Non-Monotonic Inference Properties for Assumption-Based Argumentation

Čyras, Kristijonas; Toni, Francesca

doi:10.1007/978-3-319-28460-6_6

Cited by 20 publications

(26 citation statements)

References 26 publications

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“…Studies of inferential behavior of logical argumentation, and in particular its relation to nonmonotonic reasoning, can also be found in (Arieli and Straßer 2019, Section 5), in the context of dynamic proof systems. Similar studies for ABA and ASPIC systems appear, respectively, in ( Čyras and Toni 2015;Heyninck and Arieli 2020;Heyninck and Straßer 2021) and in (Li, Oren, and Parsons 2018).…”

Section: Literature Reviewsupporting

confidence: 59%

Characterizations and Classifications of Argumentative Entailments

Arieli

Borg

Straßer

2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

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In this paper we provide a detailed analysis of the inference process induced by logical argumentation frameworks. The frameworks may be defined with respect to any propositional language and logic, different arguments that represent deductions in the logic, various support-based attack relations between arguments, and all the complete Dung-style semantics for the frameworks. We show that, ultimately, for characterizing the inference process with respect to a given framework, extension-based semantics may be divided into two types: single-extension and multiple-extension, which induce respective kinds of entailment relations. These entailments are further classified by the way they tolerate new information (nonmonotonicity-related properties) and maintain conflicts among arguments (inconsistency-related properties).

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Section: Literature Reviewsupporting

confidence: 59%

Characterizations and Classifications of Argumentative Entailments

Arieli

Borg

Straßer

2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

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“…Several works investigate postulates for nonmonotonic reasoning known from conditional logics [23] for specific structured argumentation formalisms, such as assumptionbased argumentation [1,8,16,18] and ASPIC + [25]. These works revealed gaps between nonmonotonic reasoning and argumentation which we try to bridge in this paper.…”

Section: Related Workmentioning

confidence: 99%

On the correspondence between abstract dialectical frameworks and nonmonotonic conditional logics

Heyninck

Kern-Isberner

Thimm

et al. 2021

Ann Math Artif Intell

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The exact relationship between formal argumentation and nonmonotonic logics is a research topic that keeps on eluding researchers despite recent intensified efforts. We contribute to a deeper understanding of this relation by investigating characterizations of abstract dialectical frameworks in conditional logics for nonmonotonic reasoning. We first show that in general, there is a gap between argumentation and conditional semantics when applying several intuitive translations, but then prove that this gap can be closed when focusing on specific classes of translations.

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“…A number of works have studied the conditional inferential behaviour of formal argumentation formalisms. In structured argumentation, there are a number of works that study KLM-like properties of argumentative inference relations (Borg, Straßer, and Arieli 2020;Heyninck and Arieli 2018;Heyninck and Straßer 2020;Čyras and Toni 2015;Cyras and Toni 2016;Li, Oren, and Parsons 2017). These work differ both in host formalism (various formalisms for structured argumentation versus ADFs) and the way conditional inference is defined.…”

Section: Related Workmentioning

confidence: 99%

Revision and Conditional Inference for Abstract Dialectical Frameworks

Heyninck

Kern-Isberner

Rienstra

et al. 2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

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For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that similar relationships between belief revision, defeasible conditionals and nonmonotonic inference hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

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Non-Monotonic Inference Properties for Assumption-Based Argumentation

Cited by 20 publications

References 26 publications

Characterizations and Classifications of Argumentative Entailments

Characterizations and Classifications of Argumentative Entailments

On the correspondence between abstract dialectical frameworks and nonmonotonic conditional logics

Revision and Conditional Inference for Abstract Dialectical Frameworks

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