Abstract and concrete categories
Abstract and concrete categories
Boolean connection algebras: a new approach to the Region-Connection Calculus
Artificial Intelligence
A note on proximity spaces and connection based mereology
Proceedings of the international conference on Formal Ontology in Information Systems - Volume 2001
A representation theorem for Boolean contact algebras
Theoretical Computer Science
Qualitative Spatial Representation and Reasoning: An Overview
Fundamenta Informaticae - Qualitative Spatial Reasoning
Contact Algebras and Region-based Theory of Space: Proximity Approach - II
Fundamenta Informaticae
On the Computational Complexity of Spatial Logics with Connectedness Constraints
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Stonian p-ortholattices: A new approach to the mereotopology RT0
Artificial Intelligence
On the Skeleton of Stonian p-Ortholattices
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
The lattice of contact relations on a Boolean algebra
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
On the computability of region-based euclidean logics
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Splitting atoms in relational algebras
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Tools and techniques in qualitative reasoning about space
FoIKS'10 Proceedings of the 6th international conference on Foundations of Information and Knowledge Systems
Hi-index | 0.00 |
This work is 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. Different axiomatizations for region-based (or Whiteheadian) theory of space are given. The most general one is introduced under the name "Contact Algebra" Adding some extra first- or secondorder axioms to those of contact algebras, some new or already known algebraic notions are obtained. Representation theorems and completion theorems for all such algebras are proved. Extension theories of the classes of all semiregular T$_0$-spaces and all N-regular (a notion introduced here) T$_1$-spaces are developed.