What is modal logic

http://bcpw.bg.pw.edu.pl/Content/1968/Rudiments.pdf

Rudiments of rough sets

General Topology-I

We introduce two notions related to any information system, namely the discernibility matrix and discernibility function. We present some properties of these notions and as corollaries we obtain several algorithms for solving problems related among other things to the rough definability, reducts, core and dependencies generation.

The Discernibility Matrices and Functions in Information Systems

A comparative study of fuzzy rough sets

Notes on N-lattices and constructive logic with strong negation

This paper is the second part of the paper [2]. Both of themare in the field of region-based (or Whitehedian) theory of space, which is an important subfield of Qualitative Spatial Reasoning (QSR). The paper can be considered also as an application of abstract algebra and topology to some problems arising and motivated in Theoretical Computer Science and QSR. In [2], different axiomatizations for region-based theory of space were given. The most general one was introduced under the name "Contact Algebra". In this paper some categories defined in the language of contact algebras are introduced. It is shown that they are equivalent to the category of all semiregular T$_0$-spaces and their continuous maps and to its full subcategories having as objects all regular (respectively, completely regular; compact; locally compact) Hausdorff spaces. An algorithm for a direct construction of all, up to homeomorphism, finite semiregular T$_0$-spaces of rank n is found. An example of an RCC model which has no regular Hausdorff representation space is presented. The main method of investigation in both parts is a lattice-theoretic generalization of methods and constructions from the theory of proximity spaces. Proximity models for various kinds of contact algebras are given here. In this way, the paper can be regarded as a full realization of the proximity approach to the region-based theory of space.

Contact Algebras and Region-based Theory of Space: Proximity Approach - II

A Modal Logic for Similarity Relations in Pawlak Knowledge Representation Systems

Elementary canonical formulae: extending Sahlqvist’s theorem

We introduce Boolean proximity algebras as a generalization of Efremovi? proximities which are suitable in reasoning about discrete regions Following Stone's representation theorem for Boolean algebras, it is shown that each such algebra is isomorphic to a substructure of a complete and atomic Boolean proximity algebra

/pdf/region-based-theory-of-discrete-spaces-a-proximity-approach-2b5xnewiyi.pdf

Dimiter Vakarelov

Papers

Notes on N-lattices and constructive logic with strong negation

Contact Algebras and Region-based Theory of Space: Proximity Approach - II

A Modal Logic for Similarity Relations in Pawlak Knowledge Representation Systems

Elementary canonical formulae: extending Sahlqvist’s theorem

Region---based theory of discrete spaces: A proximity approach