Multi-Modal CTL: Completeness, Complexity, and an Application [Book Review]

Studia Logica 92 (1):1-26 (2009)
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Abstract

We define a multi-modal version of Computation Tree Logic (ctl) by extending the language with path quantifiers E δ and A δ where δ denotes one of finitely many dimensions, interpreted over Kripke structures with one total relation for each dimension. As expected, the logic is axiomatised by taking a copy of a ctl axiomatisation for each dimension. Completeness is proved by employing the completeness result for ctl to obtain a model along each dimension in turn. We also show that the logic is decidable and that its satisfiability problem is no harder than the corresponding problem for ctl. We then demonstrate how Normative Systems can be conceived as a natural interpretation of such a multi-dimensional ctl logic

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Author Profiles

Wiebe Van Der Hoek
University of Liverpool
Juan Rodriguez
Long Island University

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References found in this work

Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema.
Contrary-to-duty obligations.Henry Prakken & Marek Sergot - 1996 - Studia Logica 57 (1):91 - 115.
Adding a temporal dimension to a logic system.Marcelo Finger & Dov M. Gabbay - 1992 - Journal of Logic, Language and Information 1 (3):203-233.

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