A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB


  • Takao Inoue Meiji Pharmaceutical University, Department of Medical Molecular Informatics, Tokyo, Japan; Hosei University, Graduate School of Science and Engineering Tokyo, Japan https://orcid.org/0000-0002-2080-7480




Le´sniewski’s ontology, propositional ontology, translation, interpretation, modal logic, KTB, soundness, Grzegorczyk’s modal logic


In this paper, we shall show that the following translation \(I^M\) from the propositional fragment \(\bf L_1\) of Leśniewski's ontology to modal logic \(\bf KTB\) is sound: for any formula \(\phi\) and \(\psi\) of \(\bf L_1\), it is defined as

(M1) \(I^M(\phi \vee \psi) = I^M(\phi) \vee I^M(\psi)\),

(M2) \(I^M(\neg \phi) = \neg I^M(\phi)\),

(M3) \(I^M(\epsilon ab) = \Diamond p_a \supset p_a . \wedge . \Box p_a \supset \Box p_b .\wedge . \Diamond p_b \supset p_a\),

where \(p_a\) and \(p_b\) are propositional variables corresponding to the name variables \(a\) and \(b\), respectively. In the last, we shall give some comments including some open problems and my conjectures.


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How to Cite

Inoue, T. (2021). A Sound Interpretation of Leśniewski’s Epsilon in Modal Logic KTB. Bulletin of the Section of Logic, 50(4), 455–463. https://doi.org/10.18778/0138-0680.2021.25



Research Article