Undivided and Indistinguishable Histories in Branching-Time Logics

Authors:
Alberto Zanardo
Affiliations:
Dipartimento di Matematica P. ed A., Università di Padova, Via Belzoni 7, I-35131 Padova, Italy (E-mail: azanardo@math.unipd.it)
Venue:
Journal of Logic, Language and Information
Year:
1998

Citing 1
Cited 3

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Temporal logic (vol. 1): mathematical foundations and computational aspects

An Extended Branching-Time Ockhamist Temporal Logic

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Completeness of a Branching-Time Logic with Possible Choices

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Indistinguishability, Choices, and Logics of Agency

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Abstract

In the tree-like representation of Time, two historiesare ’’undivided‘‘ at a moment t whenever they share a commonmoment in the future of t. In the present paper, it will first be proved that Ockhamist and Peircean branching-timelogics are unable to express some important sentences inwhich the notion of undividedness is involved. Then, a newsemantics 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.