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ECAI 2008: Proceedings, 18th European Conference on by Malik Ghallab, Constantine D. Spyropoulos, Nikos Fakotakis,

By Malik Ghallab, Constantine D. Spyropoulos, Nikos Fakotakis, Nikos Avouris

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Extra info for ECAI 2008: Proceedings, 18th European Conference on Artificial Intelligence, July 21-25, 2008, Patras, Greece : Including Prestigious Applications of Intelligent ... in Artifical Intelligence and Applications)

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Most of the set-based similarities can be grouped into two parametrized families. The first one σα has been proposed by Caillez and Kuntz [6]. It is defined by a ratio between the cardinality of the intersection |A ∩ B| 21 E. Blanchard et al. / A Generic Framework for Comparing Semantic Similarities on a Subsumption Hierarchy and the Cauchy’s mean [5] of the cardinalities of the respective sets |A| and |B|: σα (A, B) = fα (|A| , |B| , |A ∩ B|) = |A∩B| μα (|A|,|B|) (1) ”1 “ α α α where μα (|A| , |B|) = |A| +|B| for α ∈ IR.

9] V-T. Vu, F. Br´emond, and M. Thonnat, ‘Automatic video interpretation: A novel algorithm for temporal scenario recognition’, in The Eighteenth International Joint Conference on Artificial Intelligence (IJCAI’03), Acapulco, Mexico, (2003). [10] V-T. Vu, F. Br´emond, and M. Thonnat, ‘Automatic video interpretation: A recognition algorithm for temporal scenarios based on pre-compiled scenario models’, in The 3rd International Conference on Vision System (ICVS’03), Graz, Austria, (2003). [11] N.

Note that applying σν leaves the introduction of body propositions (cf. (1)) implicit. In our example, we get VFν1 (Π1 , A2 , E ) = CF (Π1 , {b, c, d, g, h})σν1 = {v ↔ v; v ↔ v; d ↔ ⊥; g ↔ ⊥; h ↔ ⊥} . Note that LF (Π1 ) is empty (since Π1 is tight), and so is BF (A2 \A). Clearly, CF (Π1 , {b, c, d, g, h})σν1 possesses the models ∅ and {v}. , EFν1 (E ) = {b ↔ v; e ↔ v; f ↔ v; c ↔ v}. Formally, we have the following result. ∗ Theorem 8 Let Π → (Π , A, E), for logic program Π over A, and let ν be a variable mapping induced by (Π , A, E).

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