An Extended Branching-Time Ockhamist Temporal Logic

Authors:
Mark Brown;Valentin Goranko
Affiliations:
Department of Philosophy, Syracuse University, 541 Hall of Languages, Syracuse, NY 13244, U.S.A.;Department of Mathematics, Rand Afrikaans University, P.O. Box 524, Auckland Park 2006, Johannesburg, South Africa (E-mail: vfg@raua.rau.ac.za)
Venue:
Journal of Logic, Language and Information
Year:
1999

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Abstract

For branching-time temporal logic based on an Ockhamist semantics, weexplore a temporal language extended with two additional syntactictools. For reference to the set of all possible futures at amoment of time we use syntactically designated ’’restrictedvariables‘‘ called fan-names. For reference to all possiblefutures alternative to the actual one we use a modification of adifference modality, localized to the set of all possiblefutures at the actual moment of time.We construct an axiomatic system for this extended branching-timelogic and prove its soundness and completeness with respect to bundletree semantics. Finally, we show how our axiomatic system can beextended with a variety of important additional operators, suchas Since and Until, a global difference operator,operators for undivided and divided histories, reference pointers, etc.