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Temporal Modality

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Temporal Logic

Part of the book series: LEP Library of Exact Philosophy ((LEP,volume 3))

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Abstract

In classical antiquity, Diodorus Cronus defined the necessary as that which is and always will be the case, and correspondingly, defined the possible as that which is or will be the case1. Using our standard notation for necessity and possibility, we can express these definitions in a tense calculus by:

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References

  1. For a comprehensive treatment of modal logic the reader should consult G. E. Hughes and M. J. Cresswell, Introduction to Modal Logic ( London, Methuen and Co., 1968 ).

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  2. For a proof, see Saul Kripke, Semantical Analysis of Modal Logic I, Normal Propositional Calculi, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 9 (1963), pp. 67–96.

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  3. In his paper: Modal Systems in the neighborhood of T, Notre Dame Journal of Formal Logic, vol. 5 (1965), pp. 59–61.

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  4. A. N. Prior, Past, Present and Future, Oxford University Press (1967), pp. 54–55.

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  5. A proof of this is to be found in R. A. Bull, An Algebraic Study of Diodorean Modal Systems, Journal of Symbolic Logic, vol. 33 (1968), pp. 27–38.

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  6. This formulation of deontic S5 differs from the system 0S5 of T. J. Smiley [Journal of Symbolic Logic, vol. 28 (1963), pp. 113–134], and from D5 of E. J. Lemmon Journal of Symbolic Logic, vol. 22 (1957),pp. 176–186].

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  7. See A. N. Prior, Time and Modality, Oxford University Press (1957) and R.A. Bull, An Axiomatization of Prior’s Modal Calculus Q, Notre Dame Journal of Formal Logic, vol. 5 (1964), pp. 211–214.

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Authors and Affiliations

  1. Pittsburgh, USA

    Nicholas Rescher & Alasdair Urquhart

Authors
  1. Nicholas Rescher
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  2. Alasdair Urquhart
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© 1971 Springer-Verlag/Wien

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Rescher, N., Urquhart, A. (1971). Temporal Modality. In: Temporal Logic. LEP Library of Exact Philosophy, vol 3. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7664-1_12

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  • DOI: https://doi.org/10.1007/978-3-7091-7664-1_12

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-7666-5

  • Online ISBN: 978-3-7091-7664-1

  • eBook Packages: Springer Book Archive

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