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Dynamic Topological Logic provides a context for studying the confluence of the topological semantics for S4, based on topological spaces rather than Kripke frames; topological dynamics; and temporal logic. In the topolog-ical semantics for S4, 2 is interpreted as topological interior: thus S4 can be understood as the logic of topological spaces.… (More)

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In this paper, we define some consequence relations based on supervaluation semantics for partial models, and we investigate their properties. For our main consequence relation, we show that natural versions of the following fail: upwards and downwards Lowenheim–Skolem, axiomatizability, and compactness. We also consider an alternate version for… (More)

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)

Let L be a propositional language with standard Boolean connec-tives 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 and f… (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)