论文标题
模态逻辑教学和教科书中的一些常见错误
Some Common Mistakes in the Teaching and Textbooks of Modal Logic
论文作者
论文摘要
我们讨论了模态逻辑教学和教科书中的四个常见错误。第一个缺少Axiom $ \diamondφ\ leftrightArrow \ neg \ box \negφ$，当选择$ \ diamond $作为原始模态操作员时，误解了$ \ box $和$ \ diamond $的对称。第二个是忘记在通过过滤证明有限的模型属性时，将过滤的公式集关闭，忽略了$ \boxφ$和$ \diamondφ$可能是公式的缩写。第三个是在最小的规范模型中给出的规范关系的错误定义，这些模型与原始模态运算符无与伦比。最后一个是误解了必需品的规则，而不知道其与作法元素规则的区别。为了更好地理解必要条件的规则，我们总结了模态逻辑中定义演绎后果的六种方法：省略的定义，经典定义，三元定义，缩小定义，定义定义和缩写定义，并证明了最后三个定义相当于彼此。
We discuss four common mistakes in the teaching and textbooks of modal logic. The first one is missing the axiom $\Diamondφ\leftrightarrow\neg\Box\negφ$, when choosing $\Diamond$ as the primitive modal operator, misunderstanding that $\Box$ and $\Diamond$ are symmetric. The second one is forgetting to make the set of formulas for filtration closed under subformulas, when proving the finite model property through filtration, neglecting that $\Boxφ$ and $\Diamondφ$ may be abbreviations of formulas. The third one is giving wrong definitions of canonical relations in minimal canonical models that are unmatched with the primitive modal operators. The final one is misunderstanding the rule of necessitation, without knowing its distinction from the rule of modus ponens. To better understand the rule of necessitation, we summarize six ways of defining deductive consequence in modal logic: omitted definition, classical definition, ternary definition, reduced definition, bounded definition, and deflationary definition, and show that the last three definitions are equivalent to each other.
