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Causality, Modality, and Explanation
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"... Abstract We start with Fodor’s critique of cognitive science in [8]: 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 contextfree, and is thus not capable of being formalised by a ..."
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Abstract We start with Fodor’s critique of cognitive science in [8]: 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 contextfree, and is thus not capable of being formalised by a Turinglike mental architecture. We look at the use of nonmonotonic logic in the Artificial Intelligence community, particularly with the discussion of the socalled “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 McCainTurner system, and show that it satisfies cut elimination. We have two substantive conclusions: firstly, that Fodor’s argument depends on assumptions about logical form which not all nonmonotonic theories satisfy; and, secondly, that metatheory plays an important role
The Frame Problem and the Semantics of Classical Proofs
"... We outline the logic of current approaches to the socalled “frame problem ” (that is, the problem of predicting change in the physical world by using logical inference), and we show that these approaches are not completely extensional since none of them is closed under uniform substitution. The und ..."
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We outline the logic of current approaches to the socalled “frame problem ” (that is, the problem of predicting change in the physical world by using logical inference), and we show that these approaches are not completely extensional since none of them is closed under uniform substitution. The underlying difficulty is something known, in the philosophical community, as Goodman’s “new riddle of induction ” or the “Grue paradox”. Although it seems, from the philosophical discussion, that this paradox cannot be solved in purely a priori terms and that a solution will require some form of realworld data, it nevertheless remains obscure both what the logical form of this realworld data might be, and also how such data actually interacts with logical deduction. We show, using work of McCain and Turner, that this data can be captured using the semantics of classical proofs developed by Bellin, Hyland and Robinson, and, consequently, that the appropriate arena for solutions of the frame problem lies in proof theory. We also give a very explicit model for the categorical semantics of classical proof theory using techniques derived from work on the frame problem.