Belief revision in Horn theories

Delgrande, JP; Peppas, P

Belief revision in Horn theories

Delgrande, JP Peppas, P

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Publication Type:: Journal Article
Citation:: Artificial Intelligence, 2015, 218 pp. 1 - 22
Issue Date:: 2015-01-01

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Field	Value	Language
dc.contributor.author	Delgrande, JP	en_US
dc.contributor.author	Peppas, P https://orcid.org/0000-0002-0008-5505	en_US
dc.date.issued	2015-01-01	en_US
dc.identifier.citation	Artificial Intelligence, 2015, 218 pp. 1 - 22	en_US
dc.identifier.issn	0004-3702	en_US
dc.identifier.uri	http://hdl.handle.net/10453/121580
dc.description.abstract	© 2014 Elsevier B.V. This paper investigates belief revision where the underlying logic is that governing Horn clauses. We show that classical (AGM) belief revision doesn't immediately generalise to the Horn case. In particular, a standard construction based on a total preorder over possible worlds may violate the accepted (AGM) postulates. Conversely, in the obvious extension to the AGM approach, Horn revision functions are not captured by total preorders over possible worlds. We address these difficulties by introducing two modifications to the AGM approach. First, the semantic construction is restricted to "well behaved" orderings, what we call Horn compliant orderings. Second, the revision postulates are augmented by an additional postulate. Both restrictions are redundant in the AGM approach, but not in the Horn case. In a representation result we show that the class of revision functions captured by Horn compliant total preorders over possible worlds is precisely that given by the (extended) set of Horn revision postulates. Further, we show that Horn revision is compatible with work in iterated revision and work concerning relevance in revision. We also consider specific revision operators. Arguably this work is interesting for several reasons. It extends AGM revision to inferentially-weaker Horn theories; hence it sheds light on the theoretical underpinnings of belief change, as well as generalising the AGM paradigm. Thus, this work is relevant to revision in areas that employ Horn clauses, such as deductive databases and logic programming, as well as areas in which inference is weaker than classical logic, such as in description logic.	en_US
dc.relation.ispartof	Artificial Intelligence	en_US
dc.relation.isbasedon	10.1016/j.artint.2014.08.006	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	Belief revision in Horn theories	en_US
dc.type	Journal Article
utslib.citation.volume	218	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
utslib.for	1702 Cognitive Sciences	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Computer Science
pubs.organisational-group	/University of Technology Sydney/Strength - CAI - Centre for Artificial Intelligence
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US
pubs.volume	218	en_US

Abstract:

© 2014 Elsevier B.V. This paper investigates belief revision where the underlying logic is that governing Horn clauses. We show that classical (AGM) belief revision doesn't immediately generalise to the Horn case. In particular, a standard construction based on a total preorder over possible worlds may violate the accepted (AGM) postulates. Conversely, in the obvious extension to the AGM approach, Horn revision functions are not captured by total preorders over possible worlds. We address these difficulties by introducing two modifications to the AGM approach. First, the semantic construction is restricted to "well behaved" orderings, what we call Horn compliant orderings. Second, the revision postulates are augmented by an additional postulate. Both restrictions are redundant in the AGM approach, but not in the Horn case. In a representation result we show that the class of revision functions captured by Horn compliant total preorders over possible worlds is precisely that given by the (extended) set of Horn revision postulates. Further, we show that Horn revision is compatible with work in iterated revision and work concerning relevance in revision. We also consider specific revision operators. Arguably this work is interesting for several reasons. It extends AGM revision to inferentially-weaker Horn theories; hence it sheds light on the theoretical underpinnings of belief change, as well as generalising the AGM paradigm. Thus, this work is relevant to revision in areas that employ Horn clauses, such as deductive databases and logic programming, as well as areas in which inference is weaker than classical logic, such as in description logic.

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http://hdl.handle.net/10453/121580