What About Generic "And"- and "Or"-Operations: from Levels of Certainty (Philosophical-Physical-Mathematical) to a Natural Interpretation of Quantum-Like Negative Degrees of Certainty
Technical Report: UTEP-CS-22-53
Abstract
Fuzzy techniques -- techniques designed to convert imprecise human knowledge into precise computer-understandable terms -- have many successful applications. Traditional applications of fuzzy techniques use only important general features of human reasoning and, to make an implement more efficient, ignore subtle details, details which are not important for the corresponding application. But from the more fundamental viewpoint, it is desirable to understand, in all the detail, how people actually reason. In this paper, we use general ideas of fuzzy approach to answer this question. Interestingly -- and somewhat unexpectedly -- the resulting analysis leads to a natural explanation of existence of several distinct levels of certainty and to a natural appearance of quantum-like negative degrees of certainty.