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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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References

Bondarenko, A., Dung, P. M., Kowalski, R. A., and Toni, F. 1997. An abstract, argumentation-theoretic approach to default reasoning. Art. Intelligence 93, 1-2, 63–101.Google Scholar
Brass, S. and Dix, J. 1995. Characterizations of the stable semantics by partial evaluation. In International Conf. on Logic Programming and Nonmonotonic Reasoning. Springer, 85–98.Google Scholar
Brewka, G., Ellmauthaler, S., Strass, H., Wallner, J. P., and Woltran, S. 2013. Abstract dialectical frameworks revisited. In Proceedings of the Twenty-Third international joint conference on Artificial Intelligence. AAAI Press, 803–809.Google Scholar
Brewka, G. and Woltran, S. 2010. Abstract dialectical frameworks. In Twelfth International Conf. on the Principles of Knowledge Representation and Reasoning. AAAI Press, 102–111.Google Scholar
Buss, S. R. 1987. The boolean formula value problem is in alogtime. In Proceedings of the nineteenth annual ACM symposium on Theory of computing. ACM, 123–131.Google Scholar
Caminada, M. 2006. Semi-stable semantics. 1st International Conference on Computational Models of Argument (COMMA) 144, 121–130.Google Scholar
Caminada, M., Sá, S., Alcântara, J., and Dvořák, W. 2015a. On the equivalence between logic programming semantics and argumentation semantics. International Journal of Approximate Reasoning 58, 87–111.Google Scholar
Caminada, M. and Schulz, C. 2017. On the equivalence between assumption-based argumentation and logic programming. Journal of Artificial Intelligence Research 60, 779–825.Google Scholar
Caminada, M. W. A., Sá, S., Alcântara, J., and Dvořák, W. 2015b. On the difference between assumption-based argumentation and abstract argumentation. IfCoLog Journal of Logics and their Applications.Google Scholar
Dung, P. 1995. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence 77, 321–357.Google Scholar
Dung, P. M., Kowalski, R. A., and Toni, F. 2009. Assumption-based argumentation. In Argumentation in artificial intelligence. Springer, 199–218.Google Scholar
Eiter, T., Leone, N., and Saccá, D. 1997. On the partial semantics for disjunctive deductive databases. Ann. Math. Artif. Intell. 19, 1-2, 59–96.Google Scholar
Ellmauthaler, S. 2012. Abstract Dialectical Frameworks: Properties, Complexity, and Implementation. M.S. thesis, Technische Universität Wien, Institut für Informationssysteme.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proc. of the 5th International Conference on Logic Programming (ICLP). Vol. 88. 1070–1080.Google Scholar
Kleene, S. C., de Bruijn, N., de Groot, J., and Zaanen, A. C. 1952. Introduction to metamathematics. Vol. 483. van Nostrand New York.Google Scholar
Nielsen, S. H. and Parsons, S. 2006. A generalization of Dungs abstract framework for argumentation: Arguing with sets of attacking arguments. In International Workshop on Argumentation in Multi-Agent Systems. Springer, 54–73.Google Scholar
Polberg, S. 2016. Understanding the abstract dialectical framework. In European Conference on Logics in Artificial Intelligence. Springer, 430–446.CrossRefGoogle Scholar
Prakken, H. and Sartor, G. 1997. Argument-based extended logic programming with defeasible priorities. Journal of applied non-classical logics 7, 1-2, 25–75.Google Scholar
Przymusinski, T. C. 1990. The well-founded semantics coincides with the three-valued stable semantics. Fundamenta Informaticae 13, 4, 445–463.Google Scholar
Schulz, C. and Toni, F. 2015. Logic programming in assumption-based argumentation revisited-semantics and graphical representation. In 29th AAAI Conf. on Art. Intelligence.Google Scholar
Simari, G. R. and Loui, R. P. 1992. A mathematical treatment of defeasible reasoning and its implementation. Artificial intelligence 53, 2-3, 125–157.Google Scholar
Strass, H. 2013. Approximating operators and semantics for abstract dialectical frameworks. Artificial Intelligence 205, 39–70.Google Scholar
Toni, F. 2014. A tutorial on assumption-based argumentation. Argument & Computation 5, 1, 89–117.Google Scholar
Wu, Y., Caminada, M., and Gabbay, D. M. 2009. Complete extensions in argumentation coincide with 3-valued stable models in logic programming. Studia logica 93, 2-3, 383.CrossRefGoogle Scholar
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