New PDF release: Belief Revision in Non-Classical Logics

By Márcio Moretto Ribeiro

ISBN-10: 1447141857

ISBN-13: 9781447141853

ISBN-10: 1447141865

ISBN-13: 9781447141860

Since the appearance of the Semantic net, curiosity within the dynamics of ontologies (ontology evolution) has grown considerably. trust revision provides an exceptional theoretical framework for facing this challenge; even if, classical trust revision isn't like minded for logics equivalent to Description Logics.

Belief Revision in Non-Classical Logics offers a framework that are utilized to a large classification of logics that come with – along with so much Description Logics comparable to those at the back of OWL – Horn common sense and Intuitionistic common sense, among others. the writer additionally offers algorithms for crucial buildings in trust bases. Researchers and practitioners in theoretical computing will locate this a useful resource.

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Contraction consists of the removal of a sentence α from the belief set K . Besides guarantying that the input is indeterminate in the new belief set (α ∈ / K − α) contraction should guaranty that K − α is a belief set and that the change is somehow minimal. Contraction also depends on “extra-logical” factors. Its postulates are presented in the following subsection. 1 AGM Contraction In this section contraction will be defined through rationality postulates called AGM postulates for contraction.

1,2 α hyp. p. 3,4 Hence, for any β ∈ LCPL were have that A β. There is a close relation between the semantic consequence presented in the beginning of the section and the syntactic consequence presented above. , A α implies A α. t. 9 (Soundness) If A α then A α. Proof First we need to check that for each rule αA in it holds that if σ(A) then σ(α). Since this is very simple and tedious, we will show only two examples: the first axiom and modus ponens: Let σ(ξ1 → (ξ2 → ξ1 )) = α → (β → α) for α, β ∈ LCPL .

Suppose that K ⊆ Cn(Z), then Cn(A) ⊆ Cn(Z). Since Cn(∅) ⊂ Cn(A) there is an interpretation I such that B I = I . B)I = ∅. It follows that I Z and I A. Hence Cn(Z) = K. 39 [Flo06] If a DL admits role hierarchy and at least one of the constructors: • value restriction (∀), • existential restriction (∃) or • number restriction (≤n ). and does not admit role constructors then it is not decomposable. Proof Let K = Cn({R S}) and A = {x ∈ K : Cn(x) K }. 9 we only need to prove that (1) Cn(A) = Cn(∅) and (2) Cn(A) ⊂ K .

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Belief Revision in Non-Classical Logics by Márcio Moretto Ribeiro

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