Affiliation:
1. Aix-Marseille Université, CNRS, Marseille, France
2. Technische Universität Wien, Wien, Austria
3. Linköping University, Linköping, Sweden
Abstract
We consider logic-based argumentation in which an argument is a pair (Φ, α), where the support Φ is a minimal consistent set of formulae taken from a given knowledge base (usually denoted by Δ) that entails the claim α (a formula). We study the complexity of three central problems in argumentation: the existence of a support Φ⊆Δ, the verification of a support, and the relevance problem (given ψ, is there a support Φ such that ψ ∈ Φ?). When arguments are given in the full language of propositional logic, these problems are computationally costly tasks: the verification problem is DP-complete; the others are Σ
p
2
-complete. We study these problems in Schaefer's famous framework where the considered propositional formulae are in generalized conjunctive normal form. This means that formulae are conjunctions of constraints built upon a fixed finite set of Boolean relations Γ (the constraint language). We show that according to the properties of this language Γ, deciding whether there exists a support for a claim in a given knowledge base is either polynomial, NP-complete, coNP-complete, or Σ
p
2
-complete. We present a dichotomous classification, P or DP-complete, for the verification problem and a trichotomous classification for the relevance problem into either polynomial, NP-complete, or Σ
p
2
-complete. These last two classifications are obtained by means of algebraic tools.
Funder
Austrian Science Fund
National Graduate School in Computer Science
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Cited by
3 articles.
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