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Paracoherent Answer Set Semantics meets Argumentation Frameworks

Published online by Cambridge University Press:  20 September 2019

GIOVANNI AMENDOLA Open the ORCID record for GIOVANNI AMENDOLA [Opens in a new window]  and
FRANCESCO RICCA Open the ORCID record for FRANCESCO RICCA [Opens in a new window]
GIOVANNI AMENDOLA
Affiliation:
University of Calabria, Rende, Italy (e-mails: amendola@mat.unical.it, ricca@mat.unical.it)
FRANCESCO RICCA
Affiliation:
University of Calabria, Rende, Italy (e-mails: amendola@mat.unical.it, ricca@mat.unical.it)
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Abstract

In the last years, abstract argumentation has met with great success in AI, since it has served to capture several non-monotonic logics for AI. Relations between argumentation framework (AF) semantics and logic programming ones are investigating more and more. In particular, great attention has been given to the well-known stable extensions of an AF, that are closely related to the answer sets of a logic program. However, if a framework admits a small incoherent part, no stable extension can be provided. To overcome this shortcoming, two semantics generalizing stable extensions have been studied, namely semi-stable and stage. In this paper, we show that another perspective is possible on incoherent AFs, called paracoherent extensions, as they have a counterpart in paracoherent answer set semantics. We compare this perspective with semi-stable and stage semantics, by showing that computational costs remain unchanged, and moreover an interesting symmetric behaviour is maintained.

Keywords

Answer Set ProgrammingAbstract ArgumentationParacoherent reasoning
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. 688 - 704
Copyright
© Cambridge University Press 2019 

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References

Alcântara, J., Damásio, C. V., and Pereira, L. M. 2005. An encompassing framework for paraconsistent logic programs. J. Applied Logic 3, 1, 67–95.CrossRefGoogle Scholar
Amendola, G. 2018. Solving the stable roommates problem using incoherent answer set programs. In RiCeRcA@AI*IA. CEUR Workshop Proceedings, vol. 2272. CEUR-WS.org.Google Scholar
Amendola, G., Dodaro, C., Faber, W., Leone, N., and Ricca, F. 2017. On the computation of paracoherent answer sets. In AAAI. AAAI Press, 1034–1040.Google Scholar
Amendola, G., Dodaro, C., Faber, W., Pulina, L., and Ricca, F. 2019. Algorithm selection for paracoherent answer set computation. In JELIA. Lecture Notes in Computer Science, vol. 11468. Springer, 479–489.Google Scholar
Amendola, G., Dodaro, C., Faber, W., and Ricca, F. 2018. Externally supported models for efficient computation of paracoherent answer sets. In AAAI. AAAI Press, 1720–1727.Google Scholar
Amendola, G., Dodaro, C., and Ricca, F. 2019. Better paracoherent answer sets with less resources. TPLP this volume, this number, to appear.Google Scholar
Amendola, G., Eiter, T., Fink, M., Leone, N., and Moura, J. 2016. Semi-equilibrium models for paracoherent answer set programs. Artif. Intell. 234, 219–271.Google Scholar
Amgoud, L., Parsons, S., and Maudet, N. 2000. Arguments, dialogue, and negotiation. In ECAI. IOS Press, 338–342.Google Scholar
Arieli, O. 2016. On the acceptance of loops in argumentation frameworks. J. Log. Comput. 26, 4, 1203–1234.10.1093/logcom/exu009CrossRefGoogle Scholar
Balduccini, M. and Gelfond, M. 2003. Logic programs with consistency-restoring rules. In ISLFCR, AAAI 2003 Spring Symposium Series. 9–18.Google Scholar
Baroni, P., Dunne, P. E., and Giacomin, M. 2011. On the resolution-based family of abstract argumentation semantics and its grounded instance. Artif. Intell. 175, 3-4, 791–813.CrossRefGoogle Scholar
Baroni, P., Gabbay, D. M., and Giacomin, M. 2016. Introduction to the special issue on loops in argumentation. J. Log. Comput. 26, 4, 1051–1053.Google Scholar
Baroni, P. and Giacomin, M. 2007. On principle-based evaluation of extension-based argumentation semantics. Artif. Intell. 171, 10-15, 675–700.Google Scholar
Baroni, P., Giacomin, M., and Guida, G. 2005. Scc-recursiveness: a general schema for argumentation semantics. Artif. Intell. 168, 1-2, 162–210.Google Scholar
Baumann, R., Linsbichler, T., and Woltran, S. 2016. Verifiability of argumentation semantics. In COMMA’16. 83–94.Google Scholar
Bench-Capon, T. J. M. 2016. Dilemmas and paradoxes: cycles in argumentation frameworks. J. Log. Comput. 26, 4, 1055–1064.CrossRefGoogle Scholar
Bench-Capon, T. J. M. and Dunne, P. E. 2007. Argumentation in artificial intelligence. Artif. Intell. 171, 10-15, 619–641.CrossRefGoogle Scholar
Bodanza, G. A., Tohmé, F. A., and Simari, G. R. 2016. Beyond admissibility: accepting cycles in argumentation with game protocols for cogency criteria. J. Log. Comput. 26, 4, 1235–1255.CrossRefGoogle Scholar
Brewka, G., Eiter, T., and Truszczynski, M. 2011. Answer set programming at a glance. Commun. ACM 54, 12, 92–103.CrossRefGoogle Scholar
Caminada, M. 2006. Semi-stable semantics. In COMMA’06. 121–130.Google Scholar
Caminada, M. 2007. Comparing two unique extension semantics for formal argumentation: ideal and eager. In BNAIC’07.Google Scholar
Caminada, M., Sá, S., Alcântara, J., and Dvorák, W. 2015. On the equivalence between logic programming semantics and argumentation semantics. Int. J. Approx. Reasoning 58, 87–111.Google Scholar
Caminada, M. W. A., Carnielli, W. A., and Dunne, P. E. 2012. Semi-stable semantics. J. Log. Comput. 22, 5, 1207–1254.Google Scholar
Costantini, S. and Provetti, A. 2005. Normal forms for answer sets programming. TPLP 5, 6, 747–760.Google Scholar
Cramer, M. and Guillaume, M. 2019. Empirical study on human evaluation of complex argumentation frameworks. In JELIA. Lecture Notes in Computer Science, vol. 11468. Springer, 102–115.Google Scholar
Dung, P. M. 1995. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77, 2, 321–358.CrossRefGoogle Scholar
Dung, P. M., Mancarella, P., and Toni, F. 2007. Computing ideal sceptical argumentation. Artif. Intell. 171, 10-15, 642–674.CrossRefGoogle Scholar
Dunne, P. E. and Caminada, M. 2008. Computational complexity of semi-stable semantics in abstract argumentation frameworks. In JELIA’08. 153–165.Google Scholar
Dunne, P. E. and Wooldridge, M. 2009. Complexity of abstract argumentation. In Argumentation in Artificial Intelligence. 85–104.Google Scholar
Dvorák, W. and Gaggl, S. A. 2016. Stage semantics and the scc-recursive schema for argumentation semantics. J. Log. Comput. 26, 4, 1149–1202.CrossRefGoogle Scholar
Dvorák, W. and Woltran, S. 2010. Complexity of semi-stable and stage semantics in argumentation frameworks. Inf. Process. Lett. 110, 11, 425–430.Google Scholar
Eiter, T., Fink, M., and Moura, J. 2010. Paracoherent answer set programming. In KR. AAAI Press.Google Scholar
Eiter, T., Leone, N., and Saccà, D. 1997. On the partial semantics for disjunctive deductive databases. Ann. Math. Artif. Intell. 19, 1-2, 59–96.CrossRefGoogle Scholar
Gabbay, D. M. 2016. The handling of loops in argumentation networks. J. Log. Comput. 26, 4, 1065–1147.Google Scholar
Gaggl, S. A., Linsbichler, T., Maratea, M., and Woltran, S. 2016. Introducing the second international competition on computational models of argumentation. In SAFA@COMMA. 4–9.Google Scholar
Gaggl, S. A., Linsbichler, T., Maratea, M., and Woltran, S. 2018. Summary report of the second international competition on computational models of argumentation. 39, 4, 77–79.Google Scholar
Gaggl, S. A., Rudolph, S., and Thomazo, M. 2015. What is a reasonable argumentation semantics? In Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation. 309–324.Google Scholar
Gaggl, S. A. and Woltran, S. 2013. The cf2 argumentation semantics revisited. J. Log. Comput. 23, 5, 925–949.Google Scholar
Gale, D. and Shapley, L. S. 1962. College admissions and the stability of marriage. The American Mathematical Monthly 69, 9–15.Google Scholar
Galindo, M. J. O., Ramríez, J. R. A., and Carballido, J. L. 2008. Logical weak completions of paraconsistent logics. J. Log. Comput. 18, 6, 913–940.Google Scholar
Gebser, M., Lee, J., and Lierler, Y. 2011. On elementary loops of logic programs. TPLP 11, 6, 953–988.Google Scholar
Gelder, A. V., Ross, K. A., and Schlipf, J. S. 1991. The well-founded semantics for general logic programs. J. ACM 38, 3, 620–650.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Logic Programming, Proceedings of the Fifth International Conference and Symposium, Seattle, Washington, August 15-19, 1988 (2 Volumes). 1070–1080.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Comput. 9, 3/4, 365–386.Google Scholar
Jakobovits, H. and Vermeir, D. 1999. Robust semantics for argumentation frameworks. J. Log. Comput. 9, 2, 215–261.Google Scholar
Lee, J. and Lifschitz, V. 2003. Loop formulas for disjunctive logic programs. In ICLP. Lecture Notes in Computer Science, vol. 2916. Springer, 451–465.Google Scholar
Lifschitz, V. 1999. Answer set planning. In ICLP. MIT Press, 23–37.Google Scholar
Lin, F. and Zhao, X. 2004. On odd and even cycles in normal logic programs. In AAAI. AAAI Press / The MIT Press, 80–85.Google Scholar
Pereira, L. M. and Pinto, A. M. 2005. Revised stable models - a semantics for logic programs. In EPIA. 29–42.Google Scholar
Pereira, L. M. and Pinto, A. M. 2007. Approved models for normal logic programs. In LPAR. 454–468.Google Scholar
Pollock, J. L. 1998. The logical foundations of goal-regression planning in autonomous agents. Artif. Intell. 106, 2, 267–334.Google Scholar
Prakken, H. and Sartor, G. 1996. A dialectical model of assessing conflicting arguments in legal reasoning. Artif. Intell. Law 4, 3-4, 331–368.Google Scholar
Przymusinski, T. C. 1991a. Stable semantics for disjunctive programs. New Generation Comput. 9, 3/4, 401–424.Google Scholar
Przymusinski, T. C. 1991b. Three-valued nonmonotonic formalisms and semantics of logic programs. Artif. Intell. 49, 1-3, 309–343.Google Scholar
Saccà, D. and Zaniolo, C. 1991. Partial models and three-valued models in logic programs with negation. In LPNMR. The MIT Press, 87–101.Google Scholar
Sakama, C. and Inoue, K. 1995. Paraconsistent stable semantics for extended disjunctive programs. J. Log. Comput. 5, 3, 265–285.Google Scholar
Schulz, C. and Toni, F. 2018. On the responsibility for undecisiveness in preferred and stable labellings in abstract argumentation. Artif. Intell. 262, 301–335.Google Scholar
Seipel, D. 1997. Partial evidential stable models for disjunctive deductive databases. In LPKR. Lecture Notes in Computer Science, vol. 1471. Springer, 66–84.Google Scholar
Simari, G. R. and Rahwan, I., Eds. 2009. Argumentation in Artificial Intelligence. Springer.Google Scholar
Simons, P., Niemelä, I., and Soininen, T. 2002. Extending and implementing the stable model semantics. Artif. Intell. 138, 1-2, 181–234.Google Scholar
Strass, H. 2013. Approximating operators and semantics for abstract dialectical frameworks. Artif. Intell. 205, 39–70.Google Scholar
Verheij, B. 1996. Two approaches to dialectical argumentation: Admissible sets and argumentation stages. In FAPR. 357–368.Google Scholar
Verheij, B. 2003. Artificial argument assistants for defeasible argumentation. Artif. Intell. 150, 1-2, 291–324.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, 383–403.Google Scholar
You, J. and Yuan, L. 1994. A three-valued semantics for deductive databases and logic programs. J. Comput. Syst. Sci. 49, 2, 334–361.Google Scholar