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arXiv · 2007.12006

A sound interpretation of Le\'sniewski's epsilon in modal logic KTB

Takao Inoué
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Abstract

In this paper, we shall show that the following translation $I^M$ from the propositional fragment $\bf L_1$ of Le\'{s}niewski's ontology to modal logic $\bf KTB$ is sound: for any formula $\phi$ and $\psi$ of $\bf L_1$, it is defined as \smallskip (M1) $I^M(\phi \vee \psi)$ = $I^M(\phi) \vee I^M(\psi),$ (M2) $I^M(\neg \phi)$ = $\neg I^M(\phi),$ (M3) $I^M(\epsilon ab)$ = $\Diamond p_a \supset p_a . \wedge . \Box p_a \supset \Box p_b . \wedge . \Diamond p_b \supset p_a,$ \smallskip \noindent where $p_a$ and $p_b$ are propositional variables corresponding to the name variables $a$ and $b$, respectively. In the last section, we shall give some open problems and my conjectures.

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Takao Inoué. 2020-07-22. A sound interpretation of Le\'sniewski's epsilon in modal logic KTB. https://arxiv.org/abs/2007.12006

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