Argument-based Belief in Topological Structures

Abstract

This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and we use argumentation theory to single out the relevant sets of evidence through which a notion of beliefs grounded on arguments is defined. We discuss the formal properties of this newly defined notion, providing also a formal language with a matching modality together with a sound and complete axiom system for it. Despite the fact that our agent can combine her evidence in a 'rational' way (captured via the topological structure), argument-based beliefs are not closed under conjunction. This illustrates the difference between an agent's reasoning abilities (i.e. the way she is able to combine her available evidence) and the closure properties of her beliefs. We use this point to argue for why the failure of closure under conjunction of belief should not bear the burden of the failure of rationality.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Beliefs supported by binary arguments

“…Another aspect we have not explored in this paper deals with combined arguments of claims that together provide the support in favor or against their conjunction. The study of combined arguments ties in nicely with an ongoing project by the authors on a topological setting that provides a semantics for arguments (Shi et al, 2017), very much in the spirit of the topological semantics for evidence-based beliefs in Baltag et al (2016a). Moreover, a multi-agent extension of some of the ideas presented in this paper has been provided in Shi (2016), in order to deal with argumentation games and the notion of distributed belief.…”

“…Still, for applications, one can briefly mention Shi (2016), where the logic is used not only to discuss the notion of distributed belief, but also to analyse a 'two-player argumentation game', illustrating how a single agent's belief and the group's distributed belief are decided by the corresponding argumentation. For a deeper discussion about using arguments (and, more generally, using evidence/justifications) for supporting beliefs, the reader is referred to Baltag et al (2014), Baltag, Bezhanishvili, Özgün, and Smets (2016b) and Shi, Smets, and Velázquez-Quesada (2017).…”

An Awareness Epistemic Framework for Belief, Argumentation and Their Dynamics

“…Yet another natural candidate to model justification consists in using conceptual and technical tools coming from argumentation theory (as done, e.g. in [23,36,28,15]).…”

Classical verification of quantum circuits containing few basis changes

“…Among different attempts to find a solution to this quandary, it has been suggested that the answer might lie in the particular structure of the computation. In particular, it was proposed in [1] that the quantumness of a quantum circuit is derived from layers of operations that do not preserve the computational basis. The intuition behind this claim follows from a simple but insightful observation.…”

“…the Hadamard gates. With this view in mind, the Fourier hierarchy FH was introduced in [1]. Each level FH k of the hierarchy corresponds to the class of problems solvable by polynomial-size quantum circuits, composed of gates that preserve the computational basis and k layers of operations that do not preserve it.…”