Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T19:44:43.386Z Has data issue: false hasContentIssue false
  • English
  • Français

CONTEXTUAL LOGIC WITH MODALITIES FOR TIME AND SPACE

Published online by Cambridge University Press:  01 December 2008

HAIM GAIFMAN
HAIM GAIFMAN*
Affiliation:
Philosophy Department, Columbia University
*
*PHILOSOPHY DEPARTMENT COLUMBIA UNIVERSITY 715 PHILOSOPHY HALL NEW YORK, NY 10027 E-mail:[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We develop a formal apparatus to be used as a tool in analyzing common kinds of context dependence in natural language, and their interaction with temporal and spatial modalities. It is based on context-operators, which act on wffs. The interplay between the various modalities and the context-operators is one of the main targets of the analysis. Statements made by different people at different times in different places, using the same personal temporal and spatial indexicals, can be represented in the system, and can be combined by sentential connectives and be subject to quantification. The use of spatial modality and the suggested treatment of adverbial phrases are new as far as we know. So is a certain variant of temporal modality. In the nontechnical part, consisting of Sections 1 and 2, we discuss the role that formalisms can, in principle, play in the analysis of linguistic usage; this is followed by a philosophical discussion of various kinds of context dependence. The semitechnical part, Section 3, introduces the system's components, the context, and the modal operators, and explains their use via natural language examples. In Section 4 the formal language and its semantics are defined, in full detail. The temporal and spatial sublanguages constitute separate sorts, which interact through the modal operators and the context-operators. A sound deductive system is given and a completeness result is stated, without proof.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 1 , Issue 4 , December 2008 , pp. 433 - 458
Copyright
Copyright © Association for Symbolic Logic 2008

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

BIBLIOGRAPHY

Bach, K. (1999). The semantics-pragmatics distinction: what it is and why it matters. In Turner, K., editor. The Semantic-Pragmatic Interface From Different Points of View. Oxford: Elsevier, pp. 65–84.Google Scholar
Burgess, J. (1984). Basic tense logic. In Gabbay, D., and Guenthner, F., editors. Handbook of Philosophical Logic. Dordrecht, The Netherlands: Kluwer Academic Publications, pp. 89–133.CrossRefGoogle Scholar
Donnellan, K. (1966). Reference and definite descriptions. Philosophical Review, 75, 281–304.CrossRefGoogle Scholar
Emerson, E. (1990). Temporal and modal logic. In van Leeuwen, J., editor. Handbook of Theoretical Computer Science, Vol. B. Cambridge, MA: MIT Press, pp. 995–1067.Google Scholar
Gaifman, H. (2001, September). Contextual logic and its applications to vagueness. The Bulletin of Symbolic Logic, 7(3), 241(Abstracts of Invited Talks of the Annual 2001 Meeting of the ASL).Google Scholar
Gaifman, H. (2002). Vagueness, Tolerance and Contextual Logic. Available from: http://www.columbia.edu/~hg17/. pp. 41. Accessed January 5, 2002.Google Scholar
Kamp, H., & Reyle, W. (1993). From Discourse to Logic. Dordrecht, The Netherlands: Kluwer Academic.Google Scholar
Kaplan, D. (1989). Demonstratives. In Almog, J., Wettstein, H., and Perry, J. editors. Themes From Kaplan. New York: Oxford University Press, pp. 481–563.Google Scholar
Kripke, S. (1977). Speaker's reference and semantic reference. Midwest Studies in Philosophy, 2, 255–276.CrossRefGoogle Scholar
Pnueli, A. (1977). The temporal logic of programs. Proceedings of the 18th Annual IEEE on Foundations of Computer Science, 46–57.Google Scholar
Quine, W. (1951). Mathematical Logic. Cambridge, MA: Harvard University Press.CrossRefGoogle Scholar
Quine, W. (1960). Word and Object. Cambridge, MA: MIT Press.Google Scholar
Recanati, F. (2004). Literal Meaning. Cambridge, UK: Cambridge University Press.Google Scholar
Searle, J. (1992). The Rediscovery of the Mind. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Soames, S. (2002). Beyond Rigidity. New York: Oxford University Press.CrossRefGoogle Scholar
Tennant, N. (1981). Formal games and forms for games. Linguistics and Philosophy, 4, 311–320.CrossRefGoogle Scholar
Vendler, Z. (1962). Each and every and any and all. Mind, 71. A shorter version appears as the entry Any and all. In Edwards P., editor. The Encyclopedia of Philosophy. New York: Macmillan and Free Press, pp. 145–160.Google Scholar