Abstract
In this paper we extend our first results concerning the characterisation of the graph structure of logic based argumentation graphs with two main classes of findings. First we provide full proofs for the structural results of argumentation graphs built over Datalog± knowledge base composed of facts and negative constraints solely. Second, we also provide some structural properties for the general case of knowledge bases composed of facts, rules and negative constraints.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In the rest of the paper, and in order to simplify the notation, we omit cycles corresponding to singleton orbits.
- 2.
We say that a tuple of arguments \((a_1, \ldots , a_n)\) is a cycle if and only if \(a_1 \mathcal {C}a_2\), \(\ldots \), \(a_{n-1} \mathcal {C}a_n\) and \(a_n \mathcal {C}a_1\).
References
Amgoud, L.: Postulates for logic-based argumentation systems. Int. J. Approx. Reasoning 55(9), 2028–2048 (2014)
Arioua, A., Croitoru, M.: A dialectical proof theory for universal acceptance in coherent logic-based argumentation frameworks. In: 22nd European Conference on Artificial Intelligence, ECAI 2016, 29 August–2 September 2016, The Hague, The Netherlands - Including Prestigious Applications of Artificial Intelligence, PAIS 2016, pp. 55–63 (2016)
Arioua, A., Croitoru, M., Buche, P.: DALEK: a tool for dialectical explanations in inconsistent knowledge bases. In: Computational Models of Argument - Proceedings of COMMA 2016, Potsdam, Germany, 12–16 September, 2016, pp. 461–462 (2016)
Arioua, A., Buche, P., Croitoru, M.: Explanatory dialogues with argumentative faculties over inconsistent knowledge bases. Expert Syst. Appl. 80, 244–262 (2017)
Arioua, A., Croitoru, M., Vesic, S.: Logic-based argumentation with existential rules. Int. J. Approx. Reasoning 90, 76–106 (2017)
Baget, J.-F., Leclère, M., Mugnier, M.-L., Salvat, E.: On rules with existential variables: walking the decidability line. Artif. Intell. 175(9–10), 1620–1654 (2011)
Baroni, P., Giacomin, M., Guida, G.: SCC-recursiveness: a general schema for argumentation semantics. Artif. Intell. 168(1–2), 162–210 (2005)
Baroni, P., Caminada, M., Giacomin, M.: An introduction to argumentation semantics. Knowl. Eng. Rev. 26(4), 365–410 (2011)
Bienvenu, M.: On the complexity of consistent query answering in the presence of simple ontologies. In: Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence, 22–26 July 2012, Toronto, Ontario, Canada (2012)
Bisquert, P., Croitoru, M., de Saint-Cyr, F.D., Hecham, A.: Substantive irrationality in cognitive systems. In: 22nd European Conference on Artificial Intelligence, ECAI 2016, 29 August–2 September 2016, The Hague, The Netherlands - Including Prestigious Applications of Artificial Intelligence (PAIS 2016), pp. 1642–1643 (2016)
Calì, A., Gottlob, G., Lukasiewicz, T.: A general datalog-based framework for tractable query answering over ontologies. In: Proceedings of the Twenty-Eighth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2009, 19 June–1 July 2009, Providence, Rhode Island, USA, pp. 77–86 (2009)
Caminada, M., Amgoud, L.: On the evaluation of argumentation formalisms. Artif. Intell. 171(5–6), 286–310 (2007)
Cerutti, F., Dunne, P.E., Giacomin, M., Vallati, M.: Computing preferred extensions in abstract argumentation: a SAT-Based approach. In: Theory and Applications of Formal Argumentation - Second International Workshop, TAFA 2013, Beijing, China, 3–5 August 2013, Revised Selected papers, pp. 176–193 (2013)
Croitoru, M., Vesic, S.: What can argumentation do for inconsistent ontology query answering? In: Liu, W., Subrahmanian, V.S., Wijsen, J. (eds.) SUM 2013. LNCS (LNAI), vol. 8078, pp. 15–29. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40381-1_2
Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-Person games. Artif. Intell. 77(2), 321–358 (1995)
Gaggl, S.A., Woltran, S.: The cf2 argumentation semantics revisited. J. Log. Comput. 23(5), 925–949 (2013)
Hecham, A., Arioua, A., Stapleton, G., Croitoru, M.: An empirical evaluation of argumentation in explaining inconsistency tolerant query answering. In: 30th International Workshop on Description Logics, DL 2017, Montpellier, France (2017)
Hecham, A., Croitoru, M., Bisquert, P.: Argumentation-based defeasible reasoning for existential rules. In: Proceedings of the 16th Conference on Autonomous Agents and MultiAgent Systems, AAMAS 2017, São Paulo, Brazil, 8–12 May 2017, pp. 1568–1569 (2017)
Lagniez, J.-M., Lonca, E., Mailly, J.-G.: CoQuiAAS: a constraint-based quick abstract argumentation solver. In: 2015 IEEE 27th International Conference on Tools with Artificial Intelligence (ICTAI), pp. 928–935. IEEE (2015)
Lembo, D., Lenzerini, M., Rosati, R., Ruzzi, M., Savo, D.F.: Inconsistency-tolerant semantics for description logics. In: Hitzler, P., Lukasiewicz, T. (eds.) RR 2010. LNCS, vol. 6333, pp. 103–117. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15918-3_9
Thimm, M., Villata, S., Cerutti, F., Oren, N., Strass, H., Vallati, M.: Summary report of the first international competition on computational models of argumentation. AI Mag. 37(1), 102 (2016)
Thomazo, M., Rudolph, S.: Mixing materialization and query rewriting for existential rules. In: 21st European Conference on Artificial Intelligence, ECAI 2014, 18–22 August 2014, Prague, Czech Republic - Including Prestigious Applications of Intelligent Systems, PAIS 2014, pp. 897–902 (2014)
Yun, B., Croitoru, M.: An argumentation workflow for reasoning in ontology based data access. In: Computational Models of Argument - Proceedings of COMMA 2016, Potsdam, Germany, 12–16 September 2016, pp. 61–68 (2016)
Yun, B., Croitoru, M., Bisquert, P.: Are ranking semantics sensitive to the notion of core? In: Autonomous Agents and Multiagent Systems - Proceedings of AAMAS 2017, Sao Paulo, Bresil, 8–12 May 2017
Yun, B., Vesic, S., Croitoru, M., Bisquert, P., Thomopoulos, R.: A structural benchmark for logical argumentation frameworks. In: Proceedings of the 20th International Symposium on Intelligent Data Analysis (2017)
Yun, B., Croitoru, M., Vesic, S., Bisquert, P.: A structural benchmark for logical argumentation frameworks. In: Proceedings of the 17th Conference on Autonomous Agents and MultiAgent Systems, AAMAS (2018)
Zhang, H., Zhang, Y., You, J.-H.: Expressive completeness of existential rule languages for ontology-based query answering. In: Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI 2016, New York, NY, USA, 9–15 July 2016, pp. 1330–1337 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Yun, B., Croitoru, M., Vesic, S., Bisquert, P. (2018). Graph Theoretical Properties of Logic Based Argumentation Frameworks: Proofs and General Results. In: Croitoru, M., Marquis, P., Rudolph, S., Stapleton, G. (eds) Graph Structures for Knowledge Representation and Reasoning. GKR 2017. Lecture Notes in Computer Science(), vol 10775. Springer, Cham. https://doi.org/10.1007/978-3-319-78102-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-78102-0_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78101-3
Online ISBN: 978-3-319-78102-0
eBook Packages: Computer ScienceComputer Science (R0)