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Graphical representation of covariant-contravariant modal formulae

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Aceto , Luca and Fábregas, Ignacio and Frutos Escrig, David de and Ingolfsdottir, Anna and Palomino, Miguel (2011) Graphical representation of covariant-contravariant modal formulae. Electronic proceedings in theoretical computer science, 64 . pp. 1-15. ISSN 2075-2180

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Official URL: http://dx.doi.org/10.4204/EPTCS.64.1


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http://arXiv:1108.4464v1Organisation


Abstract

Covariant-contravariant simulation is a combination of standard (covariant) simulation, its contravariant counterpart and bisimulation. We have previously studied its logical characterization by means of the covariant-contravariant modal logic. Moreover, we have investigated the relationships between this model and that of modal transition systems, where two kinds of transitions (the so-called may and must transitions) were combined in order to obtain a simple framework to express a notion of refinement over state-transition models. In a classic paper, Boudol and Larsen established a precise connection between the graphical approach, by means of modal transition systems, and the logical approach, based on Hennessy-Milner logic without negation, to system specification. They obtained a (graphical) representation theorem proving that a formula can be represented by a term if, and only if, it is consistent and prime. We show in this paper that the formulae from the covariant-contravariant modal logic that admit a "graphical" representation by means of processes, modulo the covariant-contravariant simulation preorder, are also the consistent and prime ones. In order to obtain the desired graphical representation result, we first restrict ourselves to the case of covariant-contravariant systems without bivariant actions. Bivariant actions can be incorporated later by means of an encoding that splits each bivariant action into its covariant and its contravariant parts.


Item Type:Article
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Proceedings 18th International Workshop on Expressiveness in Concurrency (EXPRESS 2011), Aachen, Germany, 5th September 2011

Subjects:Sciences > Computer science
ID Code:20795
Deposited On:12 Apr 2013 09:36
Last Modified:25 Nov 2014 13:33

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