||A syntactical comparison between pair sentential calculus PSC and Gupta's definitional calculus Cn
A syntactical comparison between pair sentential calculus PSC and Gupta's definitional calculus Cn
13 , 2016-04-01 , 新潟国際情報大学情報文化学部
In this paper we will compare two logical systems PSC and Cn with a syntactical point of view. Because both notions of the pair-sentence with stage number in PSC and Gupta's sentence-definition with revision stage number in Cn are very similar, and both can deal with paradoxical sentences like a simple Liar sentence. His system was defined as a predicate calculus, but here we will introduce the propositional version of Cn for the comparison, and we had the following results: (1) C0 is a sublogic of PSC, or PSC is an extension of C0 under the two translations tC and tP. Similarly, PSCn is an extension of Cn. (2) If we extend the systems C0 and Cn by adding three properties: exchangeability, transitivity and relativity of revision indices, then two logics C0 and PSC (also Cn and PSCn) are syntactically equivalent. (3) We can calculate a cycle number of each pair sentence in PSC, but not in C0. (4) PSC can deal with multiple pair sentences, but difficult to deal with such multiple defnitions in Cn.