A Concise Introduction to Propositional Dynamic Logic by Krister Segerberg

By Krister Segerberg

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In particular, for the delta operator it is not enough to consider just runs that terminate: if we do not wish to adopt path semantics in all its rich complexity, at least we must find some other way to register the possibility that paths may fail or be infinite. [Readers interested in a further discussion of these matters are referred to the author's article "Action incompletencss" in Studia logic:a, vol. ] 4. 1. Historical remarks 1. Modal logic. Philosophers have been interested in modal notions-necessity, possibility, contingency-since Aristotle, and some, for example Aristotle himself, have tried to study their logic.

II? AIL Our formal result is of course informally absurd: no-one would wish to claim that, in general, a;? A is a reliable way of seeing to it that A. The mistake in the formal analysis sketched above was to try to carry out within the relational semantics of PDL a project that evidently requires greater resources. In particular, for the delta operator it is not enough to consider just runs that terminate: if we do not wish to adopt path semantics in all its rich complexity, at least we must find some other way to register the possibility that paths may fail or be infinite.

Fhe "Lemmon Notes") American Philosophical Quarterly, monograph series, vol. 11. Oxford: Basil Blackwell, 1977. ) 2. Survey articles BULL, ROBERT and SEGERBERG, KRISTER. " In Dov Gabbay and Franz Guenthner (eds), Handbook of philosophical logic, vol 2, pp. 1-88. Dordrecht, Holland: Reidel, 1984. JrrA>;:). JOHN. , pp. 89-133. HAREL, DAVID. 497-604. 3. Original articles FISCHER, MICHAEL J. and LADNER, RICHARD E. " Journal of computer and system sciences, vol. 18 (1979), pp. 194-21 L KaZEN, DEXTER and PARIKH.

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