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

Castilho, Marcos A. and Gasquet, Olivier and Herzig, Andreas


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.




        author  = "Castilho, Marcos A. 
                   and Gasquet, Olivier and Herzig, Andreas",
        title   = "Formalizing action and change in modal logic {I}: 
		   the frame problem",
	journal = "Journal of Logic and Computation",
	year =    "1999",
	volume =  "9",
	number =  "5",