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By Rocío Alaiz-Rodríguez (auth.), Sabine Bergler (eds.)

ISBN-10: 3540688218

ISBN-13: 9783540688211

ISBN-10: 3540688250

ISBN-13: 9783540688259

This publication constitutes the refereed lawsuits of the twenty first convention of the Canadian Society for Computational experiences of Intelligence, Canadian AI 2008, held in Windsor, Canada, in could 2008.

The 30 revised complete papers awarded including five revised brief papers have been rigorously reviewed and chosen from seventy five submissions. The papers current unique top of the range learn in all parts of synthetic Intelligence and practice old AI concepts to fashionable challenge domain names in addition to contemporary concepts to old challenge settings.

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One is based on the procedure MPV defined in the previous section, and the other is based on deduction systems. Proposition 5. If ψ is satisfiable, then RdU (ψ, 0) = mod(ψ) and RdU (ψ, i) = Λ for every i > 0. 42 O. Arieli and A. Zamansky Proposition 6. The function GU : 2Λ → 2Λ defined by GU (V ) = Λ for all V ⊆ Λ, is an inductive representation of dU . Proof. Immediate from Proposition 5. Corollary 4. For every theory Γ , the procedure MPV(GU , Γ ) terminates after at most maxdU Λ iterations and computes ΔdU,max (Γ ).

Definition 10. Denote: Kni = i j=1 j . n Definition 11. A formula ψ is i-validated for i ∈ N+ , if among the 2|Atoms(ψ)| |Atoms(ψ)| valuations on Atoms(ψ), at most Ki valuations do not satisfy ψ. Note 4. An i-validated formula ψ is also j-validated, for 1 ≤ i ≤ j ≤ |Atoms(ψ)|. Example 5. Any tautology is 1-validated (thus it is i-validated for any i). , an atomic formula or its negation) is 1-validated. Moreover, as a disjunction of literals is either a tautology or is falsified by only one valuation, Lemma 2.

42 O. Arieli and A. Zamansky Proposition 6. The function GU : 2Λ → 2Λ defined by GU (V ) = Λ for all V ⊆ Λ, is an inductive representation of dU . Proof. Immediate from Proposition 5. Corollary 4. For every theory Γ , the procedure MPV(GU , Γ ) terminates after at most maxdU Λ iterations and computes ΔdU,max (Γ ). Proof. By Propositions 3 and 6. Another way of computing consequences of the entailment relation |=dU ,max is by the deduction system Su max , defined in Figure 2. This system manipulates expressions of the form Γ : V , where Γ is a theory and V ⊆ Λ.

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Advances in Artificial Intelligence: 21st Conference of the Canadian Society for Computational Studies of Intelligence, Canadian AI 2008 Windsor, Canada, May 28-30, 2008 Proceedings by Rocío Alaiz-Rodríguez (auth.), Sabine Bergler (eds.)


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