Completeness and Complexity of Multi-modal CTL

Authors:
Thomas Ågotnes;Wiebe van der Hoek;Michael Wooldridge
Affiliations:
Department of Computer Engineering, Bergen University College, Bergen, Norway;Department of Computer Science, University of Liverpool, Liverpool, UK;Department of Computer Science, University of Liverpool, Liverpool, UK
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
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^@d and A^@d where @d 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 at a time. We also show that the logic is decidable and that its satisfiability problem is no harder than the corresponding problem for ctl.