Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-09T08:45:47.307Z Has data issue: false hasContentIssue false

Regular relations for temporal propositions

Published online by Cambridge University Press:  21 March 2011

TIM FERNANDO*
Affiliation:
Trinity College Dublin, Ireland e-mail: [email protected]

Abstract

Relations computed by finite-state transducers are applied to interpret temporal propositions in terms of strings representing finite contexts or situations. Carnap–Montague intensions mapping indices to extensions are reformulated as relations between strings that can serve as indices and extensions alike. Strings are related according to information content, temporal span and granularity, the bounds on which reflect the partiality of natural language statements. That partiality shapes not only strings-as-extensions (indicating what statements are about) but also strings-as-indices (underlying truth conditions).

Type
Papers
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Areces, C. and tenCate, B. Cate, B. 2007. Hybrid logics. In Blackburn, P., Wolter, F., and van Benthem, J. (eds.), Handbook of Modal Logic, pp. 821–68. Amsterdam, The Netherlands: Elsevier.CrossRefGoogle Scholar
Barwise, J. and Perry, J. 1983. Situations and Attitudes. Cambridge, MA, USA: The MIT Press.Google Scholar
Beesley, K. R. and Karttunen, L. 2003. Finite State Morphology. Stanford, CA, USA: CSLI Publications.Google Scholar
Bouajjani, A., Jonsson, B., Nilsson, M. and Touili, T. 2000. Regular model checking. In Computer Aided Verification, pp. 403–18. LNCS 1855. Berlin, Germany: Springer-Verlag.CrossRefGoogle Scholar
Brink, C., Britz, K. and Schmidt, R. 1994. Peirce algebras. Formal Aspects of Computing 6 (3):339–58.CrossRefGoogle Scholar
Condoravdi, C. 2009. Punctual until as a scalar NPI. In Hanson, K., and Inkelas, S. (eds.), The Nature of the Word: Studies in Honor of Paul Kiparsky, pp. 631–53. Cambridge, MA, USA: The MIT Press.Google Scholar
Davidson, D. 1967. The logical form of action sentences. In Rescher, N. (ed.), The Logic of Decision and Action, pp. 8195. Pittsburgh, PA, USA: University of Pittsburgh Press.Google Scholar
Emerson, E. A. 1992. Temporal and modal logic. In van Leeuwen, J. (ed.), Handbook of Theoretical Computer Science, volume B: Formal Methods and Semantics, pp. 9951072. Cambridge, MA, USA: The MIT Press.Google Scholar
Fernando, T. 2004. A finite-state approach to events in natural language semantics. Journal of Logic and Computation 14 (1): 7992.CrossRefGoogle Scholar
Fernando, T. 2007. Observing events and situations in time. Linguistics and Philosophy 30 (5): 527–50.CrossRefGoogle Scholar
Fernando, T. 2008a. Branching from inertia worlds. Journal of Semantics 25 (3): 321344.CrossRefGoogle Scholar
Fernando, T. 2008b. Temporal propositions as regular languages. In Hanneforth, T., and Würzner, K-M. (eds.), Finite-State Methods and Natural Language Processing, 6th International Workshop, pp. 132–48. Potsdam, Germany: Universitätsverlag Potsdam.Google Scholar
Fernando, T. 2009a. Situations in LTL as strings. Information and Computation 207 (10): 980–99.CrossRefGoogle Scholar
Fernando, T. 2009b. Situations as indices and as denotations. Linguistics and Philosophy 32 (2): 185206.CrossRefGoogle Scholar
Fernando, T. 2010. Constructing situations and time. Journal of Philosophical Logic, doi:10.1007/s10992-010-9155-1.Google Scholar
Harel, D., Kozen, D. and Tiuryn, J. 2000. Dynamic Logic. Cambridge, MA, USA: The MIT Press.CrossRefGoogle Scholar
Kamp, H. and Reyle, U. 1993. From Discourse to Logic. Dordrecht: Kluwer.Google Scholar
Karttunen, L. 1974 Until. In Papers from the Tenth Regional Meeting of the Chicago Linguistic Society, Chicago, pp. 284–97.Google Scholar
McCarthy, J. and Hayes, P. 1969. Some philosophical problems from the standpoint of artificial intelligence. In Meltzer, M., and Michie, D. (eds.), Machine Intelligence 4, pp. 463502. Edinburgh, UK: Edinburgh University Press.Google Scholar
Mulligan, K., Simons, P. and Smith, B. 1984. Truth-makers. Philosophy and Phenomenological Research 44: 287321.CrossRefGoogle Scholar
Niemi, J. and Koskenniemi, K. 2009. Representing and combining calendar information by using finite-state transducers. In Piskorski, J., Watson, B., and Yli-Jyrä, A. (eds.), Finite-State Methods and Natural Language Processing: Post-proceedings of the 7th International Workshop FSMNLP 2008, pp. 122–33. Amsterdam, The Netherlands: IOS Press.Google Scholar
Reichenbach, H. 1947. Elements of Symbolic Logic. London, UK: Macmillan.Google Scholar
Vardi, M. Y. 2007. Automata-theoretic techniques for temporal reasoning. In Blackburn, P., Wolter, F., and van Benthem, J. (eds.), Handbook of Modal Logic, pp. 971–89. Amsterdam, The Netherlands: Elsevier.CrossRefGoogle Scholar