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

100%

Inoue T.

Bulletin of the Section of Logic

2021

tom 50

nr 4

455-463

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.

Ograniczanie wyników

1 Bulletin of the Section of Logic

1 Inoue T.

1 2021

Wyniki wyszukiwania

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