Dynamic epistemic logics for abstract argumentation

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.

Abstract Argumentation with Qualitative Uncertainty: An Analysis in Dynamic Logic

“…Epistemic Interpretation of CAFs. In order to throw some intuition, let us briefly recall the epistemic interpretation of CAFs provided in [32]. A CAF can be thought as modelling an agent (the proponent) who is trying to convince another agent (the opponent) to accept certain argument(s).…”

“…A completion can be seen as a provisional removal of uncertainty or, in epistemic terms, as a possible world (cf. [27,32]). This removal lets the proponent reason under the assumption that the opponent's AF is such-and-such.…”

On the Epistemic Logic of Incomplete Argumentation Frameworks

“…Epistemic logic of visibility or observability was born as a lightweight alternative to standard epistemic logic (van der Hoek, Troquard, and Wooldridge 2011;Herzig, Lorini, and Maffre 2018;Cooper et al 2021). We consider its singleagent version and adapt it to our purposes.…”

“…The formal argumentation community has recently made efforts to relax this assumption. This has been done using quantitative methods, mainly probabilistic (Li, Oren, and Norman 2011), and qualitative ones. Among the second type, incomplete argumentation frameworks (IAFs) are prominent (Coste-Marquis et al 2007;Baumeister, Neugebauer, and Rothe 2018;Baumeister et al 2018b;Fazzinga, Flesca, and Furfaro 2020).…”

An Awareness Epistemic Framework for Belief, Argumentation and Their Dynamics

“…These can be divided in two groups. On the one hand, there are works using epistemic logic tools to reason about argumentation frameworks [35,34,33]. On the other hand, there are works using argumentation tools to provide an (argumentatively inspired) notion of justified belief (the already mentioned [23,36,28,15]).…”