A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB - Inoue, Takao (Bulletin of the Section of Logic, 2021)
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 \(φ\) and \(ψ\) of \(\bf L_1\), it is defined as (M1) \(I^M(φ \vee ψ) = I^M(φ) \vee I^M(ψ)\), (M2) \(I^M( eg φ) = eg I^M(φ)\), (M3) \(I^M(ε ab) = \Diamond p_a \supset p_a . \wedge . \Box p_a \supset \Box p_b .\wedge . \Diamond p_b \supset p_a\), 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.