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New PDF release: Logic for Programming, Artificial Intelligence, and

By Martin Davis, Ansgar Fehnker, Annabelle McIver, Andrei Voronkov

ISBN-10: 3662488981

ISBN-13: 9783662488980

ISBN-10: 366248899X

ISBN-13: 9783662488997

This booklet constitutes the complaints of the 20 th overseas convention on common sense for Programming, synthetic Intelligence, and Reasoning, LPAR-20, held in November 2015, in Suva, Fiji.

The forty three average papers offered including 1 invited speak integrated during this quantity have been rigorously reviewed and chosen from ninety two submissions. The sequence of foreign meetings on good judgment for Programming, synthetic Intelligence and Reasoning, LPAR, is a discussion board the place, 12 months after 12 months, the most popular researchers within the parts of common sense, automatic reasoning, computational common sense, programming languages and their functions come to offer state-of-the-art effects, to debate advances in those fields, and to interchange rules in a scientifically rising a part of the world.

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Additional info for Logic for Programming, Artificial Intelligence, and Reasoning: 20th International Conference, LPAR-20 2015, Suva, Fiji, November 24-28, 2015, Proceedings

Example text

Ym } \ {x1 , . . , xn } and – φ is a (possibly empty) conjunction of relational atoms using all of the variables x1 , . . , xn ; – ψ is a conjunction of relational and equality atoms using all of the variables z1 , . . , zk ; – there are no equality atoms in ψ involving existentially quantified variables. If at most one relation symbol occurs in an ed, then we say that the ed is unirelational, and otherwise it is multirelational. An ed is called typed if there is an assignment of variables to column positions such that variables in relation atoms occur only in their assigned position, and each equality atom involves a pair of variables assigned to the same position.

It is well-known that the chase algorithm captures unrestricted implication of dependencies. For the proof of the following proposition, see Appendix of the arXiv version of the paper [17]. Proposition 1. Let Σ ∪ {σ} be a set of egd’s and tgd’s over R. Then the following are equivalent: (i) Σ |= σ, (ii) there is a chasing sequence (Σ, σ) = σ0 , σ1 , . . of σ over Σ such that chase(Σ, σ) is trivial, (iii) there is a chasing sequence (Σ, σ) = σ0 , σ1 , . . of σ over Σ such that σn is trivial, for some n.

Now we can define the worst/average case complexity of σ, denoted by Cworst (σ) and Cavg (σ), in the following way: Cworst (σ) = max{#λσv | v ∈ Val (ϕ0 )} Cavg (σ) = v∈Val(ϕ0 ) #λσv |Val (ϕ0 )| Note that the worst/average case complexity of σ is finite iff every v ∈ Val (ϕ0 ) is discovered by σ after a finite number of experiments. We say that G is solvable iff there exists a strategy σ with a finite worst/average case complexity. Further, we say that a strategy σ is worst case optimal iff for every strategy σ we have that Cworst (σ) ≤ Cworst (σ ).

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Logic for Programming, Artificial Intelligence, and Reasoning: 20th International Conference, LPAR-20 2015, Suva, Fiji, November 24-28, 2015, Proceedings by Martin Davis, Ansgar Fehnker, Annabelle McIver, Andrei Voronkov


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