Abstract
In this paper we propose a new presentation of logic-based argumentation theory through Gentzen-style sequent calculi. We show that arguments may be represented by Gentzen-type sequents and that attacks between arguments may be represented by sequent elimination rules. This framework is logic-independent, i.e., it may be based on arbitrary languages and consequence relations. Moreover, the usual conditions of minimality and consistency of support sets are relaxed, allowing for a more flexible way of expressing arguments, which also simplifies their identification. This generic representation implies that argumentation theory may benefit from incorporating techniques of proof theory and that different non-classical formalisms may be used for backing up intended argumentation semantics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Amgoud, L., Besnard, P.: Bridging the gap between abstract argumentation systems and logic. In: Godo, L., Pugliese, A. (eds.) SUM 2009. LNCS, vol. 5785, pp. 12–27. Springer, Heidelberg (2009)
Amgoud, L., Besnard, P.: A formal analysis of logic-based argumentation systems. In: Deshpande, A., Hunter, A. (eds.) SUM 2010. LNCS, vol. 6379, pp. 42–55. Springer, Heidelberg (2010)
Amgoud, L., Besnard, P., Vesic, S.: Identifying the core of logic-based argumentation systems. In: Proc. ICTAI 2011, pp. 633–636. IEEE (2011)
Arieli, O., Avron, A.: The value of the four values. Artificial Intelligence 102(1), 97–141 (1998)
Avron, A.: A constructive analysis of RM. J. Symbolic Logic 52, 939–951 (1987)
Baroni, P., Caminada, M.W.A., Giacomin, M.: An introduction to argumentation semantics. The Knowledge Engineering Review 26(4), 365–410 (2011)
Baroni, P., Giacomin, M.: Semantics for abstract argumentation systems. In: Rahwan, Simary (eds.) [32], pp. 25–44
Batens, D.: Dynamic dialectical logics. In: Priest, G., Routely, R., Norman, J. (eds.) Paraconsistent Logic. Essay on the Inconsistent, pp. 187–217. Philosophia Verlag (1989)
Batens, D.: A survey on inconsistency-adaptive logics. In: Batens, D., Mortensen, C., Priest, G., Van Bendegem, J. (eds.) Frontiers of Paraconsistent Logic. Studies in Logic and Computation, vol. 8, pp. 69–73. Research Studies Press (2000)
Belnap, N.D.: A useful four-valued logic. In: Dunn, M., Epstein, G. (eds.) Modern Uses of Multiple-Valued Logics, pp. 7–37. Reidel Publishing (1977)
Besnard, P., Grégoire, É., Piette, C., Raddaoui, B.: MUS-based generation of arguments and counter-arguments. In: Proc. IRI 2010, pp. 239–244. IEEE (2010)
Besnard, P., Hunter, A.: A logic-based theory of deductive arguments. Artificial Intelligence 128(1-2), 203–235 (2001)
Besnard, P., Hunter, A.: Argumentation based on classical logic. In: Rahwan, Simary (eds.) [32], pp. 133–152
Besnard, P., Hunter, A., Woltran, S.: Encoding deductive argumentation in quantified boolean formulae. Artificial Intelligence 173(15), 1406–1423 (2009)
Brünnler, K.: Nested Sequents. PhD thesis, Institut für Informatik und Angewandte Mathematik, Universität Bern (2010)
Caminada, M.W.A.: Contamination in formal argumentation systems. In: Proc. BNAIC 2005, pp. 59–65 (2005)
Caminada, M.W.A.: Semi-stable semantics. In: Dunne, P.E., Bench-Capon, T.J.M. (eds.) Proc. COMMA 2006, pp. 121–130. IOS Press (2006)
Caminada, M.W.A., Carnielli, W.A., Dunne, P.E.: Semi-stable semantics. Journal of Logic and Computation 22(5), 1207–1254 (2012)
Caminada, M.W.A., Vesic, S.: On extended conflict-freeness in argumentation. In: Uiterwijk, J., Roos, N., Winands, M. (eds.) Proc. BNAIC 2012, pp. 43–50 (2012)
Chesñevar, C.I., Maguitman, A.G., Loui, R.P.: Logical models of argument. ACM Computing Surveys 32(4), 337–383 (2000)
da Costa, N.C.A.: On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic 15, 497–510 (1974)
Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence 77, 321–357 (1995)
Dung, P.M., Mancarella, P., Toni, F.: Computing ideal sceptical argumentation. Artificial Intelligence 171(10-15), 642–674 (2007)
Efstathiou, V., Hunter, A.: Algorithms for generating arguments and counterarguments in propositional logic. Journal of Approximate Reasoning 52(6), 672–704 (2011)
Eiter, T., Gottlob, G.: The complexity of logic-based abduction. Journal of the ACM 42, 3–42 (1995)
Gentzen, G.: Investigations into logical deduction (1934) (in German); An English translation appears in ‘The Collected Works of Gerhard Gentzen’, edited by M. E. Szabo. North-Holland (1969)
Gorogiannis, N., Hunter, A.: Instantiating abstract argumentation with classical logic arguments: Postulates and properties. Artificial Intelligence 175(9-10), 1479–1497 (2011)
Pollock, J.L.: Defeasible reasoning. Cognitive Science 11(4), 481–518 (1987)
Pollock, J.L.: How to reason defeasibly. Artificial Intelligence 57, 1–42 (1992)
Prakken, H., Vreeswijk, G.: Logical systems for defeasible argumentation. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosochical Logic, vol. 14, pp. 219–318. Kluwer Academic Publishers (2002)
Priest, G.: Reasoning about truth. Artificial Intelligence 39, 231–244 (1989)
Rahwan, I., Simari, G.R.: Argumentation in Artificial Intelligence. Springer (2009)
Simari, G.R., Loui, R.P.: A mathematical treatment of defeasible reasoning and its implementation. Artificial Intelligence 53(2-3), 125–157 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arieli, O. (2013). A Sequent-Based Representation of Logical Argumentation. In: Leite, J., Son, T.C., Torroni, P., van der Torre, L., Woltran, S. (eds) Computational Logic in Multi-Agent Systems. CLIMA 2013. Lecture Notes in Computer Science(), vol 8143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40624-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-40624-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40623-2
Online ISBN: 978-3-642-40624-9
eBook Packages: Computer ScienceComputer Science (R0)