Causality, Modality, and Explanation



Notre Dame Journal of Formal Logic

Causality, Modality, and Explanation

Graham White

Source: Notre Dame J. Formal Logic Volume 49, Number 3 (2008), 313-343.

Abstract

We start with Fodor's critique of cognitive science in "The mind doesn't work that way: The scope and limits of computational psychology": he argues that much mental activity cannot be handled by the current methods of cognitive science because it is nonmonotonic and, therefore, is global in nature, is not context-free, and is thus not capable of being formalized by a Turing-like mental architecture. We look at the use of nonmonotonic logic in the artificial intelligence community, particularly with the discussion of the so-called frame problem. The mainstream approach to the frame problem is, we argue, probably susceptible to Fodor's critique; however, there is an alternative approach, due to McCain and Turner, which is, when suitably reformulated, not susceptible. In the course of our argument, we give a proof theory for the McCain-Turner system and show that it satisfies cut elimination. We have two substantive conclusions: first, that Fodor's argument depends on assumptions about logical form which not all nonmonotonic theories satisfy and, second, that metatheory plays an important role in the context of evolutionary accounts of rationality.

Primary Subjects: 03B45
Secondary Subjects: 03B45, 03F05
Keywords: explanation; causality; modal logic; cut elimination

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1216152554
Digital Object Identifier: doi:10.1215/00294527-2008-015
Mathematical Reviews number (MathSciNet): MR2428558

References

[1] Barnes, J., Aristotle, Oxford University Press, London, 1982.
[2] Belnap, N. D., Jr., and T. B. Steel, Jr., The Logic of Questions and Answers, Yale University Press, New Haven, 1976.
Mathematical Reviews (MathSciNet): MR0536640
Zentralblatt MATH: 0345.02015
[3] van Benthem, J., "Correspondence theory", pp. 167--247 in Handbook of Philosophical Logic, Vol. 2, edited by D. Gabbay and F. Guenther, vol. 165 of Synthese Library, Reidel, Dordrecht, 1984.
Mathematical Reviews (MathSciNet): MR844599
Zentralblatt MATH: 0875.03048
[4] van Benthem, J., A Manual of Intensional Logic, vol. 1 of CSLI Lecture Notes, Center for the Study of Language and Information, Stanford, 1985.
Mathematical Reviews (MathSciNet): MR867084
Zentralblatt MATH: 0678.03010
[5] Bochman, A., A Logical Theory of Nonmonotonic Inference and Belief Change, Springer-Verlag, Berlin, 2001.
Mathematical Reviews (MathSciNet): MR1880387
Zentralblatt MATH: 0977.03001
[6] Brewka, G., Nonmonotonic Reasoning: Logical Foundations of Commonsense, vol. 12 of Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, Cambridge, 1991.
Mathematical Reviews (MathSciNet): MR1115897
Zentralblatt MATH: 0723.68099
[7] Cadoli, M., F. M. Donini, and M. Schaerf, ``Is intractability of non-monotonic reasoning a real drawback?'' pp. 946--51 in Proceedings of the Twelfth National Conference on Artificial Intelligence, Vol. 1, 2 (Seattle, 1994), AAAI Press, Menlo Park, 1994. citeseer.ist.psu.edu/art% icle/cadoli96is.html.
Mathematical Reviews (MathSciNet): MR1301592
Zentralblatt MATH: 0907.68182
[8] Fairtlough, M., and S. S. Wainer, "Hierarchies of provably recursive functions", pp. 149--207 in Handbook of Proof Theory, vol. 137 of Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1998.
Mathematical Reviews (MathSciNet): MR1640327
Zentralblatt MATH: 0961.03053
Digital Object Identifier: doi:10.1016/S0049-237X(98)80018-9
[9] Falcon, A., ``Aristotle on causality,'' The Stanford Encyclopedia of Philosophy, % http://plato.stanford.edu/archives/spr2006/entries/aristotle-causality, 2006.
[10] Fodor, J. A., The Mind Doesn't Work That Way: The Scope and Limits of Computational Psychology, The MIT Press, Cambridge, 2000.
[11] Hallnäs, L., and P. Schroeder-Heister, "A proof-theoretic approach to logic programming. I. Clauses as rules", Journal of Logic and Computation, vol. 1 (1990), pp. 261--83.
Mathematical Reviews (MathSciNet): MR1152923
Zentralblatt MATH: 0723.68028
Digital Object Identifier: doi:10.1093/logcom/1.2.261
[12] Hallnäs, L., and P. Schroeder-Heister, "A proof-theoretic approach to logic programming. II". Programs as definitions, Journal of Logic and Computation, vol. 1 (1991), pp. 635--60.
Mathematical Reviews (MathSciNet): MR1152930
Zentralblatt MATH: 0769.68014
Digital Object Identifier: doi:10.1093/logcom/1.5.635
[13] Harrah, D., "Questions", pp. 1--3 in Routledge Encyclopedia of Philosophy, vol. 8, Routledge, London, 1998.
[14] Lewis, D., "Causation", pp. 159--213 in Philosophical Papers, vol. 2, Oxford University Press, London, 1986. Originally published in Journal of Philosophy, vol. 70 (1973), pp. 556--67.
Mathematical Reviews (MathSciNet): MR61194
Digital Object Identifier: doi:10.1007/BF02843760
[15] Lewis, D., "Counterfactual dependence and time's arrow", pp. 32--66 in Philosophical Papers, vol. 2, Oxford University Press, London, 1986. Originally published in Noûs, vol. 13 (1979), pp. 455--76.
[16] Lewis, D., "Counterfactuals and comparative possibility", pp. 3--31 in Philosophical Papers, vol. 2, Oxford University Press, London, 1986. Originally published in the Journal of Philosophical Logic, vol. 2 (1973), pp. 418--46.
Mathematical Reviews (MathSciNet): MR421987
Digital Object Identifier: doi:10.1007/BF00262950
[17] Lifschitz, V., "Circumscription", pp. 297--352 in Handbook of Logic in Artificial Intelligence and Logic Programming. Nonmonotonic Reasoning and Uncertain Reasoning, Vol. 3, Oxford Science Publications, Oxford University Press, New York, 1994.
Mathematical Reviews (MathSciNet): MR1281426
Zentralblatt MATH: 0804.03017
[18] Lifschitz, V., "On the logic of causal explanation", Artificial Intelligence, vol. 96 (1997), pp. 451--65.
Mathematical Reviews (MathSciNet): MR1605309
Zentralblatt MATH: 0901.03022
Digital Object Identifier: doi:10.1016/S0004-3702(97)00057-X
[19] Makinson, D., ``Ways of doing logic: What was different about AGM 1985?'' Journal of Logic and Computation, vol. 13 (2003), pp. 3--13.
Mathematical Reviews (MathSciNet): MR1973446
Zentralblatt MATH: 1043.03008
Digital Object Identifier: doi:10.1093/logcom/13.1.3
[20] Masini, A., "$2$"-sequent calculus: A proof theory of modalities", Annals of Pure and Applied Logic, vol. 58 (1992), pp. 229--46.
Mathematical Reviews (MathSciNet): MR1191942
Zentralblatt MATH: 0819.03045
Digital Object Identifier: doi:10.1016/0168-0072(92)90029-Y
[21] Masini, A., "$2$"-sequent calculus: Intuitionism and natural deduction", Journal of Logic and Computation, vol. 3 (1993), pp. 533--62.
Mathematical Reviews (MathSciNet): MR1253870
Zentralblatt MATH: 0793.03013
Digital Object Identifier: doi:10.1093/logcom/3.5.533
[22] McCain, N., and H. Turner, "Causal theories of action and change", pp. 460--65 in Proceedings of the Fourteenth National Conference on Artificial Intelligence and Ninth Innovative Applications of Artificial Intelligence Conference (Providence, 1997), AAAI Press, Menlo Park, 1997.
Mathematical Reviews (MathSciNet): MR1484760
[23] McCarthy, J., "Towards an abstract science of computation", http://www-formal.stanford.edu/jmc/towards.html, 1962.
[24] Parsons, S., and N. R. Jennings, "Negotiation through argumentation: A preliminary report", pp. ???--??? in Proceedings of the International Conference on Multi Agent Systems (ICMAS'96), ???, Kyoto, 1996.
[25] Parsons, S., C. Sierra, and N. Jennings, "Agents that reason and negotiate by arguing", Journal of Logic and Computation, vol. 8 (1998), pp. 261--92. citeseer.nj.nec.com/parsons9% 8agents.html.
Mathematical Reviews (MathSciNet): MR1642062
Zentralblatt MATH: 0904.68061
Digital Object Identifier: doi:10.1093/logcom/8.3.261
[26] Pohlers, W., Proof Theory: An Introduction, vol. 1407 of Lecture Notes in Mathematics, Springer, Berlin, 1989.
Mathematical Reviews (MathSciNet): MR1026933
Zentralblatt MATH: 0695.03024
[27] Pratt, V., "A roadmap of some two-dimensional logics", pp. 149--62 in Logic and Information Flow, edited by J. van Eijck and A. Visser, Foundations of Computing Series, The MIT Press, Cambridge, 1994.
Mathematical Reviews (MathSciNet): MR1295065
Zentralblatt MATH: 0876.03014
[28] Reiter, R., Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems, The MIT Press, Cambridge, 2001.
Zentralblatt MATH: 1018.03022
[29] Scriven, M., "Explanations, predictions, and laws", pp. 51--74 in Theories of Explanation, Oxford University Press, London, 1988.
[30] Shanahan, M., Solving the Frame Problem. A Mathematical Investigation of the Common Sense Law of Inertia, The MIT Press, Cambridge, 1997.
Mathematical Reviews (MathSciNet): MR1445066
[31] Strachey, C., "Fundamental concepts of programming languages", Lecture notes at the International Summer School in Programming Languages (Copenhagen, August 1967), 1967.
[32] Turner, H., "A logic of universal causation", Artificial Intelligence, vol. 113 (1999), pp. 87--123.
Mathematical Reviews (MathSciNet): MR1724108
Zentralblatt MATH: 0940.03031
Digital Object Identifier: doi:10.1016/S0004-3702(99)00058-2
[33] White, G. G., "Intensionality and circumscription", pp. 372--79 in Proceedings of the 9th International Conference on Non-Monotonic Reasoning (NMR2002), edited by S. Benferhat and E. Giunchiglia, ???, Toulouse, 2002.
[34] White, G., "Lewis, causality, and possible worlds", Dialectica, vol. 54 (2000), pp. 133--37.
Mathematical Reviews (MathSciNet): MR1770070
[35] White, G., "A modal formulation of McCain and Turner's theory of causal reasoning", pp. 211--22 in Logics in Artificial Intelligence (8th European Conference, JELIA 2002), edited by S. Flesca, S. Greco, N. Leone, and G. Ianni, vol. 2424 of Lecture Notes in Computer Science, Springer, Berlin, 2002.
Mathematical Reviews (MathSciNet): MR2052799
Zentralblatt MATH: 1013.03026
Digital Object Identifier: doi:10.1007/3-540-45757-7_18
[36] Wittgenstein, L., Philosophical Investigations, 3d edition, edited by G. E. M. Anscombe and R. Rhees, Blackwell Publishers, Oxford, 2001.
Mathematical Reviews (MathSciNet): MR1971335
Zentralblatt MATH: 1028.03003

2008 © Duke University Press