A semantical investigation into leśniewski's axiom of his ontology

Studia Logica 44 (1):71 - 77 (1985)
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Abstract

A structure A for the language L, which is the first-order language (without equality) whose only nonlogical symbol is the binary predicate symbol , is called a quasi -struoture iff (a) the universe A of A consists of sets and (b) a b is true in A ([p) a = {p } & p b] for every a and b in A, where a(b) is the name of a (b). A quasi -structure A is called an -structure iff (c) {p } A whenever p a A. Then a closed formula in L is derivable from Leniewski's axiom x, y[x y u (u x) u; v(u, v x u v) u(u x u y)] (from the axiom x, y(x y x x) x, y, z(x y z y x z)) iff is true in every -structure (in every quasi -structure).

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Citations of this work

Syntactical Proof of Translation and Separation Theorems on Subsystems of Elementary Ontology.Mitio Takano - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (9-12):129-138.
A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB.Takao Inoue - 2021 - Bulletin of the Section of Logic 50 (4):455-463.
A Sequent Calculus for the Lesniewskian Modal Logic.Mitio Takano - 1994 - Annals of the Japan Association for Philosophy of Science 8 (4):191-201.

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References found in this work

Mathematical logic.Joseph Robert Shoenfield - 1967 - Reading, Mass.,: Addison-Wesley.
S. Leśniewski's Calculus of Names.Jerzy Słupecki - 1984 - In Jan T. J. Srzednicki, V. F. Rickey & J. Czelakowski (eds.), Leśniewski's systems. Hingham, MA, USA: Distributors for the United States and Canada, Kluwer Boston. pp. 59--122.
S. leśniewski's calculus of names.Jerzy Słupecki - 1955 - Studia Logica 3 (1):7-72.
On leśniewski's elementary ontology.Bogusław Iwanuś - 1973 - Studia Logica 31 (1):73 - 125.

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