A short introduction to intuitionistic logic
A short introduction to intuitionistic logic
Belief Revision in a Nonclassical Logic
KI '96 Proceedings of the 20th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Multiple contraction. A further case against Gärdenfors' principle of recovery
Proceedings of the Workshop on The Logic of Theory Change
Classical Mathematical Logic: The Semantic Foundations of Logic
Classical Mathematical Logic: The Semantic Foundations of Logic
The Description Logic Handbook
The Description Logic Handbook
On Generalizing the AGM Postulates
Proceedings of the 2006 conference on STAIRS 2006: Proceedings of the Third Starting AI Researchers' Symposium
Horn complements: towards horn-to-horn belief revision
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Next steps in propositional horn contraction
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Model-based revision operators for terminologies in description logics
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Base Revision for Ontology Debugging
Journal of Logic and Computation
Horn contraction via epistemic entrenchment
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
On applying the AGM theory to DLs and OWL
ISWC'05 Proceedings of the 4th international conference on The Semantic Web
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
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The operation of contraction (referring to the removal of knowledge from a knowledge base) has been extensively studied in the research field of belief change, and different postulates (e.g., the AGM postulates with recovery, or relevance) have been proposed, as well as several constructions (e.g., partial meet) that allow the definition of contraction operators satisfying said postulates. Most of the related work has focused on classical logics, i.e., logics that satisfy certain intuitive assumptions; in such logics, several nice properties and equivalences related to the above postulates and constructions have been shown to hold. Unfortunately, previous work has shown that the postulates@? applicability and the related results generally fail for non-classical logics. Motivated by the fact that non-classical logics (like Description Logics or Horn logic) are increasingly being used in various applications, we study contraction for all monotonic logics, classical or not. In particular, we identify several sufficient conditions for the various postulates to be applicable, and show that, in practice, relevance is a more suitable (i.e., applicable) minimality criterion than recovery for non-classical logics. In addition, we revisit some important related results from the classical belief change literature and study conditions sufficient for them to hold for non-classical logics; the corresponding results for classical logics emerge as corollaries of our more general results. Our work is another step towards the aim of exploiting the rich belief change literature for addressing the evolution problem in a larger class of logics.