Formal Argumentation and Modal Logic

The interrelationship between defeasible argumentation and modal logic is rooted in their shared goal of capturing and modelling reasoning under uncertainty and changing conditions. In the last years, researchers have explored different ways to combine these two formalizations to create more robust systems for handling complex reasoning tasks, in which modal operators can be incorporated into argumentation systems.In this article we analyse three different lines of work to combine modal logic and argumentation: a) a logic-based framework that combines dynamic logic and argumentation for value-based planning; b) alternating-time temporal logic extended with coalitional argumentation; c) different combined approaches for integrating epistemic logics and argumentation. These three alternatives will help the reader to understand different interplays that can take place when combining argumentation and modal logic. On the one hand, we show that argumentation systems can be combined with very different readings of modal operators (i.e., dynamic, temporal and epistemic). On the other hand, modal logic and argumentation can be used in different relative positions. When representing and reasoning about plans, modal logic is applied for the reasoning on the object level and a structured argumentation framework is built on the meta-level over modal logic. When epistemically reasoning about opponents’ argumentative information, modal logic can be built over argumentation. For checking the strategic properties of coalitions of agents, argumentation is put inside modal logic so that the coalition can enlarge according to the theory of coalitional argumentation.