On the Decomposition of Abstract Dialectical Frameworks and the Complexity of Naive-based Semantics

Abstract dialectical frameworks (ADFs) are a recently introduced powerful generalization of Dung’s popular abstract argumentation frameworks (AFs). Inspired by similar work for AFs, we introduce a decomposition scheme for ADFs, which proceeds along the ADF’s strongly connected components. We find th...

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Bibliographic Details
Published in:The Journal of artificial intelligence research Vol. 70; pp. 1 - 64
Main Authors: Gaggl, Sarah Alice, Rudolph, Sebastian, Straß, Hannes
Format: Journal Article
Language:English
Published: San Francisco AI Access Foundation 01.01.2021
Subjects:
Artificial intelligence
Boolean algebra
Complexity
Decomposition
Dialectics
Dung
Logic programs
Polynomials
Semantics
ISSN:1076-9757, 1076-9757, 1943-5037
Online Access:Get full text
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Summary:Abstract dialectical frameworks (ADFs) are a recently introduced powerful generalization of Dung’s popular abstract argumentation frameworks (AFs). Inspired by similar work for AFs, we introduce a decomposition scheme for ADFs, which proceeds along the ADF’s strongly connected components. We find that, for several semantics, the decompositionbased version coincides with the original semantics, whereas for others, it gives rise to a new semantics. These new semantics allow us to deal with pertinent problems such as odd-length negative cycles in a more general setting, that for instance also encompasses logic programs. We perform an exhaustive analysis of the computational complexity of these new, so-called naive-based semantics. The results are quite interesting, for some of them involve little-known classes of the so-called Boolean hierarchy (another hierarchy in between classes of the polynomial hierarchy). Furthermore, in credulous and sceptical entailment, the complexity can be different depending on whether we check for truth or falsity of a specific statement.
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ISSN:1076-9757
1076-9757
1943-5037
DOI:10.1613/jair.1.11348