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

Abstract

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 B3, 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 B3 consisting of external formulas only. In conclusion, we structure a four-element lattice of threevalued paralogics with respect to the possession of paraproperties.

Automated Proof-searching for Strong Kleene Logic and its Binary Extensions via Correspondence Analysis

“…In the case of the only designated value 1, this class contains implications → i , 1 i 8. Note that → 7 is an implication of Karpenko and Tomova's literal paralogic TK 2 [22] (TK 1 's implication is → 4 ). Moreover, → 8 is Sette's implication [45].…”

A Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics

“…The class of LPP logics is well studied. Among the LPP logics considered in this paper, there are the logics described in [19], [18], [21], [16], [7], [12], [5], [15].…”

“…There are several algorithms of constructing classes of such logics, for example, we can note the following ones: (1) construction of LPP logics by combination of isomorphs of classical logic CP C [11]; (2) construction of LPP logics by using literal-paraconsistent-paracomplete matrices (or LPPmatrices) [13]. But the classes of LPP logics constructed by these two methods are not equal: the class obtained by (1) is a subclass of the class obtained by (2).…”

Truth and legal argumentation in Fyodor Dostoevsky's The Karamazov Brothers

“…The difference between employing (iii) and (iv) for modelling the DM case is discussed in[1]; the formalisms based on such orderings -in[11,12].…”