M. Gerson, "An extension of S4 complete for the neighbourhood semantics but incomplete for the relational semantics", Studia Logica, 34(1975), pp. 333-342.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....question concerning the topological semantics. Namely, is there a Kripke incomplete extension of S4, which is topologically complete In other words, is the topological semantics really more general than the frame semantics, from the completeness point of view The answer is a#rmative. In [Gerson 1975] the extension of S4 is presented which is complete with respect to the neighbourhood semantics, but incomplete with respect to the Kripke semantics. We can prove that for S4 and its extensions, the neighbourhood semantics is equivalent to the topological semantics (cf. Shehtman 1998] It ....

M. Gerson, "An extension of S4 complete for the neighbourhood semantics but incomplete for the relational semantics", Studia Logica, 34(1975), pp. 333-342.

....quickly ends in despair when there is no apparent or natural way to determine the action of I on a boolean combination of sets which were forced into our subalgebra. 16 A similar result was independently found by DOV M. GABBAY [7] and GERSON himself extended the result to a logic above S4 [10]. 9 Acknowledgements The author is grateful to BRIAN CHELLAS and KRISTER SEGERBERG for bringing this question to his attention and for all their helpful assistance and suggestions. Also, the author would like to thank GREG RESTALL, RAJEEV GOR E, FRANK WOLTER, and MARCUS KRACHT for their helpful ....

GERSON, MARTIN. "An extension of S4 complete for the neighbourhood semantics but incomplete for the relational semantics." Studia Logica, vol. 36 (1975), no. 4, pp. 333--342.

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