Static Knowledge vs. Dynamic Argumentation: A Dual Theory Based on Kripke Semantics

TL;DR

This paper introduces a dual framework linking knowledge and argumentation through epistemic and argument Kripke models, establishing a formal duality and illustrating its practical and philosophical implications.

Contribution

It develops a dual theory connecting knowledge and argumentation using Kripke semantics, including a generation method and a duality theorem, bridging epistemic logic and argumentation theory.

Findings

Established duality between epistemic and argument Kripke models

Provided a generation method for dual models with formal justification

Demonstrated practical utility through realistic examples

Abstract

This paper establishes a dual theory about knowledge and argumentation. Our idea is rooted at both epistemic logic and argumentation theory, and we aim to merge these two fields, not just in a superficial way but to thoroughly disclose the intrinsic relevance between knowledge and argumentation. Specifically, we define epistemic Kripke models and argument Kripke models as a dual pair, and then work out a two-way generation method between these two types of Kripke models. Such generation is rigorously justified by a duality theorem on modal formulae's invariance. We also provide realistic examples to demonstrate our generation, through which our framework's practical utility gets strongly advocated. We finally propose a philosophical thesis that knowledge is essentially dynamic, and we draw certain connection to Maxwell's demon as well as the well-known proverb "knowledge is power".