Peritopological spaces and bisimulations

• Autorzy: Hamal A. , Terziler M.

Identyfikatory

DOI

10.4467/20842589RM.15.005.3914

• Języki publikacji: EN

Abstrakty

EN

Generalizing ordinary topological and pretopological spaces, we introduce the notion of peritopology where neigh-borhoods of a point need not contain that point, and some points might even have an empty neighborhood. We briefly describe various intrinsic aspects of this notion. Applied to modal logic, it gives rise to peritopological models, a generalization of topo- logical models, a spacial case of neighborhood semantics. A new cladding for bisimulation is presented. The concept of Alexandroff peritopology is used in order to determine the logic of all peritopo- logical spaces, and we prove that the minimal logic K is strongly complete with respect to the class of all peritopological spaces. We also show that the classes of T0, T1 and T2-peritopological spaces are not modal definable, and that D is the logic of all proper peritopological spaces. Finally, among our conclusions, we show that the question whether T0, T1 peritopological spaces are modal definable in H(@) remains open.

Słowa kluczowe

EN

peritopological spaces; bisimulations; modal definability

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2015
• Tom: Vol. 50
• Strony: 67--81
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Hamal A.

• Ege University Department of Mathematics, 35040 Bornova-Izmir, Turkey

autor

Terziler M.

• Yasar University, Department of Mathematics, 35040 Bornova-Izmir, Turkey

Bibliografia

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• [3] J. van Benthem, G. Bezhanishvili, B. ten Cate and D. Sarenac, Modal logics for products of topologies, Studia Logica 84:3 (2006), 369- 392.
• [4] P. Blackburn, M. de Rijke and Y. Venema, Modal Logic, Cambridge tracts in theoretical computer science, Vol. 53. CUP, Cambridge, 2001.
• [5] G. Choquet, Convergences, Ann. Univ. Grenoble, Sect. Sci. Math. Phys., 23 (1947-1948), 57-112.
• [6] D. Gabelaia, Modal Definability in Topology, Master Thesis, ILLC, University of Amsterdam 2001.
• [7] A. Hamal, Spacial Modal Logics, Ph.D Thesis, Ege University, 2007.
• [8] B. ten Cate, Model theory for extended modal languages Ph.D. Thesis, University of Amsterdam, iLLC Dissertation Series, DS - 2005 - 01.
• [9] B. ten Cate, D. Gabelaia and D. Sustretov, Modal languages for topology: expressivity and definability, Ann. Pure Appl. Logic 159:1-2 (2009), 146 - 170.