Paraconsistent structure inside of many-valued logic

Abstract

Here we shall extract those minimal functional means of many-valued logic which are sufficient for the construction of paraconsistent logic. Thereby we shall define a rather wide class of many-valued logics which contain paraconsistent logic as a fragment. Thus one may speak of paraconsistent structure in terms of many-valued logic exactly as one may speak of, for example, modal structure in terms of many-valued logic. Also it will be shown that paraconsistent logic extracted from many-valued logic in its turn contains a fragment which is isomorphous to classical two-valued logic. As will be evidently found out the difference between constructed paraconsistent logic and the specified model for classical logic consists only in the properties of the operation of negation (and in the choice of the set of designated truth values for paraconsistent logic).