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Anil Gupta and Nuel Belnap's The Revision Theory of Truth presents revision theoretic systems of circular definitions. Part I of the present paper shows that the revision theories S # and S* are not axiomatis-able. Part II refines this result. Among other things, Part II shows that there is a strong relationship between revision theories and the theory of(More)
'Entailment' can be said in many ways. In the present paper, we sketch a linguistic theory which motivates taking 'A entails B' to mean 'commitment to A is, in part, commitment to B', and we present four formal systems designed to capture this concept. These four systems turn out (somewhat surprisingly) to be the strict implicational fragments of the modal(More)
Let L • be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality and a temporal modality • , understood as 'next'. We extend the topological semantic for S4 to a semantics for the language L • by interpreting L • in dynamic topological systems, i.e., ordered pairs X, f , where X is a topological space(More)
Fine and Kripke extended S5, S4, S4.2 and such to produce propo-sitionally quantified systems S5π+, S4π+, S4.2π+: given a Kripke frame, the quantifiers range over all the sets of possible worlds. S5π+ is decidable and, as Fine and Kripke showed, many of the other systems are recursively isomorphic to second-order logic. In the present paper I consider the(More)