Publication Date



Technical Report: UTEP-CS-19-44


It is well known that the traditional 2-valued logic is only an approximation to how we actually reason. To provide a more adequate description of how we actually reason, researchers proposed and studied many generalizations and modifications of the traditional logic, generalizations and modifications in which some rules of the traditional logic are no longer valid. Interestingly, for some of such rules (e.g., for law of excluded middle), we have a century of research in logics that violate this rule, while for others (e.g., commutativity of ``and''), practically no research has been done. In this paper, we show that fuzzy ideas can help explain why some non-classical logics are more studied and some less studied: namely, it turns out that most studied are the violations which can be implemented by the simplest expressions (specifically, by polynomials of the lowest order).