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Justifying answer sets using argumentation

Published online by Cambridge University Press:  11 February 2015

CLAUDIA SCHULZ  and
FRANCESCA TONI
CLAUDIA SCHULZ
Affiliation:
Department of Computing, Imperial College London, London SW7 2AZ, UK (e-mail: claudia.schulz@imperial.ac.uk, f.toni@imperial.ac.uk)
FRANCESCA TONI
Affiliation:
Department of Computing, Imperial College London, London SW7 2AZ, UK (e-mail: claudia.schulz@imperial.ac.uk, f.toni@imperial.ac.uk)
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Abstract

An answer set is a plain set of literals which has no further structure that would explain why certain literals are part of it and why others are not. We show how argumentation theory can help to explain why a literal is or is not contained in a given answer set by defining two justification methods, both of which make use of the correspondence between answer sets of a logic program and stable extensions of the assumption-based argumentation (ABA) framework constructed from the same logic program. Attack Trees justify a literal in argumentation-theoretic terms, i.e. using arguments and attacks between them, whereas ABA-Based Answer Set Justifications express the same justification structure in logic programming terms, that is using literals and their relationships. Interestingly, an ABA-Based Answer Set Justification corresponds to an admissible fragment of the answer set in question, and an Attack Tree corresponds to an admissible fragment of the stable extension corresponding to this answer set.

Keywords

answer set programmingassumption-based argumentationstable extensionexplanation
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 16 , Issue 1 , January 2016 , pp. 59 - 110
Copyright
Copyright © Cambridge University Press 2015 

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References

Arora, T., Ramakrishnan, R., Roth, W. G., Seshadri, P. and Srivastava, D. 1993. Explaining program execution in deductive systems. In Proc. of the 3rd International Conference on Deductive and Object-Oriented Databases (DOOD), Ceri, S., Tanaka, K., and Tsur, S., Eds. Lecture Notes in Computer Science, vol. 760. Springer, Berlin Heidelberg, 101–119.CrossRefGoogle Scholar
Baral, C., Chancellor, K., Tran, N., Tran, N., Joy, A. M. and Berens, M. E. 2004. A knowledge based approach for representing and reasoning about signaling networks. Bioinformatics 20, supplement 1, 15–22.CrossRefGoogle ScholarPubMed
Bench-Capon, T., Lowes, D. and McEnery, A. M. 1991. Argument-based explanation of logic programs. Knowledge-Based Systems 4, 3, 177–183.CrossRefGoogle Scholar
Boenn, G., Brain, M., Vos, M. D. and Fitch, J. 2011. Automatic music composition using answer set programming. Theory and Practice of Logic Programming 11, 2–3, 397–427.Google Scholar
Bondarenko, A., Dung, P. M., Kowalski, R. A. and Toni, F. 1997. An abstract, argumentation-theoretic approach to default reasoning. Artificial Intelligence 93, 1–2, 63–101.CrossRefGoogle Scholar
Brain, M. and De Vos, M. 2008. Answer set programming - a domain in need of explanation: A position paper. In Proc. of the 3rd International Workshop on Explanation-aware Computing (ExaCt), Roth-Berghofer, T. R., Schulz, S., Bahls, D. and Leake, D. B., Eds. CEUR Workshop Proceedings, vol. 391. CEUR-WS.org, 37–48.Google Scholar
Brain, M. and Vos, M. D. 2005. Debugging logic programs under the answer set semantics. In Proc. of the 3rd International Workshop on Answer Set Programming (ASP), Vos, M. D. and Provetti, A., Eds. CEUR Workshop Proceedings, vol. 142. CEUR-WS.org, 141–152.Google Scholar
Dung, P. M. 1995a. An argumentation-theoretic foundation for logic programming. The Journal of Logic Programming 22, 2, 151–177.CrossRefGoogle Scholar
Dung, P. M. 1995b. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence 77, 2, 321–357.CrossRefGoogle Scholar
Dung, P. M., Kowalski, R. A. and Toni, F. 2006. Dialectic proof procedures for assumption-based, admissible argumentation. Artificial Intelligence 170, 2, 114–159.CrossRefGoogle Scholar
Dung, P. M., Kowalski, R. A. and Toni, F. 2009. Assumption-based argumentation. In Argumentation in Artificial Intelligence, Simari, G. R. and Rahwan, I., Eds. Springer US, New York, 199–218.CrossRefGoogle Scholar
Dung, P. M., Mancarella, P. and Toni, F. 2007. Computing ideal sceptical argumentation. Artificial Intelligence 171, 10–15, 642–674.CrossRefGoogle Scholar
Dung, P. M. and Ruamviboonsuk, P. 1991. Well-founded reasoning with classical negation. In Proc. of the 1st International Workshop on Logic Programming and Nonmonotonic Reasoning (LPNMR), Nerode, A., Marek, V. W. and Subrahmanian, V. S., Eds. The MIT Press, Cambridge MA, 120–132.Google Scholar
Eiter, T., Leone, N., Mateis, C., Pfeifer, G. and Scarcello, F. 1997. A deductive system for non-monotonic reasoning. In Proc. of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), Dix, J., Furbach, U., and Nerode, A., Eds. Lecture Notes in Computer Science, vol. 1265. Springer, Berlin Heidelberg, 364–375.Google Scholar
Erdem, E. and Oztok, U. 2015. Generating explanations for biomedical queries. Theory and Practice of Logic Programming 15, 1, 35–78.CrossRefGoogle Scholar
Eshghi, K. and Kowalski, R. A. 1989. Abduction compared with negation by failure. In Proc. of the 6th International Conference on Logic Programming (ICLP), Levi, G. and Martelli, M., Eds. The MIT Press, Cambridge, MA, 234–254.Google Scholar
Febbraro, O., Reale, K. and Ricca, F. 2011. ASPIDE: Integrated development environment for answer set programming. In Proc. of the 11th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), Delgrande, J. P. and Faber, W., Eds. Lecture Notes in Computer Science, vol. 6645. Springer, Berlin Heidelberg, 317–330.CrossRefGoogle Scholar
Ferrand, G., Lesaint, W. and Tessier, A. 2012. Explanations and proof trees. Computing and Informatics 25, 2–3, 105–125.Google Scholar
García, A. J., Chesñevar, C. I., Rotstein, N. D. and Simari, G. R. 2013. Formalizing dialectical explanation support for argument-based reasoning in knowledge-based systems. Expert Systems with Applications 40, 8, 3233–3247.CrossRefGoogle Scholar
García, A. J. and Simari, G. R. 2004. Defeasible logic programming: An argumentative approach. Theory and Practice of Logic Programming 4, 1–2, 95–138.CrossRefGoogle Scholar
Gebser, M., Kaminski, R., Kaufmann, B., Ostrowski, M., Schaub, T. and Schneider, M. 2011. Potassco: The Potsdam answer set solving collection. AI Communications 24, 2, 107–124.CrossRefGoogle Scholar
Gelfond, M. 2008. Answer sets. In Handbook of Knowledge Representation, van Harmelen, F., Lifschitz, V., and Porter, B., Eds. Foundations of Artificial Intelligence, vol. 3. Elsevier, San Diego, Chapter 7, 285–316.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 3–4, 365–385.CrossRefGoogle Scholar
Governatori, G., Maher, M. J., Antoniou, G. and Billington, D. 2004. Argumentation semantics for defeasible logic. Journal of Logic and Computation 14, 5, 675–702.CrossRefGoogle Scholar
Lacave, C. and Diez, F. J. 2004. A review of explanation methods for heuristic expert systems. The Knowledge Engineering Review 19, 2, 133–146.CrossRefGoogle Scholar
Moulin, B., Irandoust, H., Bélanger, M. and Desbordes, G. 2002. Explanation and argumentation capabilities: Towards the creation of more persuasive agents. Artificial Intelligence Review 17, 3, 169–222.CrossRefGoogle Scholar
Niemelä, I., Simons, P. and Syrjänen, T. 2000. Smodels: A system for answer set programming. In Proc. of the 8th International Workshop on Non-Monotonic Reasoning (NMR), Baral, C. and Truszczynski, M., Eds. Vol. cs.AI/0003033. CoRR.Google Scholar
Pontelli, E., Son, T. C. and Elkhatib, O. 2009. Justifications for logic programs under answer set semantics. Theory and Practice of Logic Programming 9, 1, 1–56.CrossRefGoogle Scholar
Prakken, H. 2010. An abstract framework for argumentation with structured arguments. Argument and Computation 1, 2, 93–124.CrossRefGoogle Scholar
Satoh, K., Asai, K., Kogawa, T., Kubota, M., Nakamura, M., Nishigai, Y., Shirakawa, K. and Takano, C. 2010. Proleg: An implementation of the presupposed ultimate fact theory of Japanese civil code by prolog technology. In Proc. of the 2010 International Conference on New Frontiers in Artificial Intelligence, Onada, T., Bekki, D. and McCready, E., Eds. Lecture Notes in Computer Science, vol. 6797. Springer, Berlin Heidelberg, 153–164.Google Scholar
Schulz, C., Sergot, M. and Toni, F. 2013. Argumentation-based answer set justification. In Working Notes of the 11th International Symposium on Logical Formalizations of Commonsense Reasoning (Commonsense).Google Scholar
Son, T. C., Pontelli, E. and Sakama, C. 2009. Logic programming for multiagent planning with negotiation. In Proc. of the 25th International Conference on Logic Programming (ICLP), Hill, P. M. and Warren, D. S., Eds. Lecture Notes in Computer Science, vol. 5649. Springer, Berlin Heidelberg, 99–114.Google Scholar
Thimm, M. and Kern-Isberner, G. 2008. On the relationship of defeasible argumentation and answer set programming. In Proc. of the 2nd International Conference on Computational Models of Argument (COMMA), Besnard, P., Doutre, S. and Hunter, A., Eds. vol. 172. IOS Press, Amsterdam, 393–404.Google Scholar
Toni, F. and Sergot, M. 2011. Argumentation and answer set programming. In Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning, Balduccini, M. and Son, T. C., Eds. Lecture Notes in Computer Science, vol. 6565. Springer, Berlin Heidelberg, 164–180.CrossRefGoogle Scholar