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Multi-Modal CTL: Completeness, complexity, and an application

AuthorsAgotnes, Thomas; Hoek, Wiebe van der; Rodríguez-Aguilar, Juan Antonio ; Sierra, Carles ; Wooldridge, Michael
KeywordsNormative systems
Social laws
Computation tree logic (ctl)
Issue Date2009
CitationStudia Logica 92: 1- 26 (2009)
AbstractWe 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. © 2009 Springer Science+Business Media B.V.
Identifiersdoi: 10.1007/s11225-009-9184-3
issn: 0039-3215
Appears in Collections:(IIIA) Artículos
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