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The Logic of Sortals pp 43–62Cite as

A Temporal Logic for Sortals

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Part of the book series: Synthese Library ((SYLI,volume 408))

Abstract

A formal language for sortals with temporal operators and its formal semantics is characterized in this chapter. A formal system for this language is also stated and proved to be absolutely consistent. Soundness and completeness theorems for the system in relation to the semantics are proved as well. There is also a justification for considering time as a factor for the logic of sortals.

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Notes

  1. 1.

    As the reader might have noticed, we are approaching time in terms of instants or points of time and not in terms of time intervals. Our approach will be reflected in the sort of formal semantics that we shall characterize in this and subsequent chapters. We should point out that both approaches have been shown to be formally equivalent. For details, see van Benthem (1983).

  2. 2.

    These operators include since, until, now, tomorrow, yesterday. For details on their propositional logic, see Thomason (1984), Goldblatt (1987), and Kamp (1968, 1971).

  3. 3.

    For a philosophical justification of this feature of the semantics, see Sect. 2.5 (Chap. 2).

References

  • van Benthem, J. (1983). The logic of time. Dordrecht/Boston/London: Kluwer Academic Publishers.

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  • Goldblatt, R. (1987). Logics of time and computation (CSLI lecture notes, Vol. 7). Stanford: CSLI Publications.

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  • Kamp, J. (1968). Tense logic and the theory of linear order. Ph.D. Thesis, University of California at Los Angeles.

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  • Kamp, J. (1971). Formal properties of now. Theoria, 37, 227–273.

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  • Thomason, R. (1984). Combinations of tense and modality. In Gabbay and Guenthner (2002) (pp. 205–234).

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Authors and Affiliations

  1. Professor of Logic and Philosophy, Graduate Program in Philosophy, University of Costa Rica, San José, Costa Rica

    Max A. Freund

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  1. Max A. Freund
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Freund, M.A. (2019). A Temporal Logic for Sortals. In: The Logic of Sortals. Synthese Library, vol 408. Springer, Cham. https://doi.org/10.1007/978-3-030-18278-6_3

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