Abstract
For branching-time temporal logic based on an Ockhamist semantics, we explore a temporal language extended with two additional syntactic tools. For reference to the set of all possible futures at a moment of time we use syntactically designated “restricted variables” called fan-names. For reference to all possible futures alternative to the actual one we use a modification of a difference modality, localized to the set of all possible futures at the actual moment of time.
We construct an axiomatic system for this extended branching-time logic and prove its soundness and completeness with respect to bundle tree semantics. Finally, we show how our axiomatic system can be extended with a variety of important additional operators, such as Since and Until, a global difference operator, operators for undivided and divided histories, reference pointers, etc.
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Brown, M., Goranko, V. An Extended Branching-Time Ockhamist Temporal Logic. Journal of Logic, Language and Information 8, 143–166 (1999). https://doi.org/10.1023/A:1008398102653
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DOI: https://doi.org/10.1023/A:1008398102653