In this paper, we study operator dependent modifiers and we interpret the dual pair of modal operators based on an algebraic definition. It is a known fact that the substantiating and weakening modifier operators can be induced by repeating the arguments of conjunctive and disjunctive operators. We provide the conditions for which these modifier operators satisfy the requirements for a dual pair of necessity and possibility operators. Next, the necessary and sufficient condition for the distributivity of unary operators over conjunctive and disjunctive operators is presented. This also means that setting the distributivity as a requirement results in a unary operator that is identical to the modal operators mentioned above. Using this property, we establish an important connection between modal operators and linguistic hedges. Previously, we demonstrated that the unary operators induced by compositions of two strong negations satisfy the requirements for a dual pair of modal operators. Here, we view the negation operator as a modifier operator. Then, it is shown that (1) the strong negations, (2) the substantiating and weakening modifier operators, modal operators and linguistic hedges mentioned above, and (3) the unary operators, which are distributive over conjunctive and disjunctive operators, may be viewed as special cases of a unified unary operator class.

在本文中，我们研究依赖于算子的修饰语，并基于代数定义解释对偶模态算子。众所周知的事实是，可以通过重复使用合取和不合取算符的参数来诱发实体化和弱化修饰符运算符。我们提供了这些修饰符运算符满足双对必要性和可能性运算符的要求的条件。接下来，给出一元算子在合取和析取算符上的分布性的充要条件。这也意味着将分布性设置为要求会导致一元运算符，该运算符与上述模态运算符相同。利用此属性，我们在模态运算符和语言对冲之间建立了重要的联系。之前，我们证明了由两个强否定的合成所引起的一元算子满足了对双模态算子的要求。在这里，我们将求反运算符视为修饰符运算符。然后，表明（1）强否定，（2）上述实体化和弱化的修饰语运算符，模态运算符和语言对冲，以及（3）一元运算符，它们分布在合取和析取运算符之上。被视为统一一元运算符类的特殊情况。