Argument-based Belief in Topological Structures
This work addresses foundational issues in epistemic logic and argumentation theory, offering a novel framework for understanding belief closure, but it is incremental as it builds on existing theories.
The paper tackles the problem of defining belief grounded in arguments by combining topological semantics for evidence structure with abstract argumentation theory, resulting in a formal language and axiom system for argument-based beliefs that are not closed under conjunction.
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.