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. We shall give some comments including some open problems and my conjectures.

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In this paper, we shall show that the following translation I M from the propositional fragment L 1 of Leśniewski's ontology to modal logic KTB is sound: for any formula φ and ψ of L 1 , it is defined as (M1), where p a and p b are propositional variables corresponding to the name variables a and b, respectively. We shall give some comments including some open problems and my conjectures.

On March 8, 1995, was found the following nontrivial single axiomschema characteristic of Leśniewski-Ishimoto's propositional ontologyIn this paper, we shall present the progress about the above axiomschema from 1995 and conjectures about it. Here we shall give two criteria nontiriviality and quasi-nontriviality in order to distinguish two axiom-schemata.