A generalized notion of consistency with applications to formal argumentation

We propose a generic notion of consistency in an abstract labelling setting, based on two relations: one of intolerance between the labelled elements and one of incompatibility between the labels assigned to them, thus allowing a spectrum of consistency requirements depending on the actual choice of these relations. As a first application to formal argumentation, we show that traditional Dung's semantics can be put in correspondence with different consistency requirements in this context. We consider then the issue of consistency preservation when a labelling is obtained as a synthesis of a set of labellings, as is the case for the traditional notion of argument justification. In this context we provide a general characterization of consistency-preserving synthesis functions and analyze the case of argument justification in this respect

Stability and Relevance in Incomplete Argumentation Frameworks

We explore the computational complexity of stability and relevance in incomplete argumentation frameworks (IAFs), abstract argumentation frameworks that encode qualitative uncertainty by distinguishing between certain and uncertain arguments and attacks. IAFs can be specified by, e.g., making uncertain arguments or attacks certain; the justification status of arguments in an IAF is determined on the basis of the certain arguments and attacks. An argument is stable if its justification status is the same in all specifications of the IAF. For arguments that are not stable in an IAF, the relevance problem is of interest: which uncertain arguments or attacks should be investigated for the argument to become stable? We redefine stability and define relevance for IAFs and study their complexity

A generalized notion of consistency with applications to formal argumentation

We propose a generic notion of consistency in an abstract labelling setting, based on two relations: one of intolerance between the labelled elements and one of incompatibility between the labels assigned to them, thus allowing a spectrum of consistency requirements depending on the actual choice of these relations. As a first application to formal argumentation, we show that traditional Dung’s semantics can be put in correspondence with different consistency requirements in this context. We consider then the issue of consistency preservation when a labelling is obtained as a synthesis of a set of labellings, as is the case for the traditional notion of argument justification. In this context we provide a general characterization of consistency-preserving synthesis functions and analyze the case of argument justification in this respect

Arguments to believe and beliefs to argue. Epistemic logics for argumentation and its dynamics

Arguing and believing are two skills that have typically played a crucial role in the analysis of human cognition. Both notions have received notable attention from a broad range of disciplines, including linguistics, philosophy, psychology, and computer science. The main goal of this dissertation consists in studying from a logical perspective (that is, focused on reasoning) some of the existing relations between beliefs and argumentation. From a methodological point of view, we propose to combine two well-known families of formalisms for knowledge representation that have been relatively disconnected (with some salient exceptions): epistemic logic (Fagin et al., 2004; Meyer and van der Hoek, 1995) together with its dynamic extensions (van Ditmarsch et al., 2007; van Benthem, 2011), on the one hand, and formal argumentation (Baroni et al., 2018; Gabbay et al., 2021), on the other hand. This choice is arguably natural. Epistemic logic provides well-known tools for qualitatively representing epistemic attitudes (belief, among them). Formal argumentation, on its side, is the broad research field where mathematical representations of argumentative phenomena are investigated. Moreover, the notion of awareness, as treated in the epistemic logic tradition since Fagin and Halpern (1987), can be used as a theoretical bridge among both areas. This dissertation is presented as a collection of papers [compendio de publicaciones], meaning that its main contributions are contained in the reprint of six works that have been previously published, placed in Chapter 4. In chapter 1, we pursue a general introduction to the research problem. Chapter 2 is devoted to the presentation of the technical tools employed through the thesis. Chapter 3 explains how the contributions approach the research problem. Chapter 5 provides a general discussion of results, by analysing closely related work. We conclude in Chapter 6 with some remarks and open paths for future research