Abstract

This paper introduces a multi-agent dynamic epistemic logic for abstract argumentation. Its main motivation is to build a general framework for modelling the dynamics of a debate, which entails reasoning about goals, beliefs, as well as policies of communication and information update by the participants. After locating our proposal and introducing the relevant tools from abstract argumentation, we proceed to build a three-tiered logical approach. At the first level, we use the language of propositional logic to encode states of a multi-agent debate. This language allows to specify which arguments any agent is aware of, as well as their subjective justification status. We then extend our language and semantics to that of epistemic logic, in order to model individuals’ beliefs about the state of the debate, which includes uncertainty about the information available to others. As a third step, we introduce a framework of dynamic epistemic logic and its semantics, which is essentially based on so-called event models with factual change. We provide completeness results for a number of systems and show how existing formalisms for argumentation dynamics and unquantified uncertainty can be reduced to their semantics. The resulting framework allows reasoning about subtle epistemic and argumentative updates—such as the effects of different levels of trust in a source—and more in general about the epistemic dimensions of strategic communication.

Highlights

  • We aim to show that dynamic epistemic logic (DEL) can serve as a general framework to deal with many conceptual aspects of argumentation which are of interest in general argumentation theory and its more recent developments in AI and computer science, in the study of computational models of argument

  • We introduce the general semantics of epistemic argumentative models (Definition 8)

  • Standard approaches to the dynamics of argumentation framework (AF) focus almost exclusively on changes generated by addition and deletion of arguments and/or attacks, leaving epistemic updates aside (Doutre and Mailly 2018)

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Summary

Historical background and general motivations

By bringing together two different formal traditions such as epistemic modal logic and abstract argumentation, we aim to provide results of interest for both, and to show that their respective toolboxes provide powerful conceptual resources to think both traditions in a different light. 7. From a normative perspective, many interesting real-life mechanisms of information update are deemed “descriptive” and left to psychologists, when not discarded as reasoning flaws of an imperfect reasoner. Many interesting real-life mechanisms of information update are deemed “descriptive” and left to psychologists, when not discarded as reasoning flaws of an imperfect reasoner This holds for confirmation bias (Wason 1960), more adequately called myside bias (Perkins et al 1986)—that is the tendency to strictly evaluate information disconfirming our prior opinions and, vice versa, loosely filter and search for confirming evidence—and for the operation by which we reduce cognitive dissonance upon receiving information which is inconsistent with our prior beliefs (Festinger 1957). A careful logical construction is needed though, that we begin

Multi-agent argumentation frameworks
Encoding argumentative notions
Epistemic logics for abstract argumentation
Epistemic and argumentative dynamics
Relation to other formalisms
Incomplete AFs
From incomplete AFs to EA-models
From EA-models to incomplete AFs
Control AFs
Reasoning about opponent models
Encodings
Proof of Theorem 1
Preserving doxastic relations via an enhanced truth condition
Incomplete and control AFs
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