Abstract
This paper motivates and presents a nonmonotonic version of Contextual Intensional Logic, a type-theoretic logic intended as a general formalism for reasoning about context. In developing this logic, it is necessary to think through interactions between nonmonotonic and intensional logic that are interesting in their own right. The paper concludes with an extended example how nonmonotonic lifting rules can be deployed in inter-contextual reasoning.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Church, A.: A formulation of the simple theory of types. Journal of Symbolic Logic 5(1), 56–68 (1940)
Cresswell, M.J., Hughes, G.E.: A New Introduction to Modal Logic. Routledge, London (1996)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. The MIT Press, Cambridge (1995)
Gallin, D.: Intensional and Higher-Order Logic. North-Holland Publishing Company, Amsterdam (1975)
Guha, R.V.: Contexts: a formalization and some applications. Technical Report STAN-CS-91-1399, Stanford Computer Science Department, Stanford, California (1991)
Lewis, D.K.: Counterfactuals. Harvard University Press, Cambridge (1973)
Lifschitz, V.: Circumscription. In: Gabbay, D., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming. Nonmonotonic Reasoning and Uncertain Reasoning, vol. 3, pp. 298–352. Oxford University Press, Oxford (1994)
Lin, F.: Circumscription in a modal logic. In: Vardi, M.Y. (ed.) Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, pp. 113–127. Morgan Kaufmann, San Francisco (1988)
McCarthy, J.: Notes on formalizing contexts. In: Bajcsy, R. (ed.) Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, San Mateo, California, pp. 555–560. Morgan Kaufmann, San Francisco (1993)
Montague, R.: Pragmatics and intensional logic. Synth̀ese 22, 68–94 (1970); Reprinted in Montague, R.: Formal Philosophy, pp. 119–147. Yale University Press, New Haven (1974)
Shoham, Y.: Reasoning about Change: Time and Causation From the Standpoint of Artificial Intelligence. The MIT Press, Cambridge (1988)
Stalnaker, R.C.: A theory of conditionals. In: Rescher, N. (ed.) Studies in Logical Theory, pp. 98–112. Basil Blackwell Publishers, Oxford (1968)
Thomason, R.H.: Type theoretic foundations for context, part 1: Contexts as complex type-theoretic objects. In: Bouquet, P., Serafini, L., Brézillon, P., Benercetti, M., Castellani, F. (eds.) CONTEXT 1999. LNCS (LNAI), vol. 1688, pp. 351–374. Springer, Heidelberg (1999)
Thomason, R.H.: Modeling the beliefs of other agents. In: Minker, J. (ed.) Logic-Based Artificial Intelligence, pp. 375–473. Kluwer Academic Publishers, Dordrecht (2000)
Thomason, R.H.: Dynamic contextual intensional logic: Logical foundations and an application. In: Blackburn, P., Ghidini, C., Turner, R.M., Giunchiglia, F. (eds.) CONTEXT 2003. LNCS, vol. 2680, pp. 328–341. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Thomason, R.H. (2005). Making Contextual Intensional Logic Nonmonotonic. In: Dey, A., Kokinov, B., Leake, D., Turner, R. (eds) Modeling and Using Context. CONTEXT 2005. Lecture Notes in Computer Science(), vol 3554. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11508373_38
Download citation
DOI: https://doi.org/10.1007/11508373_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26924-3
Online ISBN: 978-3-540-31890-3
eBook Packages: Computer ScienceComputer Science (R0)