A theory of diagnosis from first principles
Artificial Intelligence
On the complexity of propositional knowledge base revision, updates, and counterfactuals
Artificial Intelligence
Knowledge compilation and theory approximation
Journal of the ACM (JACM)
Compilability and compact representations of revision of Horn knowledge bases
ACM Transactions on Computational Logic (TOCL)
The logic of knowledge bases
A Textbook of Belief Dynamics: Solutions to Exercises
A Textbook of Belief Dynamics: Solutions to Exercises
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Revisions of knowledge systems using epistemic entrenchment
TARK '88 Proceedings of the 2nd conference on Theoretical aspects of reasoning about knowledge
The Description Logic Handbook
The Description Logic Handbook
Horn complements: towards horn-to-horn belief revision
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Translating between Horn representations and their characteristic models
Journal of Artificial Intelligence Research
Next steps in propositional horn contraction
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Horn contraction via epistemic entrenchment
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
On the link between partial meet, kernel, and infra contraction and its application to Horn logic
Journal of Artificial Intelligence Research
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Transitively relational partial meet horn contraction
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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In classical, AGM-style belief change, it is assumed that the underlying logic contains classical propositional logic. This is clearly a limiting assumption, particularly in Artificial Intelligence. Consequently there has been recent interest in studying belief change in approaches where the full expressivity of classical propositional logic is not obtained. In this paper we investigate belief contraction in Horn knowledge bases. We point out that the obvious extension to the Horn case, involving Horn remainder sets as a starting point, is problematic. Not only do Horn remainder sets have undesirable properties, but also some desirable Horn contraction functions are not captured by this approach. For Horn belief set contraction, we develop an account in terms of a model-theoretic characterisation involving weak remainder sets. Maxichoice and partial meet Horn contraction is specified, and we show that the problems arising with earlier work are resolved by these approaches. As well, constructions of the specific operators and sets of postulates are provided, and representation results are obtained. We also examine Horn package contraction, or contraction by a set of formulas. Again, we give a construction and postulate set, linking them via a representation result. Last, we investigate the closely-related notion of forgetting in Horn clauses. This work is arguably interesting since Horn clauses have found widespread use in AI; as well, the results given here may potentially be extended to other areas which make use of Horn-like reasoning, such as logic programming, rule-based systems, and description logics. Finally, since Horn reasoning is weaker than classical reasoning, this work sheds light on the foundations of belief change.