The system obtained by adding full propositional quantification to S5 is known to be decidable, while that obtained by doing so for T is known to be recursively intertranslatable with full second-order logic. Recently it was shown that the system with two S5 operators and full propositional quantification is also recursively intertranslatable with second-order logic. This note establishes that the map assigning p to \squarep provides a validity and satisfaction preserving translation between the T system and the double S5 system, (...) thus providing an easier proof of the recent result. (shrink)
Applications of game theory to moral philosophy are impededby foundational issues and troublesome examples. In the first part of this paper,questions are raised about the appropriate game-theoretical frameworks for applications to moralphilosophy and about the proper interpretations of the theoretical devices employed inthese frameworks. In the second part, five examples that should be of particular interest to thoseinterested in the connections between ethics and game theory are delineated and discussed. Thefirst example comprises games in which there is an outcome unanimously (...) preferred to the``solution'' of the game, appropriately defined. The second comprises games whose solution callsfor different players to employ different strategies. The third comprises games whosesolution calls for players to adopt mixed strategies. The fourth comprises games whose solutionrequires players to cycle among a variety of strategies. The fifth comprises games whose solutionrequires players to discriminate in morally inappropriate ways. (shrink)
Montague, Prior, von Wright and others drew attention to resemblances between modal operators and quantifiers. In this paper we show that classical quantifiers can, in fact, be regarded as S5-like operators in a purely propositional modal logic. This logic is axiomatized and some interesting fragments of it are investigated.