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The foundations of DeLP: defeating relations, games and truth values

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Abstract

In this paper we examine the mechanism of DeLP (Defeasible Logic Programming). We first study the definition of the defeating relation in a formal setting that allows us to uncover some hidden assumptions, and suggest an alternative definition. Then we introduce a game-theoretic characterization of the system. We obtain a new set of truth values arising from games in which arguments for and against a given literal are played out. We study how additional constraints define protocols of admissible attacks. The DeLP protocol ensures the finiteness of the games, and therefore the existence of winning strategies for the corresponding games. The defeating relation among arguments determines the strategies that will win and consequently the truth values of queries. We find that the DeLP protocol also excludes the warranting of a literal and its negation.

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Authors and Affiliations

  1. CONICET, Avda. Rivadavia 1917, CP C1033AAJ, Cdad. de Buenos Aires, Argentina

    Ignacio Darío Viglizzo & Fernando A. Tohmé

  2. Universidad Nacional del Sur, Av. Alem 1253, B8000CPB, Bahía Blanca, Argentina

    Ignacio Darío Viglizzo, Fernando A. Tohmé & Guillermo R. Simari

Authors
  1. Ignacio Darío Viglizzo
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  2. Fernando A. Tohmé
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  3. Guillermo R. Simari
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Correspondence to Ignacio Darío Viglizzo.

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Viglizzo, I.D., Tohmé, F.A. & Simari, G.R. The foundations of DeLP: defeating relations, games and truth values. Ann Math Artif Intell 57, 181–204 (2009). https://doi.org/10.1007/s10472-010-9184-z

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