Abstract

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.