Beliefs supported by binary arguments

In this paper we explore the relation between an agent's doxastic attitude and her arguments in support of a given claim. Our main contribution is the design of a logical setting that allows us reason about binary arguments which are either in favor or against a certain claim. This is a setting in which arguments and propositions are the basic building blocks so that the concept of argument-based belief emerges in a straightforward way. We work against the background of Dung's abstract argumentation framework, extending it to a new setting in which we can study the formal properties of binary arguments as well as the larger structures they establish. This paper introduces a formal `two-dimensional' language to talk about propositions and arguments, for which a sound and complete axiom system is provided.