Abstract
In the tree-like representation of Time, two histories are “undivided” at a moment t whenever they share a common moment in the future of t. In the present paper, it will first be proved that Ockhamist and Peircean branching-time logics are unable to express some important sentences in which the notion of undividedness is involved. Then, a new semantics for branching-time logic will be presented. The new semantics is based on trees endowed with an “indistinguishability” function, a generalization of the notion of undividedness. It will be shown that Ockhamist and Peircean semantics can be viewed as limit cases of the semantics developed in this paper.
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Zanardo, A. Undivided and Indistinguishable Histories in Branching-Time Logics. Journal of Logic, Language and Information 7, 297–315 (1998). https://doi.org/10.1023/A:1008259000544
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DOI: https://doi.org/10.1023/A:1008259000544