is, joshua@ru.is
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Abstract

The concurrency theory literature offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed points of suitable functions. Such constructions and their proofs of correctness have been developed independently, but have a common underlying structure. This paper provides a general view of characteristic formulae that are expressed in terms of logics that have a facility for the recursive definition of formulae. We show how several examples of characteristic-formula constructions in the literature can be recovered as instances of the proposed general framework, and how the framework can be used to yield novel constructions. The paper also offers general results pertaining to the definition of co-characteristic formulae and of characteristic formulae expressed in terms of infinitary modal logics.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 22 , Special Issue 2: Express '09, Ice '09 and Sos '09 , April 2012 , pp. 125 - 173
Copyright
Copyright © Cambridge University Press 2012

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