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

Studia Logica 41 (2-3):181 - 195 (1982)
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Abstract

The propositional fragment L 1 of Leniewski's ontology is the smallest class (of formulas) containing besides all the instances of tautology the formulas of the forms: (a, b) (a, a), (a, b) (b,). (a, c) and (a, b) (b, c). (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 L 1 iff TA is a thesis of first-order predicate logic with equality, where T is a translation of the formulas of L 1 into those of first-order predicate logic with equality such that T(a, b) = FblxFax (Russeltian-type definite description), TA B = TA TB, T A = TA, etc.

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Citations of this work

Lesniewski and Russell's paradox: Some problems.Rafal Urbaniak - 2008 - History and Philosophy of Logic 29 (2):115-146.
A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB.Takao Inoue - 2021 - Bulletin of the Section of Logic 50 (4):455-463.

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