Abstract
This paper deals with structures \({\langle{\bf T}, I\rangle}\) 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 \({\langle{\bf T}, I\rangle}\) 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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Zanardo, A. Indistinguishability, Choices, and Logics of Agency. Stud Logica 101, 1215–1236 (2013). https://doi.org/10.1007/s11225-013-9530-3
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DOI: https://doi.org/10.1007/s11225-013-9530-3