Advances in Artificial Intelligence: 24th Canadian by Eric Aaron, Juan Pablo Mendoza (auth.), Cory Butz, Pawan

By Eric Aaron, Juan Pablo Mendoza (auth.), Cory Butz, Pawan Lingras (eds.)

This e-book constitutes the refereed court cases of the twenty fourth convention on man made Intelligence, Canadian AI 2011, held in St. John’s, Canada, in may well 2011. The 23 revised complete papers offered including 22 revised brief papers and five papers from the graduate pupil symposium have been conscientiously reviewed and chosen from eighty one submissions. The papers conceal a huge diversity of issues featuring unique paintings in all parts of synthetic intelligence, both theoretical or applied.

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Extra resources for Advances in Artificial Intelligence: 24th Canadian Conference on Artificial Intelligence, Canadian AI 2011, St. John’s, Canada, May 25-27, 2011. Proceedings

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If P is an expansion predicate, the answer is the set of all pairs (¯ a, P (¯ a)), where a ¯ is a tuple of elements from the domain A. Correctness of the method then follows, by induction on the structure of the formula, from the following proposition. Proposition 2. Suppose that R is an answer to φ1 and S is an answer to φ2 , both with respect to (wrt) structure A. Then 1. ¬R is an answer to ¬φ1 wrt A; 2. R S is an answer to φ1 ∧ φ2 wrt A; 3. R ∪ S is an answer to φ1 ∨ φ2 wrt A; 4. If Y is the set of free variables of ∃¯ z φ1 , then πY (R) is an answer to ∃¯ z φ1 wrt A.

E(1, 2) ∧ E(2, 3) is a reduced grounding of φ2 [(1, 2)]. Notice that, as φ3 does not have any free variables, its corresponding answer has just a single row. Table 1. Answers to φ1 , φ2 and φ3 xyz ψ xy ψ ψ 1 2 3 E(1, 2) ∧ E(2, 3) 1 2 E(1, 2) ∧ E(2, 3) [E(1, 2) ∧ E(2, 3)] ∨ [E(3, 4) ∧ E(4, 5)] 3 4 5 E(3, 4) ∧ E(4, 5) 3 4 E(3, 4) ∧ E(4, 5) Grounding Formulas with Complex Terms 17 The relational algebra has operations corresponding to each connective and quantifier in FO, as follows: complement (negation); join (conjunction); union (disjunction), projection (existential quantification); division or quotient (universal quantification).

Choice of these gadgets is important for some constraints. , see [12]). Our method allows these choices to be made at run time, either by the user or automatically. As it described in previous sections, to compute an answer to an aggregate one needs to find a set αR ⊂ N and a function βR which maps every integer to a ground formula. Grounding Formulas with Complex Terms 25 In section 4, we have showed what the set αR is for each term and also described the properties of the output of βR function.

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