An Abstract Look at Awareness Models and Their Dynamics

This work builds upon a well-established research tradition on modal logics of awareness. One of its aims is to export tools and techniques to other areas within modal logic. To this end, we illustrate a number of significant bridges with abstract argumentation, justification logics, the epistemic logic of knowing-what and deontic logic, where basic notions and definitional concepts can be expressed in terms of the awareness operator combined with the box modality. Furthermore, these conceptual links point to interesting properties of awareness sets beyond those standardly assumed in awareness logics, i.e. positive and negative introspection. We show that the properties we list are characterised by corresponding canonical formulas, so as to obtain a series of off-the-shelf axiomatisations for them. As a second focus, we investigate the general dynamics of this framework by means of event models. Of specific interest in this context is to know under which conditions, given a model that satisfies some property, the update with an event model keeps it within the intended class. This is known as the closure problem in general dynamic epistemic logics. As a main contribution, we prove a number of closure theorems providing sufficient conditions for the preservation of our properties. Again, these results enable us to axiomatize our dynamic logics by means of reduction axioms.Comment: In Proceedings TARK 2023, arXiv:2307.0400

Awareness Logic: A Kripke-based Rendition of the Heifetz-Meier-Schipper Model

Heifetz, Meier and Schipper (HMS) present a lattice model of awareness. The HMS model is syntax-free, which precludes the simple option to rely on formal language to induce lattices, and represents uncertainty and unawareness with one entangled construct, making it difficult to assess the properties of either. Here, we present a model based on a lattice of Kripke models, induced by atom subset inclusion, in which uncertainty and unawareness are separate. We show the models to be equivalent by defining transformations between them which preserve formula satisfaction, and obtain completeness through our and HMS' results.Comment: 18 pages, 2 figures, proceedings of DaLi conference 202

Informe bibliográfico sobre la lógica (epistémica) de la conciencia

Awareness Logic is an extension of epistemic logic that solves the problem of logical omniscience by incorporating an awareness operator that separates the explicit knowledge from the implicit one. This report collects the most prominent works regarding the beginnings of this logic, as well as its developments in the past three decades. Specifically, it reviews the approaches from Dynamic Epistemic Logic, from the ones that combine other logics with Awareness Logic and those from Game Theory.La lógica de la conciencia es una extensión de la lógica epistémica que solventa el problema de la omnisciencia lógica incorporando un operador de conciencia para separar el conocimiento explícito del implícito. Este informe recopila los principales textos tanto de los orígenes de esta lógica, así como de sus desarrollos en las últimas tres décadas. En concreto analiza los enfoques desde la lógica epistémica dinámica, desde su combinación con otras lógicas y los enfoques de teoría de juegos

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