Justifying answer sets using argumentation. (English) Zbl 1379.68301

Summary: 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.


68T27 Logic in artificial intelligence
68N17 Logic programming
68T30 Knowledge representation


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[1] Arora, T.; Ramakrishnan, R.; Roth, W. G.; Seshadri, P.; Srivastava, D.; Ceri, S.; Tanaka, K.; Tsur, S., Proc. of the 3rd International Conference on Deductive and Object-Oriented Databases (DOOD), Explaining program execution in deductive systems, 101-119, (1993), Springer: Springer, Berlin Heidelberg
[2] Baral, C.; Chancellor, K.; Tran, N.; Tran, N.; Joy, A. M.; Berens, M. E., A knowledge based approach for representing and reasoning about signaling networks, Bioinformatics, 20, supplement 1, 15-22, (2004)
[3] Bench-Capon, T.; Lowes, D.; Mcenery, A. M., Argument-based explanation of logic programs, Knowledge-Based Systems, 4, 3, 177-183, (1991)
[4] Boenn, G.; Brain, M.; Vos, M. D.; Fitch, J., Automatic music composition using answer set programming, Theory and Practice of Logic Programming, 11, 2-3, 397-427, (2011)
[5] Bondarenko, A.; Dung, P. M.; Kowalski, R. A.; Toni, F., abstract, argumentation-theoretic approach to default reasoning, Artificial Intelligence, 93, 1-2, 63-101, (1997) · Zbl 1017.03511
[6] Brain, M.; De Vos, M.; Roth-Berghofer, T. R.; Schulz, S.; Bahls, D.; Leake, D. B., Proc. of the 3rd International Workshop on Explanation-aware Computing (ExaCt), Answer set programming - a domain in need of explanation: A position paper, 37-48, (2008), CEUR-WS.org
[7] Brain, M.; Vos, M. D.; Vos, M. D.; Provetti, A., Proc. of the 3rd International Workshop on Answer Set Programming (ASP), Debugging logic programs under the answer set semantics, 141-152, (2005), CEUR-WS.org
[8] Dung, P. M., An argumentation-theoretic foundation for logic programming, The Journal of Logic Programming, 22, 2, 151-177, (1995) · Zbl 0816.68045
[9] Dung, P. M., On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games, Artificial Intelligence, 77, 2, 321-357, (1995) · Zbl 1013.68556
[10] Dung, P. M.; Kowalski, R. A.; Toni, F., Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence, 170, 2, 114-159, (2006) · Zbl 1131.68103
[11] Dung, P. M.; Kowalski, R. A.; Toni, F.; Simari, G. R.; Rahwan, I., Argumentation in Artificial Intelligence, Assumption-based argumentation, 199-218, (2009), Springer US: Springer US, New York
[12] Dung, P. M.; Mancarella, P.; Toni, F., Computing ideal sceptical argumentation, Artificial Intelligence, 171, 10-15, 642-674, (2007) · Zbl 1168.68564
[13] Dung, P. M.; Ruamviboonsuk, P.; Nerode, A.; Marek, V. W.; Subrahmanian, V. S., Proc. of the 1st International Workshop on Logic Programming and Nonmonotonic Reasoning (LPNMR), Well-founded reasoning with classical negation, 120-132, (1991), The MIT Press: The MIT Press, Cambridge MA
[14] Eiter, T.; Leone, N.; Mateis, C.; Pfeifer, G.; Scarcello, F.; Dix, J.; Furbach, U.; Nerode, A., Proc. of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), A deductive system for non-monotonic reasoning, 364-375, (1997), Springer: Springer, Berlin Heidelberg
[15] Erdem, E.; Oztok, U., Generating explanations for biomedical queries, Theory and Practice of Logic Programming, 15, 1, 35-78, (2015) · Zbl 1379.68059
[16] Eshghi, K.; Kowalski, R. A.; Levi, G.; Martelli, M., Proc. of the 6th International Conference on Logic Programming (ICLP), Abduction compared with negation by failure, 234-254, (1989), The MIT Press: The MIT Press, Cambridge, MA
[17] Febbraro, O.; Reale, K.; Ricca, F.; Delgrande, J. P.; Faber, W., Proc. of the 11th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), ASPIDE: Integrated development environment for answer set programming, 317-330, (2011), Springer: Springer, Berlin Heidelberg · Zbl 1214.68009
[18] Ferrand, G.; Lesaint, W.; Tessier, A., Explanations and proof trees, Computing and Informatics, 25, 2-3, 105-125, (2012) · Zbl 1132.68677
[19] García, A. J.; Chesñevar, C. I.; Rotstein, N. D.; Simari, G. R., Formalizing dialectical explanation support for argument-based reasoning in knowledge-based systems, Expert Systems with Applications, 40, 8, 3233-3247, (2013)
[20] García, A. J.; Simari, G. R., Defeasible logic programming: An argumentative approach, Theory and Practice of Logic Programming, 4, 1-2, 95-138, (2004) · Zbl 1090.68015
[21] Gebser, M.; Kaminski, R.; Kaufmann, B.; Ostrowski, M.; Schaub, T.; Schneider, M., Potassco: The Potsdam answer set solving collection, AI Communications, 24, 2, 107-124, (2011) · Zbl 1215.68214
[22] Gelfond, M.; Van Harmelen, F.; Lifschitz, V.; Porter, B., Handbook of Knowledge Representation, Answer sets, 285-316, (2008), Elsevier: Elsevier, San Diego
[23] Gelfond, M.; Lifschitz, V., Classical negation in logic programs and disjunctive databases, New Generation Computing, 9, 3-4, 365-385, (1991) · Zbl 0735.68012
[24] Governatori, G.; Maher, M. J.; Antoniou, G.; Billington, D., Argumentation semantics for defeasible logic, Journal of Logic and Computation, 14, 5, 675-702, (2004) · Zbl 1067.03038
[25] Lacave, C.; Diez, F. J., A review of explanation methods for heuristic expert systems, The Knowledge Engineering Review, 19, 2, 133-146, (2004)
[26] Moulin, B.; Irandoust, H.; Bélanger, M.; Desbordes, G., Explanation and argumentation capabilities: Towards the creation of more persuasive agents, Artificial Intelligence Review, 17, 3, 169-222, (2002) · Zbl 1017.68112
[27] Niemelä, I.; Simons, P.; Syrjänen, T.; Baral, C.; Truszczynski, M., (2000)
[28] Pontelli, E.; Son, T. C.; Elkhatib, O., Justifications for logic programs under answer set semantics, Theory and Practice of Logic Programming, 9, 1, 1-56, (2009) · Zbl 1170.68005
[29] Prakken, H., An abstract framework for argumentation with structured arguments, Argument and Computation, 1, 2, 93-124, (2010)
[30] Satoh, K.; Asai, K.; Kogawa, T.; Kubota, M.; Nakamura, M.; Nishigai, Y.; Shirakawa, K.; Takano, C.; Onada, T.; Bekki, D.; Mccready, E., Proc. of the 2010 International Conference on New Frontiers in Artificial Intelligence, Proleg: An implementation of the presupposed ultimate fact theory of Japanese civil code by prolog technology, 153-164, (2010), Springer: Springer, Berlin Heidelberg
[31] Schulz, C.; Sergot, M.; Toni, F., (2013)
[32] Son, T. C.; Pontelli, E.; Sakama, C.; Hill, P. M.; Warren, D. S., Proc. of the 25th International Conference on Logic Programming (ICLP), Logic programming for multiagent planning with negotiation, 99-114, (2009), Springer: Springer, Berlin Heidelberg · Zbl 1251.68263
[33] Thimm, M.; Kern-Isberner, G.; Besnard, P.; Doutre, S.; Hunter, A., Proc. of the 2nd International Conference on Computational Models of Argument (COMMA), On the relationship of defeasible argumentation and answer set programming, 393-404, (2008), IOS Press: IOS Press, Amsterdam
[34] Toni, F.; Sergot, M.; Balduccini, M.; Son, T. C., Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning, Argumentation and answer set programming, 164-180, (2011), Springer: Springer, Berlin Heidelberg · Zbl 1213.68025
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