On argumentation logic and propositional logic
File(s)
Published version
Author(s)
Kakas, A
Mancarella, P
Toni, F
Type
Journal Article
Abstract
This paper studies the relationship between Argumentation Logic (AL), a recently defined logic based on the study of argumentation in AI, and classical Propositional Logic (PL). In particular, it shows that AL and PL are logically equivalent in that they have the same entailment relation from any given classically consistent theory. This equivalence follows from a correspondence between the non-acceptability of (arguments for) sentences in AL and Natural Deduction (ND) proofs of the complement of these sentences. The proof of this equivalence uses a restricted form of ND proofs, where hypotheses in the application of the Reductio of Absurdum inference rule are required to be “relevant” to the absurdity derived in the rule. The paper also discusses how the argumentative re-interpretation of PL could help control the application of ex-falso quodlibet in the presence of inconsistencies.
Date Issued
2017-07-19
Date Acceptance
2017-06-03
Citation
Studia Logica, 2017, 106 (2), pp.237-279
ISSN
1572-8730
Publisher
Springer Verlag (Germany)
Start Page
237
End Page
279
Journal / Book Title
Studia Logica
Volume
106
Issue
2
Copyright Statement
© The Author(s) 2017. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Subjects
Science & Technology
Arts & Humanities
Physical Sciences
Mathematics
Logic
Philosophy
Science & Technology - Other Topics
Argumentation
Propositional logic
Natural deduction
Reductio ad Absurdum
ACCEPTABILITY
01 Mathematical Sciences
08 Information And Computing Sciences
22 Philosophy And Religious Studies
General Mathematics
Publication Status
Published