Abstract
Logics of discrete time are, in Arthur Prior’s words, “applicable in limited fields of discourse in which we are concerned with what happens in a sequence of discrete states,” independent of “any serious metaphysical assumption that time is discrete.” This insight is applied to natural language semantics, a widespread assumption in which is that time is, as is the real line, dense. “Limited fields of discourse” are construed as finite sets of temporal propositions, inducing bounded notions of temporal granularity that can be refined to expand the discourse. The construal is developed in line with Prior’s view of what is “metaphysically fundamental”.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
That is, \({\mathfrak {A}}\) is \(\varphi \)-alternation bounded iff the boundary of \([\![\varphi ]\!]\) is finite (where the boundary of a subset A of T is the closure of A minus the interior of A). We assume here the order topology, given by unions of sets \((t,t^{\prime })\) of instants \(\prec \)-between t and \(t^{\prime }\).
We draw boxes (instead of the usual curly braces \(\{\) and \(\}\)) around sets-as-symbols, reinforcing their cartoon/film strip reading.
References
Allen, J. F. (1983). Maintaining knowledge about temporal intervals. Commun. ACM, 26(11), 832–843.
Areces, C., & Blackburn, P. (2005). Reichenbach, prior and montague: A semantic get-together. In S. Artemov, et al. (Eds.), We will show them: Essays in honour of Dov Gabbay (pp. 77–88). London: College Publications.
Bennett, M., & Partee, B. (1972). Towards the logic of tense and aspect in English. Bloomington: Indiana University Linguistics Club.
Blackburn, P. (2006). Arthur prior and hybrid logic. Synthese, 150(3), 329–372.
Comrie, B. (1976). Aspect. Cambridge: Cambridge University Press.
Davidson, D. (1967). The logical form of action sentences. In N. Rescher (Ed.), The logic of decision and action (pp. 81–95). Pittsburgh: University of Pittsburgh Press.
Dowty, D. R. (1979). Word meaning and Montague grammar. Dordrecht: Reidel.
Emerson, E. A. (1995). Temporal and modal logic. In J. van Leeuwen (Ed.), Handbook of theoretical computer science (Vol. B, pp. 995–1072). Cambridge: MIT Press.
Fernando, T. (2013). Dowty’s aspect hypothesis segmented. In Proceedings of the 19th Amsterdam colloquium (pp. 107–114).
Galton, A. (1987). The logic of occurrence. In A. Galton (Ed.), Temporal logics and their applications (pp. 169–196). San Diego: Academic Press.
Hamblin, C. L. (1971). Instants and intervals. Studium generale, 24, 127–134.
Johnson-Laird, P. N. (2004). The history of mental models. Psychology of reasoning: Theoretical and historical perspectives (pp. 179–212). New York: Psychology Press.
Kahneman, D. (2011). Thinking, fast and slow. London: Penguin.
Kamp, H. (2013). The time of my life. Retrieved August 10, 2014, from http://lucian.uchicago.edu/blogs/elucidations/2013/08/07/an-essay-by-hans-kamp/.
Kamp, H., & Reyle, U. (1993). From discourse to logic. Dordrecht: Kluwer.
Klein, W. (2009). How time is encoded. In W. Klein & P. Li (Eds.), The expression of time (pp. 39–81). Berlin: Mouton De Gruyter.
Montague, R. (1973). The proper treatment of quantification in ordinary English. In K. J. J. Hintikka, et al. (Eds.), Approaches to natural language (pp. 221–242). Dordrecht: Reidel.
Nishimura, H. (1980). Interval logics with applications to study of tense and aspect in English. Publications Research Institute for Mathematical Sciences, 16, 417–459.
Øhrstrøm, P., & Hasle, P. (1993). A.N. Prior’s rediscovery of tense logic. Erkenntnis, 39, 23–50.
Pratt-Hartmann, I. (2005). Temporal prepositions and their logic. Artificial Intelligence, 166, 1–36.
Prior, A. N. (1967). Past, present and future. Oxford: Clarendon Press.
Prior, A. N. (1968). Egocentric logic. Noûs, 2(3), 191–207.
Reichenbach, H. (1947). Elements of symbolic logic. New York: Random House.
Taylor, B. (1977). Tense and continuity. Linguistics and philosophy, 1, 199–220.
van Lambalgen, M., & Hamm, F. (2004). The proper treatment of events. Oxford: Wiley-Blackwell.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fernando, T. Prior and temporal sequences for natural language. Synthese 193, 3625–3637 (2016). https://doi.org/10.1007/s11229-015-0902-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-015-0902-2