A general extended disjunctive logic program (GEDP) with negation as failure in the head may have non-minimal answer sets, while answer sets of an extended disjunctive logic program (EDLP) are minimal. So far, no work has been done to relate general extended disjunctive logic programming and assumption-based argumentation (ABA). In this paper, first, we propose a novel polynomial-time translation from a GEDP to an EDLP, with which there is a one-to-one correspondence between the consistent answer sets of the original GEDP and those of the translated EDLP. Second, based on the proposed translation as well as the work to relate EDLPs and ABA frameworks (ABFs), we show a one-to-one correspondence between the consistent answer sets of a consistent propositional GEDP and the consistent stable extensions of its associated ABF.

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Assumption-Based Argumentation for General Extended Disjunctive Logic Programming with Negation as Failure in the Head

  • Toshiko Wakaki

摘要

A general extended disjunctive logic program (GEDP) with negation as failure in the head may have non-minimal answer sets, while answer sets of an extended disjunctive logic program (EDLP) are minimal. So far, no work has been done to relate general extended disjunctive logic programming and assumption-based argumentation (ABA). In this paper, first, we propose a novel polynomial-time translation from a GEDP to an EDLP, with which there is a one-to-one correspondence between the consistent answer sets of the original GEDP and those of the translated EDLP. Second, based on the proposed translation as well as the work to relate EDLPs and ABA frameworks (ABFs), we show a one-to-one correspondence between the consistent answer sets of a consistent propositional GEDP and the consistent stable extensions of its associated ABF.