Belief change under the horn fragment of propositional logic

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Copyright: Zhuang, Zhiqiang
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Abstract
The theory of belief revision studies the way in which an agent changes its beliefs as it acquires new information. The changes often involve removal of existing beliefs--the contraction operation--and incorporation of newly acquired belief--the revision operation. The dominant theory of belief revision is the so called AGM framework. This account of belief revision assumes an underlying logic that contains classical propositional logic. Due to this assumption, the framework can not be applied to systems with underlying logic less expressive than propositional logic. This assumption prohibits the usage of the AGM framework to many useful artificial intelligence systems. This thesis aims to remedy this situation by studying belief revision under the Horn fragment of propositional logic which we term as Horn logic. The study extends the applicability of the AGM framework to systems based on Horn logic and it provides theoretical underpinnings for extending the framework's applicability to other non-classical logics. When attacking the problem of belief revision there are two general strategies to follow, that is, to formulate postulates that capture the intuitions of rational belief change and to present explicit constructions of change operations that accord with the postulates. It is widely accepted that the AGM postulates best capture the intuitions behind rational belief change. The AGM constructions of the contraction and the revision operations are shown to be sound and complete with respect to their corresponding postulates. In this thesis, three constructions of the contraction operation is defined for Horn logic. These constructions are studied extensively under propositional logic, the main contribution here is their adaptations to Horn logic. Since Horn logic is a subset of propositional logic, it lacks some logical notions of propositional logic. The main challenge in the adaptation is to compromise the loss of expressivity by using alternative notions and approximation techniques and in doing so preserves the properties of AGM contraction. When we only consider the change mechanisms applied to the beliefs representable by Horn logic, our investigation shows that the adapted contraction operations perform as rationally as AGM contraction in the case of transitively relational partial meet Horn contraction and model based Horn contraction and as a restricted form of AGM contraction in the case of epistemic entrenchment Horn contraction.
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Author(s)
Zhuang, Zhiqiang
Supervisor(s)
Pagnucco, Maurice
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Publication Year
2013
Resource Type
Thesis
Degree Type
PhD Doctorate
UNSW Faculty
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