Bochvar's three-valued logic and literal paralogics: Their lattice and functional equivalence

Abstract

In the present paper, various features of the class of propositional literal paralogics are considered. Literal paralogics are logics in which the paraproperties such as paraconsistence, paracompleteness and paranormality, occur only at the level of literals; that is, formulas that are propositional letters or their iterated negations. We begin by analyzing Bochvar’s three-valued nonsense logic B 3 , which includes two isomorphs of the propositional classical logic CPC. The combination of these two ‘strong’ isomorphs leads to the construction of two famous paralogics P 1 and I 1 , which are functionally equivalent. Moreover, each of these logics is functionally equivalent to the fragment of logic B 3 consisting of external formulas only. In conclusion, we structure a four-element lattice of three-valued paralogics with respect to the possession of paraproperties.