A system of pair sentential calculus that has a representation of the Liar sentenceA system of pair sentential calculus that has a representation of the Liar sentenceAA11231962 A system of pair sentential calculus that has a representation of the Liar sentence
In this paper we will introduce a referential relation between pair-sentences similar to the identity connective in SCI. Here pair-sentence statements of the form (A,B) read as “A is referential to B”. Then by interpreting the pair-sentence (A,B) as a sequence of referential relation such that the referential recursive pattern A B0 B1 B2 . . .B0 B1 B2 . . .holds, we will formalize a pair sentential calculus and represent the behavior of Liar sentence.To formalize the pair sentential calculus, we firstly introduce the stage numbers i, j in which each of pair-sentence holds, i.e., (Ai,Bj) and which means a situation of A at a stage i is referential to the situation of B at a stage j. We also introduce a referential cycle number of (Ai,Bj) and by using of this cycle number, we may classify pair-sentences into two categories, that is, categorical and paradoxical. Then each Liar sentence has a referential cycle number of n such that n 2 and is paradoxical.