论文标题
基于有限的定位posets的时态逻辑
Tense logic based on finite orthomodular posets
论文作者
论文摘要
量子力学的逻辑是基于矫形器posets的，人们普遍认为。但是，这种逻辑不是动态的，因为它不包含时间维度。为了填补这一空白，我们以不精确的方式在这种逻辑上介绍了某些时态运算符，但是基于布尔代数或各种非经典逻辑中的经典逻辑中的时态运算符要求仍满足经典逻辑中的紧张要求。当相关的孔位是有限的时，我们的时态操作员的构造正常工作。我们研究了这些时态操作员的行为，例如我们证明其中一些形成了动态对。此外，我们证明，如果紧张的操作员保留了最近在另一篇论文中定义的不精确连接的连接或含义，那么他们也保留了另一个。最后，我们展示了如何在给定时间集上构建时间偏好的二进制关系，只要给出时态运算符，直到自然准词引起的等效性。
It is widely accepted that the logic of quantum mechanics is based on orthomodular posets. However, such a logic is not dynamic in the sense that it does not incorporate time dimension. To fill this gap, we introduce certain tense operators on such a logic in an inexact way, but still satisfying requirements asked on tense operators in the classical logic based on Boolean algebras or in various non-classical logics. Our construction of tense operators works perfectly when the orthomodular poset in question is finite. We investigate the behaviour of these tense operators, e.g. we show that some of them form a dynamic pair. Moreover, we prove that if the tense operators preserve one of the inexact connectives conjunction or implication as defined by the authors recently in another paper, then they also preserve the other one. Finally, we show how to construct the binary relation of time preference on a given time set provided the tense operators are given, up to equivalence induced by natural quasiorders.
