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On the Equivalence Between Abstract Dialectical Frameworks and Logic Programs

Published online by Cambridge University Press:  20 September 2019

JOÃO ALCÂNTARA Open the ORCID record for JOÃO ALCÂNTARA [Opens in a new window] ,
SAMY SÁ  and
JUAN ACOSTA-GUADARRAMA
JOÃO ALCÂNTARA
Affiliation:
Federal University of Ceará, Brazil (e-mail: jnando@lia.ufc.br, samy@ufc.br)
SAMY SÁ
Affiliation:
Federal University of Ceará, Brazil (e-mail: jnando@lia.ufc.br, samy@ufc.br)
JUAN ACOSTA-GUADARRAMA
Affiliation:
Autonomous University of Juarez, Mexico (e-mail: juan.acosta@uacj.mx)
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Abstract

Abstract Dialectical Frameworks (ADFs) are argumentation frameworks where each node is associated with an acceptance condition. This allows us to model different types of dependencies as supports and attacks. Previous studies provided a translation from Normal Logic Programs (NLPs) to ADFs and proved the stable models semantics for a normal logic program has an equivalent semantics to that of the corresponding ADF. However, these studies failed in identifying a semantics for ADFs equivalent to a three-valued semantics (as partial stable models and well-founded models) for NLPs. In this work, we focus on a fragment of ADFs, called Attacking Dialectical Frameworks (ADF+s), and provide a translation from NLPs to ADF+s robust enough to guarantee the equivalence between partial stable models, well-founded models, regular models, stable models semantics for NLPs and respectively complete models, grounded models, preferred models, stable models for ADFs. In addition, we define a new semantics for ADF+s, called L-stable, and show it is equivalent to the L-stable semantics for NLPs.

Keywords

Abstract Dialectical FrameworksNormal Logic ProgramsArgumentationInstantiations of Argumentation Frameworks
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 19 , Special Issue 5-6: 35th International Conference on Logic Programming , September 2019 , pp. 941 - 956
Copyright
© Cambridge University Press 2019 

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