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Graph-Based Representation and Reasoning: 21st International by Nathalie Hernandez, Robert Jäschke, Madalina Croitoru

By Nathalie Hernandez, Robert Jäschke, Madalina Croitoru

This booklet constitutes the complaints of the twenty first foreign convention on Conceptual constructions, ICCS 2014, held in Iaşi, Romania, in July 2014. The 17 ordinary papers and six brief papers offered during this quantity have been rigorously reviewed and chosen from forty and 10 submissions, respectively. the themes coated are: conceptual constructions, wisdom illustration, reasoning, conceptual graphs, formal inspiration research, semantic net, details integration, laptop studying, facts mining and data retrieval.

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Extra info for Graph-Based Representation and Reasoning: 21st International Conference on Conceptual Structures, ICCS 2014, Iaşi, Romania, July 27-30, 2014, Proceedings

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Example 1. The argumentation system depicted below d a f g c e b has five naive extensions: E1 = {a, c, g}, E2 = {d, e, f }, E3 = {b, d, f }, E4 = {a, e, g}, E5 = {a, b, g}; one stable E3 and two preferred extensions E3 and E6 = {a, g}. It is worth recalling that stable extensions are naive (respectively preferred) extensions but the converses are not always true. Moreover, an argumentation framework may have no stable extensions. Let us now define the plausible conclusions that may be drawn from a knowledge base Σ by an argumentation system.

36 M. Stojakovi´c 2 In the k-clique game, for k ≥ 4, the threshold bias is Θ(n k+1 ) and the thresh2 old probability for Maker’s win is the inverse (up to the leading constant), n− k+1 , supporting the random graph intuition. But, the threshold probability for the 2 appearance of a k-clique in G(n, p) is not at the same place, it is n− k−1 . And in the triangle game there is even more disagreement, as all three parameters are 1 5 different – they are, respectively, n 2 , n− 9 and n−1 . References 1.

These properties already distinguish this area of research from its popular relative, Game Theory, which has its roots in Economics. Some of the more prominent positional games include Tic-Tac-Toe, Hex, Bridg-It and the Shannon’s switching game. The basic structure of a positional game is fairly simple. Let X be a finite set and let F ⊆ 2X be a family of subsets of X. The set X is called the “board”, and the members of F are referred to as the “winning sets”. In the positional game (X, F ), two players take turns in claiming previously unclaimed elements of X, until all the elements are claimed.

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