Indistinguishability, Choices, and Logics of Agency |
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Authors: | Alberto Zanardo |
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Affiliation: | 1. Department of Mathematics, University of Padova, Padua, Italy
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Abstract: | This paper deals with structures ${langle{bf T}, Irangle}$ in which T is a tree and I is a function assigning each moment a partition of the set of histories passing through it. The function I is called indistinguishability and generalizes the notion of undividedness. Belnap’s choices are particular indistinguishability functions. Structures ${langle{bf T}, Irangle}$ provide a semantics for a language ${mathcal{L}}$ with tense and modal operators. The first part of the paper investigates the set-theoretical properties of the set of indistinguishability classes, which has a tree structure. The significant relations between this tree and T are established within a general theory of trees. The aim of second part is testing the expressive power of the language ${mathcal{L}}$ . The natural environment for this kind of investigations is Belnap’s seeing to it that (stit). It will be proved that the hybrid extension of ${mathcal{L}}$ (with a simultaneity operator) is suitable for expressing stit concepts in a purely temporal language. |
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