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

Authors
Wiebe Van Der Hoek
University of Liverpool
Juan Rodriguez
Long Island University
Abstract
We define a multi-modal version of Computation Tree Logic (CTL) by extending the language with path quantifiers $E^\delta $ and $E^\delta $ 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.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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DOI 10.1007/s11225-009-9184-3
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Dynamic Logic.Lenore D. Zuck & David Harel - 1989 - Journal of Symbolic Logic 54 (4):1480.
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