Abstract
This is a survey of some recent results relating Dung-style semantics for different types of logical argumentation frameworks and several forms of reasoning with maximally consistent sets (MCS) of premises. The related formalsims are also examined with respect to some rationality postulates and are carried on to corresponding proof systems for non-monotonic reasoning.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Amgoud, L.: Postulates for logic-based argumentation systems. Int. J. Approx. Reason. 55(9), 2028–2048 (2014)
Amgoud, L., Besnard, P.: Bridging the gap between abstract argumentation systems and logic. In: Proceedings of the SUM’09, LNCS 5785, pp 12–27. Springer (2009)
Amgoud, L., Besnard, P.: A formal analysis of logic-based argumentation systems. In: Proceedings of the SUM’10, LNCS 6379, pp 42–55. Springer (2010)
Amgoud, L., Besnard, P.: Logical limits of abstract argumentation frameworks. Journal of Applied Non-Classical Logics 23(3), 229–267 (2013)
Amgoud, L., Cayrol, C.: Inferring from inconsistency in preference-based argumentation frameworks. J. Autom. Reason. 29(2), 125–169 (2002)
Amgoud, L., Vesic, S.: Handling inconsistency with preference-based argumentation. In: Proceedings SUM’10, pp 56–69. Springer (2010)
Arieli, O., Borg, A., Straßer, C.: Prioritized sequent-based argumentation. In: Proceedings of the AAMAS’18, pp 1105–1113. ACM (2018)
Arieli, O., Borg, A., Straßer, C.: Reasoning with maximal consistency by argumentative approaches. J. Log. Comput. 28(7), 1523–1563 (2018)
Arieli, O., Borg, A., Straßer, C.: A proof theoretic perspective of logical argumentation. submitted (2019)
Arieli, O., Straßer, C.: Dynamic derivations for sequent-based logical argumentation. In: Proceedings of the COMMA’14, vol. 266 of Frontiers in Artificial Intelligence and Applications, pp 89–100. IOS Press (2014)
Arieli, O., Straßer, C.: Sequent-based logical argumentation. Journal of Argument and Computation 6(1), 73–99 (2015)
Arieli, O., Straßer, C.: Deductive argumentation by enhanced sequent calculi and dynamic derivations. Electron. Notes Theor. Comput. Sci. 323, 21–37 (2016)
Arieli, O., Straßer, C.: Logical argumentation by dynamic proof systems. Theoretical Computer Science, in press (https://doi.org/10.1016/j.tcs.2019.02.019) (2019)
Asenjo, F.G.: A calculus of antinomies. Notre Dame Journal of Formal Logic 7, 103–106 (1966)
Avron, A.: The method of hypersequents in the proof theory of propositional non-classical logics. In: Logic: Foundations to Applications, pp 1–32. Oxford Science Publications (1996)
Baral, C., Kraus, S., Minker, J.: Combining multiple knowledge bases. IEEE Trans. Knowl. Data Eng. 3(2), 208–220 (1991)
Baroni, P., Caminada, M., Giacomin, M.: An introduction to argumentation semantics. Knowl. Eng. Rev. 26(4), 365–410 (2011)
Baroni, P., Caminada, M., Giacomin, M.: Abstract argumentation frameworks and their semantics. In: Baroni, P., Gabay, D., Giacomin, M., van der Torre, L. (eds.) Handbook of Formal Argumentation, pp 159–236. College Publications (2018)
Baroni, P., Giacomin, M.: Semantics for abstract argumentation systems. In: Rahwan, I., Simary, G.R. (eds.) Argumentation in Artificial Intelligence, pp 25–44 (2009)
Beirlaen, M., Heyninck, J., Pardo, P., Straßer, C.: Argument strength in formal argumentation. Journal of Applied Logics-IfCoLog Journal of Logics and their Applications 5(3), 629–675 (2018)
Benferhat, S., Dubois, D., Prade, H.: Representing default rules in possibilistic logic. In: Proceedings of the KR’92, pp 673–684 (1992)
Benferhat, S., Dubois, D., Prade, H.: A local approach to reasoning under incosistency in stratified knowledge bases. In: Proceedings of the ECSQARU’95, LNCS 946, pp 36–43. Springer (1995)
Benferhat, S., Dubois, D., Prade, H.: Some syntactic approaches to the handling of inconsistent knowledge bases: a comparative study part 1: the flat case. Stud. Logica. 58(1), 17–45 (1997)
Besnard, P., García, A., Hunter, A., Modgil, S., Prakken, H., Simari, G., Toni, F.: Introduction to structured argumentation. Argument & Computation 5(1), 1–4 (2014)
Besnard, P., Hunter, A.: A logic-based theory of deductive arguments. J. Artif. Intell. 128(1–2), 203–235 (2001)
Besnard, P., Hunter, A.: Argumentation based on classical logic. In: Rahwan, I., Simary, G.R. (eds.) Argumentation in artificial intelligence, pp 133–152. Springer (2009)
Besnard, P., Hunter, A.: A review of argumentation based on deductive arguments. In: Baroni, P., Gabay, D., Giacomin, M., van der Torre, L. (eds.) Handbook of Formal Argumentation, pp 437–484. College Publications (2018)
Bondarenko, A., Dung, P.M., Kowalski, R., Toni, F.: An abstract, argumentation-theoretic approach to default reasoning. J. Artif. Intell. 93(1), 63–101 (1997)
Borg, A.: Equipping sequent-based argumentation with defeasible assumptions. In: Proceedings of the COMMA’18, vol. 305 of Frontiers in Artificial Intelligence and Applications. IOS Press (2018)
Borg, A., Arieli, O.: Hypersequential argumentation frameworks: an instantiation in the modal logic S5. In: Proceedings of the AAMAS’18, pp 1097–1104. ACM (2018)
Borg, A., Arieli, O., Straßer, C.: Hypersequent-based argumentation: an instantiation in the relevance logic RM. In: Black, E., Modgil, S., Oren, N. (eds.) Proceedings of the TAFA’17, LNCS 10757, pp 17–34. Springer (2017)
Borg, A., Straßer, C., Arieli, O.: A generalized proof-theoretic approach to structured argumentation by hypersequent calculi. Submitted (2019)
Brewka, G.: Preferred subtheories: an extended logical framework for default reasoning. In: Sridharan, N.S. (ed.) Proceedings of the IJCAI’89, pp 1043–1048. Morgan Kaufmann (1989)
Caminada, M., Amgoud, L.: On the evaluation of argumentation formalisms. J. Artif. Intell. 171, 286–310 (2007)
Caminada, M., Modgil, S., Oren, N.: Preferences and unrestricted rebut. In: Proceedings of the COMMA’14, pp 209–220. IOS Press (2014)
Cayrol, C.: On the relation between argumentation and non-monotonic coherence-based entailment. In: Proceedings IJCAI’95, pp 1443–1448. Morgan Kaufmann (1995)
Čyras, K., Toni, F.: Non-monotonic inference properties for assumption-based argumentation. In: Proceedings of the TAFA’15, pp 92–111. Springer (2015)
D’Agostino, M., Modgil, S.: Classical logic, argumentation and dialectic. Artif. Intell. 262, 15–51 (2018)
D’Agostino, M., Modgil, S.: A study of argumentative characterisations of preferred subtheories. In: Proceedings of the IJCAI’18, pp 1788–1794 (2018)
Dauphin, J., Cramer, M.: Aspic-end: structured argumentation with explanations and natural deduction. In: Proceedings of the TAFA’17, pp 51–66. Springer (2017)
Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. J. Artif. Intell. 77, 321–357 (1995)
Dung, P.M., Kowalski, R., Toni, F.: Dialectic proof procedures for assumption-based, admissible argumentation. J. Artif. Intell. 170(2), 114–159 (2006)
Elvang-Gøransson, M., Krause, P., Fox, J.: Acceptability of arguments as ‘logical uncertainty’. In: Proceedings of the ECSQARU’93, pp 85–90. Springer (1993)
García, A., Simari, G.: Defeasible logic programming: an argumentative approach. Theory Pract. Logic Program. 4(1–2), 95–138 (2004)
Gärdenfors, P., Rott, H.: Belief revision. In: Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 4, pp 35–132. Oxford University Press (1995)
Gentzen, G.: Investigations into logical deduction. In: Szabo, M.E. (ed.) German. An English Translation Appears in ‘The Collected Works of Gerhard Gentzen’. North-Holland (1969)
Gorogiannis, N., arguments, A. Hunter.: Instantiating abstract argumentation with classical logic Postulates and properties. J. Artif. Intell. 175(9–10), 1479–1497 (2011)
Heyninck, J., Arieli, O.: On the semantics of simple contrapositive assumption-based argumentation frameworks. In: Proceedings of the COMMA’18, vol. 305 of Frontiers in Artificial Intelligence and Applications. IOS Press (2018)
Heyninck, J., Arieli, O.: Simple contrapositive assumption-based frameworks. Accepted to LPNMR’19 (extended abstract in AAMAS’19) (2019)
Heyninck, J., Straßer, C.: Relations between assumption-based approaches in nonmonotonic logic and formal argumentation. In: Proceedings of the NMR’16, pp 65–76 (2016)
Heyninck, J., Straßer, C.: Revisiting unrestricted rebut and preferences in structured argumentation. In: Proceedings of the IJCAI’17, pp 1088–1092. AAAI Press (2017)
Kaci, S., van der Torre, L., Villata, S.: Preference in abstract argumentation. In: Proceedings of the COMMA’18, vol. 305 of Frontiers in Artificial Intelligence and Applications. IOS Press (2018)
Konieczny, S., Marquis, P., Vesic, S.: New inference relations from maximal consistent subsets. In: Proceedings of the KR’18, pp 649–650. AAAI Press (2018)
Konieczny, S., Pino Pérez, R.: Merging information under constraints: a logical framework. Log. Comput. 12(5), 773–808 (2002)
Lin, J.: Integration of weighted knowledge bases. J. Artif. Intell. 83(2), 363–378 (1996)
Malouf, R.: Maximal consistent subsets. Comput. Linguist. 33(2), 153–160 (2007)
Modgil, S., Prakken, H.: A general account of argumentation with preferences. J. Artif. Intell. 195, 361–397 (2013)
Modgil, S., Prakken, H.: The ASPIC+ framework for structured argumentation: a tutorial. Argument and Computation 5(1), 31–62 (2014)
Pigozzi, G., Tsoukias, A., Viappiani, P.: Preferences in artificial intelligence. Ann. Math. Artif. Intell. 77(3-4), 361–401 (2016)
Pollock, J.: How to reason defeasibly. J. Artif. Intell. 57(1), 1–42 (1992)
Prakken, H.: An abstract framework for argumentation with structured arguments. Argument and Computation 1(2), 93–124 (2010)
Prakken, H.: Historical overview of formal argumentation. In: Baroni, P., Gabay, D., Giacomin, M., van der Torre, L. (eds.) Handbook of Formal Argumentation, pp 75–143. College Publications (2018)
Prakken, H., Vreeswijk, G.: Logical systems for defeasible argumentation. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosochical Logic 14, pp 219–318. Kluwer (2002)
Priest, G.: Logic of paradox. J. Philos. Log. 8, 219–241 (1979)
Priest, G.: Reasoning about truth. J. Artif. Intell. 39, 231–244 (1989)
Rescher, N., Manor, R.: On inference from inconsistent premises. Theor. Decis. 1, 179–217 (1970)
Simari, G., Loui, R.P.: A mathematical treatment of defeasible reasoning and its implementation. J. Artif. Intell. 53(2–3), 125–157 (1992)
Straßer, C., Arieli, O.: Sequent-based argumentation for normative reasoning. In: Proceedings of the DEON’14, LNCS 8554. An extended version will appear in the Journal of Logic and Computation (https://doi.org/10.1093/logcom/exv050), pp 224–240. Springer (2014)
Thimm, M., Wallner, J.P.: Some complexity results on inconsistency measurement. In: Proceedings of the KR’16, pp 114–124 (2016)
Tonim, F.: Assumption-based argumentation for epistemic and practical reasoning. Computable Models of the Law, Languages, Dialogues, Games, Ontologies 4884, 185–202 (2008)
Toni, F.: A tutorial on assumption-based argumentation. Argument and Computation 5(1), 89–117 (2014)
Vesic, S.: Identifying the class of maxi-consistent operators in argumentation. J. Artif. Intell. Res. 47, 71–93 (2013)
Vesic, S., van der Torre, L.: Beyond maxi-consistent argumentation operators. In: Proceedings of the JELIA’12, LNCS 7519, pp 424–436. Springer (2012)
Acknowledgements
We thank Christian Straßer and the anonymous reviewers for many comments and helpful suggestions. The work on this paper is supported by the Israel Science Foundation (Grant No.817/15). AnneMarie Borg and Jesse Heyninck are also supported by the Alexander von Humboldt Foundation and the German Ministry for Education and Research.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Arieli, O., Borg, A. & Heyninck, J. A review of the relations between logical argumentation and reasoning with maximal consistency. Ann Math Artif Intell 87, 187–226 (2019). https://doi.org/10.1007/s10472-019-09629-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10472-019-09629-7
Keywords
- Logical argumentation
- Structured argumentation
- Reasoning with maximal consistency
- Defeasible reasoning
- Extension-based semantics
- Dynamic proof systems