On Conflicts

In this article a mathematical model of conflict situations, based on three binary relations: alliance, conflict and neutrality, is introduced. Axioms for alliance and conflict relations are given and some properties of these relations are investigated. Further, the strength of an object is introduced. The set of the three relations mentioned above, together with the strength of all objects, is called the situation. Some rules of transformation of situations are introduced and investigated. Finally, the notion of a capture is defined and the rules of sharing of the capture among objects in a given situation are formulated. Some theorems concerning capture sharing are given. The approach presented can be used as a starting point for an easy computer simulation of conflict situations.