论文标题
结合时间维度的量子力学的逻辑
The logic of quantum mechanics incorporating time dimension
论文作者
论文摘要
与经典的命题演算类似，基于代数基于布尔代数，量子力学的逻辑基于G. Birkhoff和J. von Neumann和K. Husimi的定向晶格。但是，尽管很明显，量子力学逻辑中出现的命题取决于时间，但这种逻辑并不包含时间维度。本文的目的是表明，也可以在给定时间集和给定时间偏好关系的逻辑中引入所谓的时态运算符。在这种情况下，我们可以以纯粹的代数方式介绍这些操作员。我们得出了此类操作员的几个重要特性，特别是我们表明它们形成了动态对，并且完全是动态代数。我们研究了这些操作员与逻辑连接词的连接以及来自Sasaki预测的含义。然后，我们解决了相反的问题，即在给定的时间集找到时，并给定时运算符一个时间偏好关系，以使所得的时间范围诱导给定的运算符。我们表明，可以作为由合适的延长时间范围引起的操作员的限制获得的给定运算符。
Similarly as classical propositional calculus is based algebraically on Boolean algebras, the logic of quantum mechanics was based on orthomodular lattices by G. Birkhoff and J. von Neumann and K. Husimi. However, this logic does not incorporate time dimension although it is apparent that the propositions occurring in the logic of quantum mechanics are depending on time. The aim of the present paper is to show that so-called tense operators can be introduced also in such a logic for given time set and given time preference relation. In this case we can introduce these operators in a purely algebraic way. We derive several important properties of such operators, in particular we show that they form dynamic pairs and, altogether, a dynamic algebra. We investigate connections of these operators with logical connectives conjunction and implication derived from Sasaki projections. Then we solve the converse problem, namely to find for given time set and given tense operators a time preference relation in order that the resulting time frame induces the given operators. We show that the given operators can be obtained as restrictions of operators induced by a suitable extended time frame.
