Journal of Automated Reasoning
Constraint logic programming languages
Communications of the ACM
Handbook of logic in artificial intelligence and logic programming (vol. 1)
Cardinality restrictions on concepts
Artificial Intelligence
Modal logics, description logics and arithmetic reasoning
Artificial Intelligence
A machine program for theorem-proving
Communications of the ACM
An Overview of Backtrack Search Satisfiability Algorithms
Annals of Mathematics and Artificial Intelligence
Contraint Logic Programming - An Informal Introduction
LPSS '92 Proceedings of the Second International Logic Programming Summer School on Logic Programming in Action
The Inverse Method Implements the Automata Approach for Modal Satisfiability
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
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Description logics are modal-like logics used to express knowledge about structured domains, and reason about them. One of the major reasoning problems in description logics is that of determining whether a given terminological knowledge base is consistent. One approach to this problem is to translate a modal satisfiability problem into stratified layers of constraint problems that can be solved by a constraint solver. We show how this approach, which was originally developed for the modal logic K, can be extended to deal effectively with cardinality restrictions on roles in the description logic ALCN. We also propose a further extension to this approach in order to deal with qualified number restrictions and arithmetic on role cardinalities.