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Journal of Logic and Computation, Volume 9, Issue 5, pp. 701-735: Abstract.

Formalizing action and change in modal logic I: the frame problem

MA Castilho1, O Gasquet2 and A Herzig3

1Université Paul Sabatier, IRIT, 118 route de Narbonne, F-31062 Toulouse Cedex, France, 1E-mail: castilho@irit.fr, 2E-mail: gasquet@irit.fr, 3E-mail: herzig@irit.fr

We present the basic framework of a logic of actions and plans defined in terms of modal logic combined with a notion of dependence. The latter is used as a weak causal connection between actions and literals. In this paper we focus on the frame problem and demonstrate how it can be solved in our framework in a simple and monotonic way. We give the semantics, and associate an axiomatics and a decision procedure to it. The decision procedure is based on a sound and complete tableau method with single step rules to treat dependence. We show how it can be used to generate plans. Our solution is formally assessed by a translation of Gelfond and Lifschitz' logic A. We briefly sketch the second part of the paper, showing how we can go beyond A by some examples involving nondeterminism and ramifications.

Keywords: Reasoning about actions, modal logic, frame problem, dependence, semantic tableaux

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