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.
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.
[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
[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
[5] Bochman, A., A Logical Theory of Nonmonotonic Inference and Belief Change, Springer-Verlag, Berlin, 2001.
[6] Brewka, G., Nonmonotonic Reasoning: Logical Foundations of Commonsense, vol. 12 of Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, Cambridge, 1991.
[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.
[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.
[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.
[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.
[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
[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
[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.
[18] Lifschitz, V., "On the logic of causal explanation", Artificial Intelligence, vol. 96 (1997), pp. 451--65.
[19] Makinson, D., ``Ways of doing logic: What was different about AGM 1985?'' Journal of Logic and Computation, vol. 13 (2003), pp. 3--13.
[20] Masini, A., "$2$"-sequent calculus: A proof theory of modalities", Annals of Pure and Applied Logic, vol. 58 (1992), pp. 229--46.
[21] Masini, A., "$2$"-sequent calculus: Intuitionism and natural deduction", Journal of Logic and Computation, vol. 3 (1993), pp. 533--62.
[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.
[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.
[26] Pohlers, W., Proof Theory: An Introduction, vol. 1407 of Lecture Notes in Mathematics, Springer, Berlin, 1989.
[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.
[28] Reiter, R., Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems, The MIT Press, Cambridge, 2001.
[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.
[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.
[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.
[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.
[36] Wittgenstein, L., Philosophical Investigations, 3d edition, edited by G. E. M. Anscombe and R. Rhees, Blackwell Publishers, Oxford, 2001.