Categorical Approach to Conflict Resolution: Integrating Category Theory into the Graph Model for Conflict Resolution

This paper introduces the Categorical Graph Model for Conflict Resolution (C-GMCR), a novel framework that integrates category theory into the traditional Graph Model for Conflict Resolution (GMCR). The C-GMCR framework provides a more abstract and general way to model and analyze conflict resolution, enabling researchers to uncover deeper insights and connections. We present the basic concepts, methods, and application of the C-GMCR framework to the well-known Prisoner's Dilemma and other representative cases. The findings suggest that the categorical approach offers new perspectives on stability concepts and can potentially lead to the development of more effective conflict resolution strategies.

State Definition for Conflict Analysis with Four-valued Logic

We examined a four-valued logic method for state settings in conflict resolution models. Decision-making models of conflict resolution, such as game theory and graph model for conflict resolution (GMCR), assume the description of a state to be the outcome of a combination of strategies or the consequence of option selection by the decision-makers. However, for a framework to function as a decision-making system, unless a clear definition of the task of placing information out of an infinite world exists, logical consistency cannot be ensured, and thus, the function may be incomputable. The introduction of paraconsistent four-valued logic can prevent incorrect state setting and analysis with insufficient information and provide logical validity to analytical methods that vary the analysis resolution depending on the degree of coarseness of the available information. This study proposes a GMCR stability analysis with state configuration based on Belnap's four-valued logic.