A Labeled Natural Deduction System for a Fragment of CTL*

Authors:
Andrea Masini;Luca Viganò;Marco Volpe
Affiliations:
Department of Computer Science, University of Verona, Italy;Department of Computer Science, University of Verona, Italy;Department of Computer Science, University of Verona, Italy
Venue:
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
Year:
2009

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Abstract

We give a sound and complete labeled natural deduction system for an interesting fragment of $\mathit{CTL^*}$, namely the until-free version of $\mathit{BCTL^*}$. The logic $\mathit{BCTL^*}$ is obtained by referring to a more general semantics than that of $\mathit{CTL^*}$, where we only require that the set of paths in a model is closed under taking suffixes (i.e. is suffix-closed) and is closed under putting together a finite prefix of one path with the suffix of any other path beginning at the same state where the prefix ends (i.e. is fusion-closed). In other words, this logic does not enjoy the so-called limit-closure property of the standard $\mathit{CTL^*}$ validity semantics.