模态逻辑KTB中列格涅夫斯基定理的合理解释
A sound interpretation of Leśniewski's epsilon in modal logic KTB
摘要：
在本文中，我们将证明以下从Lehanniewski本体论的命题片段$\bf L_1$到模态逻辑$\bf KTB$的翻译$I^M$是合理的：对于$\bf L_1$的任何式$ϕ$和$ψ$，定义为\smallskip（M1）$I^M(ϕ\vee ψ)$ = $I^M(ϕ) \vee I^M(ψ),$（M2）$I^M(\neg ϕ)$ = $\neg I^M(ϕ),$（M3）$I^M(εab)$ = $\Diamond p_a \supset p_a . \wedge . \Box p_a \supset \Box p_b . \wedge . \Diamond p_b \supset p_a,$ \smallskip \noindent其中$p_a$和$p_b$是分别对应于名称变量$a$和$b$的命题变量。在最后一节中，我们将给出一些开放的问题和我的建议。
英文摘要：
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 \smallskip (M1) $I^M(ϕ\vee ψ)$ = $I^M(ϕ) \vee I^M(ψ),$ (M2) $I^M(\neg ϕ)$ = $\neg I^M(ϕ),$ (M3) $I^M(εab)$ = $\Diamond p_a \supset p_a . \wedge . \Box p_a \supset \Box p_b . \wedge . \Diamond p_b \supset p_a,$ \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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