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

• Autorzy: Takao Inoue

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2021
• Tom: 50
• Numer: 4
• Strony: 455-463

Daty

wydano

2021

Twórcy

autor

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/0000000220807480

Bibliografia

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Identyfikatory

DOI

10.18778/0138-0680.2021.25

nonstd.3pn.id

2033852