论文标题
与真理相关的逻辑，命题演算
Truth-relevant Logic, Propositional Calculus
论文作者
论文摘要
本文的论点是，与古典逻辑相比，与真理相关的逻辑是数学的更好基础。这是理查德·迪亚兹（Richard Diaz）在1981年提出的系统。从某种意义上说，T相关逻辑是基于Kleene强度表。这些定义一个具有三个值的系统：真，错误，未知。事实证明，存在以下属性的重言术：存在适当的命题变量（t相关变量）的适当子集，因此对于所有组合都是正确的/错误，重言术是正确的，也就是说，其余的变量（冗余变量）在绷紧学中发生在次要学中。我们将这种复合句子视为既不是真的也不是错误的。提供了哲学上的理由。提出了基于Tableaux的证明系统。证明了以下定理：重言式L =（R1 V〜R1）＆（R2 V〜R2）＆...＆（RM V〜RM），其中{R1，R2，RM ... RM}是T相关的命题变量的子集，并且根据Kleene强烈的可访问量，=是相等的。
The thesis of this paper is that truth-relevant logic is a better foundation for mathematics than classical logic. It is a system proposed by Richard Diaz in 1981. In a certain sense t-relevant logic is based on Kleene strong tables. These define a system with three values: true, false, unknown. It turns out that there exist tautologies with the following property: there exists a proper subset of propositional variables (t-relevant variables) such that for all combinations true/false the tautology will be true, that is, the rest of the variables (redundant variables) occurring in the tautology can be unknown. We consider such compound sentences as neither true nor false. Philosophical justification is provided. Proof system based on tableaux is proposed. The following theorem is proved: tautology L = (R1 v ~R1) & (R2 v ~R2) & ... & (Rm v ~Rm), where {R1, R2, ... Rm} is a subset of t-relevant propositional variables, and = is equivalence according to Kleene strong tables.
