紀要論文 A system of pair sentential calculus that has a representation of the Liar sentence
A system of pair sentential calculus that has a representation of the Liar sentence

石井,忠夫

1pp.1 - 10 , 2015-04-01 , 新潟国際情報大学情報文化学部
ISSN:1343490X
NII書誌ID(NCID):AA11231962
内容記述
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.
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http://lbir.nuis.ac.jp/infolib/user_contents/lbir/kiyo/kiyo_2015.01.03.pdf

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