Rule Calculus: Semantics, Axioms and Applications

Authors:
Yi Zhou;Yan Zhang
Affiliations:
Intelligent Systems Lab School of Computing and Mathematics, University of Western Sydney, Australia Locked Bag 1797;Intelligent Systems Lab School of Computing and Mathematics, University of Western Sydney, Australia Locked Bag 1797
Venue:
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
Year:
2008

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Abstract

We consider the problem of how a default rule can be deduced from a default theory. For this purpose, we propose an axiom system which precisely captures the deductive reasoning about default rules. We show that our axiomatic system is sound and complete under the semantics of the logic of here-and-there. We also study other important properties such as substitution and monotonicity of our system and prove the essential decision problem complexity. Finally, we discuss applications of our default rule calculus to various problems.