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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)

- Wesley H. Holliday, Johan van Benthem, Prof. Krista Lawlor, Helen Longino, Prof. Eric Pacuit, Krista Lawlor +12 others
- 2013

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)