Anticipation and Hyperincursion in Belief Formation Based on Evidence

Characteristics of anticipation are considered in belief formation based on crisp evidence. In this paper, anticipation is understood as an ability of the system affording us some useful guide to seek further pieces of evidence in order to give a solution for a given problem with which we are concerned. Then two kinds of anticipation are examined in the belief formation systems depending on whether evidence is incomplete or contradictory, respectively. This examination assumes the closed-world assumption on belief formation. Further kind of anticipation is pointed out under the open-world assumption.