A propositional fragment of Leśniewski's ontology and its formulation by the tableau method

✍ Scribed by Mitsunori Kobayashi; Arata Ishimoto

• Publisher: Springer Netherlands
• Year: 1982
• Tongue: English
• Weight: 938 KB
• Volume: 41
• Category: Article
• ISSN: 0039-3215
• DOI: 10.1007/bf00370344

✦ Synopsis

The propositional fragment E1 of Legniewski's ontology is the smallest class (of formulas) containing besides all the instances of tautology the formulas o~ the forms: z(a,b) D ~(a,a), ~(a,b)^r e(a,c) and ~(a,b)Ar ~(b,a) being closed under detachment. The purpose of this paper is to furnish another more constructive proof than that given earlier by one of us for:

Theorem A is provable in ~1 iff TA is a thesis of first-order s logic with equality, where T is a translation of ~he formulas of Z 1 into those of first.order predicate logic with equality such that T~(a, b) = .FbtXFaX (Russellian.type definite description),