Logic of Conflicts and Active Set with Uncertainty and Incoherence

Abstract

An active set is a unifying space being able to act as a “bridge” for transferring information, ideas and results between distinct types of uncertainties and different types of applications. An active set is a set of agents who independently deliver true or false values for a given proposition. An active set is not a simple vector of logic values for different propositions, the results are a vector but the set is not. The difference between an ordinary set and active set is that the ordinary set has passive elements with values of the attributes defined by an external agent. In the active set, any element is an agent that internally defines the value of a given attribute for a passive element. Agents in the active set with a special criterion give the logic value for the same attribute. So agents in many cases are in a logic conflict and this generates semantic uncertainty on the logic evaluation. Criteria and agents are the two variables by which we give different logic values to the same attribute or proposition. Active set is beyond the modal logic.