93 citations · 113 across the 6 of their papers we have counts for
7 papers
Point-free theories of space and time
Dimiter Vakarelov
The paper is in the field of Region Based Theory of Space (RBTS), sometimes called mereotopology. RBTS is a kind of point-free theory of space based on the notion of region. Its or…
Distributive Mereotopology: Extended distributive contact lattices
Tatyana Ivanova, Dimiter Vakarelov
Contact algebra is one of the main tools in the region-based theory of space. It is an extension of Boolean algebra with a relation called contact. The elements of the Boolean alge…
A Generalization of the Stone Duality Theorem
G. Dimov, E. Ivanova-Dimova, D. Vakarelov
We prove a new duality theorem for the category of precontact algebras which implies the Stone Duality Theorem, its connected version obtained in arXiv:1508.02220v3, 1-44 (to appea…
Topological Representation of Precontact Algebras and a Connected Version of the Stone Duality Theorem -- I
Georgi Dimov, Dimiter Vakarelov
The notions of a {\em 2-precontact space}\/ and a {\em 2-contact space}\/ are introduced. Using them, new representation theorems for precontact and contact algebras are proved. It…
On the investigations of Ivan Prodanov in the theory of abstract spectra
Georgi Dimov, Dimiter Vakarelov
The results of Iv. Prodanov on abstract spectra and separative algebras were announced in the journal "Trudy Mat. Inst. Steklova", 154, 1983, 200--208, but their proofs were never…
A system of relational syllogistic incorporating full Boolean reasoning
Nikolay Ivanov, Dimiter Vakarelov
We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: Some A are R-related to some B; Some A are R-related…
Algorithmic correspondence and completeness in modal logic. I. The core algorithm SQEMA
Willem Conradie, Valentin Goranko, Dimiter Vakarelov
Modal formulae express monadic second-order properties on Kripke frames, but in many important cases these have first-order equivalents. Computing such equivalents is important for…