论文信息 - Discrete dualities for some algebras with relations

Discrete dualities for some algebras with relations

Abstract In this paper we present a unifying discrete framework for various representation theorems in the field of spatial reasoning. We also show that the universal and existential quantifiers of restricted scope used in first order languages and represented as binary relations in the syllogistic algebras considered by Shepherdson (1956) [1] may be studied in this framework.

Ivo Düntsch | Ewa Orlowska

[1] Ivo Düntsch,et al. Region–based theory of discrete spaces: A proximity approach , 2007, Annals of Mathematics and Artificial Intelligence.

[2] H. Priestley,et al. Distributive Lattices , 2004 .

[3] Dimiter Vakarelov,et al. Region-Based Theory of Space: Algebras of Regions, Representation Theory, and Logics , 2007 .

[4] Dimiter Vakarelov,et al. Contact Algebras and Region-based Theory of Space: A Proximity Approach - I , 2006, Fundam. Informaticae.

[5] Stephan Winter,et al. Spatial Information Theory, 8th International Conference, COSIT 2007, Melbourne, Australia, September 19-23, 2007, Proceedings , 2007, COSIT.

[6] Antony Galton,et al. The Mereotopology of Discrete Space , 1999, COSIT.

[7] John C. Shepherdson. On the Interpretation of Aristotelian Syllogistic , 1956, J. Symb. Log..

[8] Michael Winter,et al. A representation theorem for Boolean contact algebras , 2005, Theor. Comput. Sci..

[9] Michael Winter,et al. The Lattice of Contact Relations on a Boolean Algebra , 2008, RelMiCS.

[10] Johan van Benthem,et al. Handbook of Spatial Logics , 2007 .

[11] Osama A. El-Tantawy,et al. On I−Proximity Spaces , 2016 .

[12] Ewa Orlowska,et al. Discrete Duality and Its Applications to Reasoning with Incomplete Information , 2007, RSEISP.

[13] J.F.A.K. van Benthem,et al. Modal Correspondence Theory , 1977 .

[14] D. Gabbay,et al. Handbook of Philosophical Logic, Volume II. Extensions of Classical Logic , 1986 .