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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)

The completeness of the modal logic S4 for all topological spaces as well as for the real line R, the n-dimensional Euclidean space R n and the segment (0, 1) etc. (with 2 interpreted as interior) was proved by McKinsey and Tarski in 1944. Several simplified proofs contain gaps. A new proof presented here combines the ideas published later by G. Mints and… (More)