Incompleteness in the Bell Theorem Involving All Settings of Measuring Apparatus

A. Here, we consider the Bell experiment for a system described by multipartite states in the case where n-observables are measured per site.If n is two, we consider a two-setting Bell experiment.If n is infinite, we consider an infinite-setting Bell experiment.Two-setting model is an explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment.Infinite-setting model is an explicit local realistic model for the values of a correlation function, given in an infinite-setting Bell experiment.In the non-contextual scenario, there is not the essential difference between infinite-setting model and two-setting model.And we cannot classify local realistictheories in this case.This says that we can construct infinite-setting model from two-setting model.Surprisingly we can discuss incompleteness in the Bell theorem by using non-contextual models.On the other hand, in the contextual scenario, there is the essential difference between infinite-setting model and two-setting model.This says that we must distinguish infinite-setting model from two-setting model.And we can classify local realistic theories in this case.