A sound interpretation of Leśniewski's epsilon in modal logic KTB

Abstract

In this paper, we shall show that the following translation $I^M$ from the propositional fragment ${\mathbf{L}}_1$ of Leśniewski's ontology to modal logic $\mathbf{KTB}$ is sound: for any formula $\varphi$ and $\psi$ of ${\mathbf{L}}_1$, it is defined as \smallskip (M1) $I^M(\varphi \vee \psi )$ = $I^M(\varphi )\vee I^M(\psi ),$ (M2) $I^M(\neg \varphi )$ = $\neg I^M(\varphi ),$ (M3) $I^M(\epsilon ab)$ = $◊p_a\supset p_a.\wedge .\square p_a\supset \square p_b.\wedge .◊p_b\supset p_a,$ \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.

arXiv comment8 pages. arXiv admin note: text overlap with arXiv:2006.15421

References in corpus (1)

• On Blass translation for Leśniewski's propositional ontology and modal logics

Cited by in corpus (1)

• Axiomatic Rejection for the Propositional Fragment of Leśniewski's Ontology