A categorical unification algorithm
Proceedings of a tutorial and workshop on Category theory and computer programming
Two Complete Axiom Systems for the Algebra of Regular Events
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
On the structure of rough approximations
Fundamenta Informaticae
RSCTC'06 Proceedings of the 5th international conference on Rough Sets and Current Trends in Computing
Composing Partially Ordered Monads
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
Categories of direlations and rough set approximation operators
RSCTC'10 Proceedings of the 7th international conference on Rough sets and current trends in computing
Categorical foundations of variety-based topology and topological systems
Fuzzy Sets and Systems
Categorically algebraic topology versus universal topology
Fuzzy Sets and Systems
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In this paper we will show that partially ordered monads contain sufficient structure for modelling monadic topologies, rough sets and Kleene algebras. Convergence represented by extension structures over partially ordered monads includes notions of regularity and compactness. A compactification theory can be developed. Rough sets [Z. Pawlak, Rough sets, Int. J. Computer and Information Sciences 5 (1982) 341356] are modelled in a generalized setting with set functors. Further, we show how partially ordered monads can be used in order to obtain monad based examples of Kleene algebras building upon a wide range of set functors far beyond just strings [S. C. Kleene, Representation of events in nerve nets and finite automata, In: Automata Studies (Eds. C. E. Shannon, J. McCarthy), Princeton University Press, 1956, 3-41] and relations [A. Tarski, On the calculus of relations, J. Symbolic Logic 6 (1941), 65-106].