Complexity of logic-based argumentation in Schaefer's framework

• We consider logic-based argumentation in which an argument is a pair (Φ, α), where the support Φ is a minimal consistent set of formulæof a given knowledge base that entails the formula α. We study the complexity of two different problems: the existence of a support and the verification of the validity of an argument. When arguments are given in the full language of propositional logic these problems are computationally costly tasks, they are respectively ΣP 2- and DP-complete. We study these problems in Schaefer's famous framework. We consider the case where formulæare taken from a class of formulæin generalized conjunctive normal form. This means that the propositional formulæ considered are conjunctions of constraints taken from a fixed finite language Γ. 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 ΣP 2-complete. We also obtain a dichotomous classification, P or DP-complete, for the verification problem.

Ämnesord

NATURVETENSKAP  -- Data- och informationsvetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences (hsv//eng)

Nyckelord

Complexity of argumentation

Generalized satisfiability

Logic-based argumentation

Schaefer

Formal logic

Knowledge based systems

Conjunctive normal forms

Finite languages

Logic-based argumentations

Propositional logic

Satisfiability

Verification problems

Computational linguistics

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