Abstract
In a number of publications A.N. Prior considered the use of what he called ‘metric tense logic’. This is a tense logic in which the past and future operators P and F have an index representing a temporal distance, so that Pnα means that α was true n-much ago, and Fnα means that α will be true n-much hence. The paper investigates the use of metric predicate tense logic in formalising phenomena ormally treated by such devices as multiple indexing or quantification over times.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic. Cambridge: Cambridge University Press.
Cresswell, M. J. (1990). Entities and indices. Dordrecht: Kluwer.
Cresswell, M. J. (1997). Some incompletable modal predicate logics. Logique et Analyse, 160(1997), 321–334.
Cresswell, M. J. (2006). Now is the time. Australasian Journal of Philosophy, 84(2006), 311–332.
Cresswell, M. J. (2010). Temporal reference in linear tense logic. Journal of Philosophical Logic, 39, 173–200.
Cresswell, M. J. (2010). The modal predicate logic of real time. Logique et Analyse, 209, 3–7.
Forbes, G. (1983). Physicalism, instrumentalism and the semantics of modal logic. Journal of Philosophical Logic, 12, 271–298.
Forbes, G. (1985). The metaphysics of modality. Oxford: Clarendon.
Forbes, G. (1989). Languages of possibility. Oxford: Basil Blackwell.
Gabbay, D. M., Hodkinson, I., & Reynolds, M. (1994). Temporal logic: Mathematical foundations and computational aspects. Oxford: Clarendon.
Geach, P. T. (1957). Review of prior 1957. The Cambridge Review, 4.
Kamp, J. A. W. (1971). Formal properties of ‘now’. Theoria, 40, 76–109.
Koymans, R. (1990). Specifying real-time properties with metric temporal logic. Real-Time Systems, 2, 255–299.
Kuhn, S. T. (1980). Quantifiers as modal operators. Studia Logica, 39, 145–158.
Mansfield, M. J. (1963). Introduction to topology. van Nostrand: Princeton.
Marx, M., & Venema, Y. (1997). Multi-dimensional modal logic. Dordrecht: Kluwer.
Ouaknine, J., & Worrell, J. (2008). Some recent results in metric temporal logic, in Formats 2008. LNCS, 5215, 1–13.
Peacocke, C. (1978). Necessity and truth theories. Journal of Philosophical Logic, 7, 473–500.
Prior, A. N. (1957). Time and modality. Oxford: Clarendon.
Prior, A. N. (1967a). Past, present and future. Oxford: Clarendon.
Prior, A. N. (1967b). Stratified metric tense logic. Theoria, 33, 28-38. (Reprinted as chapter 2 of Papers on Time and Tense, New edition, ed, P. Hasle, P, Øhrstrøm, T. Braüner and J. Copeland), Oxford, 2003, Oxford University Press, 2003, 171-193).
Quine, W. V. O. (1960). Variables explained away. Selected Logic Papers. New York, Random House, 1966, 227-235.
Quine, W. V. O. (1971). Predicate functor logic. In J. E. Fensted (Ed.), Proceedings of the Third Scandinavian Logic Symposium (pp. 309–315). Amsterdam: North Holland Publishing Co.
Schönfinkel, M. (1924). Über die Bausteine der mathematischen Logik. Mathematische Annalen, 92, 305-316. Translated and discussed in From Frege to Gödel (ed. J. van Heijenoort), Cambridge, Mass, Harvard University Press, 1966.
Segerberg, K. (1973). Two-dimensional modal logic. Journal of Philosophical Logic, 2, 77–96.
Tarski, A. (1936). The concept of truth in formalized languages. Logic, Semantics and Metamathematics (pp. 152–278). Oxford: Clarendon Press, 1956.
Vlach, F. (1973). ‘Now’ and ‘then’. A formal study in the logic of tense anaphora. PhD dissertation, UCLA.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cresswell, M.J. Predicate Metric Tense Logic for ‘Now’ and ‘Then’. J Philos Logic 42, 1–24 (2013). https://doi.org/10.1007/s10992-011-9209-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-011-9209-z