论文标题
关于Leśniewski的命题本体论和模态逻辑的淡淡翻译
On Blass translation for Leśniewski's propositional ontology and modal logics
论文作者
论文摘要
在本文中，我们将给出另一个证明命题片段$ \ bf l_1 $ bf l_1 $yśniewski在模态逻辑$ \ bf k $ \中的忠诚度（简称为$ b $ translation）的忠诚。我们将结果扩展到von Wright型义逻辑，即Monadic Deontic逻辑的十个笑脸汉森系统。通过观察证据，我们将对$ b $ translation的忠实定理进行一般定理，相对于正常的模态逻辑完成了某些众所周知的可访问性关系，并在同一时间没有设定传递性和对称性的限制。例如，作为定理的应用，$ b $ translation对可普遍性逻辑$ \ bf prl $（= $ \ bf gl $）是忠实的，也就是说，$ \ bf k $+$ $+$ $ \ $ \ box（\ box ϕ \ supset ϕ）\ supset \ supset \ supset \ supset \ box ϕ $。忠诚也适用于普通模态逻辑，例如$ \ bf kd $，$ \ bf k4 $，$ \ bf kd4 $，$ \ bf kb $。我们将以一些开放问题和猜想的方式结束本文。
In this paper, we shall give another proof of the faithfulness of Blass translation (for short, $B$-translation) of the propositional fragment $\bf L_1$ of Leśniewski's ontology in the modal logic $\bf K$ \it by means of Hintikka formula\rm . And we extend the result to von Wright-type deontic logics, i.e., ten Smiley-Hanson systems of monadic deontic logic. As a result of observing the proofs we shall give general theorems on the faithfulness of $B$-translation with respect to normal modal logics complete to certain sets of well-known accessibility relations with a restriction that transitivity and symmetry are not set at the same time. As an application of the theorems, for example, $B$-translation is faithful for the provability logic $\bf PrL$ (= $\bf GL$), that is, $\bf K$ $+$ $\Box (\Box ϕ\supset ϕ) \supset \Box ϕ$. The faithfulness also holds for normal modal logics, e.g., $\bf KD$, $\bf K4$, $\bf KD4$, $\bf KB$. We shall conclude this paper with the section of some open problems and conjectures.
