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A Logical Framework for Graded Predicates Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Logical Argumentation Principles, Sequents, and Nondeterministic Matrices

Authors : Esther Anna Corsi, Christian G. Fermüller

Published in: Logic, Rationality, and Interaction

Publisher: Springer Berlin Heidelberg

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Abstract

The concept of “argumentative consequence” is introduced, involving only the attack relations in Dung-style abstract argumentation frames. Collections of attack principles of different strength, referring to the logical structure of claims of arguments, lead to new characterizations of classical and nonclassical consequence relations. In this manner systematic relations between structural constraints on abstract argumentation frames, sequent rules, and nondeterministic matrix semantics for corresponding calculi emerge.

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Footnotes
1
Of course, the idea to label arguments in an argumentation frame with formulas is not new (see, e.g., [6, 12, 13]). We use the labels to highlight the logical form of concrete claims, while abstracting away from their particular support or any specific form of attack.
 
2
The same formula may occur as claim of different arguments. Thus we (implictly) refer to occurrences of formulas, rather than to formulas themselves when talking about attacks in a given SAF.
 
3
Note that, if we identify arguments with counter-models and if S contains all relevant counter-models, then argumentative consequence coincides with ordinary logical consequence: every counter-model of the conclusion must invalidate some premise.
 
Literature
1.
Amgoud, L., Besnard, P., Hunter, A.: Foundations for a logic of arguments. In: Logical Reasoning and Computation: Essays dedicated to Luis Fariñas del Cerro, pp. 95–108 (2016)
2.
Arieli, O., Straßer, C.: Sequent-based logical argumentation. Argument Comput. 6(1), 73–99 (2015)CrossRef
3.
4.
Avron, A., Zamansky, A.: Non-deterministic semantics for logical systems. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 16, pp. 227–304. Springer, Dordrecht (2011). doi:10.​1007/​978-94-007-0479-4_​4 CrossRef
5.
Besnard, P., Hunter, A.: Elements of Argumentation. MIT Press, Cambridge (2008)CrossRef
6.
7.
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), 321–357 (1995)MathSciNetCrossRefMATH
8.
9.
Dyrkolbotn, S.: On a formal connection between truth, argumentation and belief. In: Colinet, M., Katrenko, S., Rendsvig, R.K. (eds.) ESSLLI Student Sessions 2013. LNCS, vol. 8607, pp. 69–90. Springer, Heidelberg (2014). doi:10.​1007/​978-3-662-44116-9_​6
10.
Gabbay, D.M.: Dungs argumentation is essentially equivalent to classical propositional logic with the peirce-quine dagger. Logica Universalis 5(2), 255–318 (2011)MathSciNetCrossRefMATH
11.
Gentzen, G.: Untersuchungen über das Logische Schließen I & II. Mathematische Zeitschrift 39(1), 176–210, 405–431 (1935)
12.
Gorogiannis, N., Hunter, A.: Instantiating abstract argumentation with classical logic arguments: Postulates and properties. Artif. Intell. 175(9–10), 1479–1497 (2011)MathSciNetCrossRefMATH
13.
14.
Grossi, D.: On the logic of argumentation theory. In: van der Hoek, W., Kaminka, G., Lesperance, Y., Luck, M., Sandip, S. (eds.) Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, vol. 1, pp. 409–416. International Foundation for Autonomous Agents and Multiagent Systems (2010)
15.
Rahwan, I., Simari, G.R.: Argumentation in Artificial Intelligence. Springer, New York (2009)
16.
Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory, 2nd edn. Cambridge University Press, Cambridge (2000)CrossRefMATH
Metadata
Title
Logical Argumentation Principles, Sequents, and Nondeterministic Matrices
Authors
Esther Anna Corsi
Christian G. Fermüller
Copyright Year
2017
Publisher
Springer Berlin Heidelberg
Book
Logic, Rationality, and Interaction

Print ISBN: 978-3-662-55664-1

Electronic ISBN: 978-3-662-55665-8

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-662-55665-8_29

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