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.

A new framework for conflict resolution is proposed by incorporating the permissible range in the decision-maker’s preference order. By setting the permissible range, the decision-maker’s preferences can be categorized as either "permissible" or "impermissible". The new method enables primary analysis based on the limited information regarding states that decision-makers cannot tolerate. The analysis and classification of the stability depending on the conditions of the decision-maker’s permissible range in conflicts are demonstrated, using a graph model for conflict resolution , followed by application to real-world conflicts.

A new analysis method that describes the influence of external factors on state transitions in an interstate conflict has been developed using the Graph Model for Conflict Resolution (GMCR). In this method, the external factors are assumed to be other than those attributed to the conflict’s decision-makers, while the analytical focus is on the resulting consequences. Thus, we assume that the primary decision-makers can be given new reachability through the influence of external factors, such as arbitrators and obstructionists. We examined the validity of this method by applying this new framework to the Cuban Missile Crisis.

In game theory and other decision-making frameworks that seek solutions in conflict situations, the ranking that ordinally expresses degrees of the decision maker's preference for possible strategies has a significant impact on the analysis results. In this paper, we examine a new method to formulate preference rankings with the perspective of avoiding escalation of conflicts that incorporates TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution). The Graph Model for Conflict Resolution (GMCR) was used for the analysis, using the preference ranks obtained by both the standard method in which the analysts set the preference ranks subjectively and the new TOPSIS method, which incorporates a de-escalation perspective. As a result, it was found that the analysis method using TOPSIS ranking with de-escalation aspect was able to obtain conflict analysis results that more clearly reflected the intention of the analysis when compared with the standard method.