Download Advances in Artificial Intelligence: 21st Conference of the by Rocío Alaiz-Rodríguez (auth.), Sabine Bergler (eds.) PDF

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

ISBN-10: 3540688218

ISBN-13: 9783540688211

This booklet constitutes the refereed complaints of the twenty first convention of the Canadian Society for Computational stories of Intelligence, Canadian AI 2008, held in Windsor, Canada, in may well 2008.

The 30 revised complete papers offered including five revised brief papers have been rigorously reviewed and chosen from seventy five submissions. The papers current unique high quality study in all parts of synthetic Intelligence and observe old AI options to fashionable challenge domain names in addition to contemporary recommendations to old challenge settings.

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Additional info for 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

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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. Every clause is 1-validated. Proposition 8. If Γ consists of 1-validated formulas, then for every aggregation function f and every formula ψ, Γ |=dH,f ψ iff Γ |=dU,f ψ. Proof (outline).

For any ψ, the sequence Rd (ψ, i) is non-decreasing in i (with respect to set inclusion). Also, for every satisfiable ψ and i ∈ N, ν ∈ Rid (ψ) iff d(ν, ψ) = i. Thus, for a satisfiable ψ, R0d (ψ) = mod(ψ) = Δd,f (ψ), and Rd (ψ, k) = Λ for k = maxd Λ. If ψ is not satisfiable, then Rd (ψ, i) = Rid (ψ) = ∅ for every i. Lemma 1. If all the formulas in a theory Γ = {ψ1 , . . , ψn } are satisfiable, then there is some 0 ≤ k ≤ maxd Λ, such that 1≤i≤n Rd (ψi , k) = ∅. Proof. By Note 2, for every 1 ≤ i ≤ n there is a ki ≤ maxd Λ such that for every j ≥ ki , Rd (ψi , j) = Λ.

N } we define mod(Γ ) = mod(ψ1 ) ∩ . . ∩ mod(ψn ). For defining distance-based entailments we recall the definitions in [1,2]. Definition 1. A pseudo-distance on U is a total function d : U× U → N so that for all ν, μ ∈ U d(ν, μ) = d(μ, ν) (symmetry), and d(ν, μ) = 0 iff ν = μ (identity preservation). A distance (metric) d on U is a pseudo-distance that satisfies the triangular inequality: for all ν, μ, σ ∈ U , d(ν, σ) ≤ d(ν, μ) + d(μ, σ). 38 O. Arieli and A. Zamansky Example 1. It is easy to verify that the following functions are distances on the space Λ of two-valued valuations on Atoms: – The drastic distance: dU (ν, μ) = 0 if ν = μ and dU (ν, μ) = 1 otherwise.

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