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.
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Masini, A., Viganò, L., Volpe, M. (2008). A Labeled Natural Deduction System for a Fragment of CTL * . In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2009. Lecture Notes in Computer Science, vol 5407. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92687-0_23
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DOI: https://doi.org/10.1007/978-3-540-92687-0_23
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