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Abstract: This thesis is mainly concerned with the definability issue when modal logic is interpreted on topological spaces. A topological analogon of Goldblatt-Thomason theorem is proved. Some new topological constructions are introduced. One of them, namely the notion of compact extension, is a generalization of the concept of Stone- known in topology. The preservation of modal validity with respect to suitable topological operations is presented. (Update)
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.... and many known results on bisimulations can be obtained as particular cases of more general results on topo bisimulations (see, e.g. [2, 3, 4, 6]) 3 Logic of serial subsets of Definition 3.1. Call C a convex subset of R if x, y C and x y imply [x, y] C. Call S a...
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BibTeX entry: (Update)
D. Gabelaia. Modal definability in topology. Master's thesis, ILLC, University of Amsterdam, 2001. http://citeseer.ist.psu.edu/gabelaia01modal.html More
@misc{ gabelaia01modal,
author = "D. Gabelaia",
title = "Modal definability in topology",
text = "D. Gabelaia. Modal definability in topology. Master's thesis, ILLC, University
of Amsterdam, 2001.",
year = "2001",
url = "citeseer.ist.psu.edu/gabelaia01modal.html" }
Citations (may not include all citations):63 Cambridge University Press (context) - Blackburn, de Rijke et al. - 2001
42 A completeness theorem in modal logic (context) - Kripke - 1959
24 The algebra of topology (context) - McKinsey, Tarski - 1944
23 The Modal Logic of Inequality (context) - de Rijke - 1992
19 Derivation rules as anti-axioms in modal logic (context) - Venema - 1993
17 Polish Scientific Publishers (context) - Engelking, Topology - 1977
14 Polish Scientific Publishers (context) - Rasiowa, Sikorski et al. - 1963
11 Modal Logics of Domains on the real plane (context) - Shehtman - 1983
11 Reasoning about Space: the Modal Way (context) - Aiello, van Benthem et al. - 2001
10 Logical patterns in space - Aiello, van Benthem - 2001
4 Diodorean Modality in Minkowski Spacetime (context) - Goldblatt - 1980
3 A completeness Proof for Propositional S4 in Cantor Space (context) - Mints - 1998
3 Intentional Logics (context) - Lemmon, Scott - 1966
2 An extension of S4 complete for the neighbourhood semantics .. (context) - Gerson - 1975
2 On Strong Neighbourhood Completeness of Modal and Intermedia.. - Shehtman - 1998
2 A New Proof of Completeness of S4 with respect to the Real L.. - Bezhanishvili, Gehrke - 2001
2 Algebraic characterizations of special Boolean rings (context) - Stone - 1937
1 the theory of modal and superintuitionistic systems (context) - Esakia - 1979
1 the syntactic construction of systems of modal logic (context) - McKinsey - 1945
1 Everywhere' and 'Here (context) - Shehtman - 1999
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