Modelling of AGM-style doxastic operations in three-valued setting

Abstract

The goal of our work is to show how a theoretical approach to modeling of reasoning can be analyzed to identify controversial issues that reveal prospects for further research. We will consider one of the basic approaches to modeling of reasoning based on the concept of belief revision AGM, which is viewed as classical because it formulates the basic concepts of belief, introduces the main ways of representing beliefs, cognitive actions, systems of postulates for cognitive actions and the basic principles for constructing epistemic systems. However, this conceptual foundation raises many controversial issues that require further research, such as the problem of purity of the doxastic operations, the problem of primacy of the doxastic operations and the problem of connection between the doxastic operations. To find a possible solution to these controversial points, we will attempt to model the main ideas of AGM within the framework of standard consistent, and complete logic \L{}3. The basic principle of our translation is the scheme for constructing an epistemic theory proposed by G\"ardenfors, which is considered the basis of AGM. We use a strict three-valued logic formalism to constrain the functioning of doxastic operators and to test how they will function when trying to express the corresponding AGM postulates in a given system. It will allow us to approach the solution of the classical AGM problems or at least to present them from a different perspective. We consider the fundamental possibility of obtaining other doxastic operators in this way and also show how we can implement the minimality criterion for the contraction operator by combining several theorems of three-valued logic. The presented method of translating an informal conceptual scheme into formal logic is convenient for teaching students the basics of modeling and makes it possible to demonstrate the relationships and limitations of the modeled objects and processes.