Semantics of the minimal logic of quantum mechanics
Semantics of the minimal logic of quantum mechanics
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量子力学最小逻辑的语义
DOI：
10.1007/bf02120818
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发表时间：
1972
期刊：
影响因子：
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通讯作者：
H. Dishkant
中科院分区：
文献类型：
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作者：
H. Dishkant
讨论G是知识的可能状态的集合。因此，一个特定的T在G可以被认为是一个集合的物理事实已知的标准？时间到了。关系R表示可能的时间序列。T* 旨在表示任何知识状态，它可以在T之后出现。从T到T* 的转变与实验的完成有关。我们假设是单身前夫？量子观测（Quantum Observation）也就是说，TRA的意思是：如果我们现在知道T，有可能以后，当一个实验完成时，我们将知道A。例如，T可以是电子在固定体积Vo中的知识。在此之后，我们可以完成一个实验，并确定这个电子的能量是E0。现在T* 是电子在体积V0中并具有能量E0的知识。请注意，通过完成一个实验，我们改变了知识和对象的状态。因此，在我们的例子中，我们不能说T* 包含一个陈述，即T *？tron在体积V0中，因为通过能量测量与设备的不受控制的相互作用可以从体积V0排斥电子。条件RO可以解释如下：从知识状态F，我们总是可以传递到相同的状态T（如果，例如，前面的实验将被重复）。条件R1？可以解释如下：如果A是从T作为实验的结果得到的，那么就有可能从A返回到任何状态21，它的不确定性小于T。这里，表述”较少的不确定性“意味着从21只能到达这样的状态Q，从T也可以立即到达。注意，从T到T** 的转变可能是不可能的，尽管从T到T* 和从T* 到T** 这两个转变当然是可能的。粗略地说？因此，知识的状态不能改变得太快。我们假设，rNX意味着：从事实T的集合中，我们可以推导出X的真理，或者：T迫使X。正如我们所看到的，新的事实可能会取代旧的事实。条件（*）可以解释如下：真理是什么不能是anni？由于一次观察而没有恢复。粗略地说，只有知识状态的可解释的变化才能发生，或者说：真理是可解释的。教学逻辑在直觉模型中，关系R受到约束。的传递性，比R1强。这里从T到T** 的过渡总是可能的，或者：在认识的许多步骤中获得的知识可能获得
Discussion. G is intended to be a collection of possible states of knowledge. Thus a particular T in G may be considered as a collection of physical facts known at a par? ticular time. The relation R represents the possible time succession. T* is intended to be any state of knowledge, which can come after T. The transition from T to T* is connected with fulfilling of an experiment. And we assume that it is a single ex? periment (quantum observation). That is, TRA means: if we now know T, it is possible that later, when an experiment will have fulfilled, we shall know A. For example T may be the knowledge that the electron is in the fixed volume V0. After this we may fulfil an experiment and determine that the energy of this electron is E0. Now T* is the knowledge that the electron was in the volume V0 and possesses the energy E0. Note, that by fulfilling an experiment we change both the state of knowledge and the object. Thus in our example we cannot say that T* contains a statement that the elec? tron is in the volume V0, because the uncontrolled interaction with the device by the energy measurement can reject the electron from the volume V0. The condition RO may be interpreted as follows: from the state of knowledge F we can always pass on to the same state T (if, for example, the previous experiment will be repeated). The condition Rl? may be interpreted as follows: if A is obtained from T as a result of an experiment, then it is possible to return from A to any state 21, which is" less uncertain55 than T. Here the expression" less uncertain55 means that from 21 one can get only to such a state Q, to which one can get also immediately from T. Note, that the transition from T to T** may be impossible despite that the both transitions: from T to T* and from T* to T**, are certainly possible. Roughly speak? ing, the state of knowledge cannot be changed too rapidly. We suppose, that r NX means: from the collection of facts T we may deduce the truth of X, or: T forces X. As we saw, the new facts may replace the old ones. The condition (*) may be interpreted as follows: the truth is what cannot be anni? hilated without restoration as a result of a single observation. Roughly speaking, only restorable changes of states of knowledge can happen, or: the truth is resto rable.An analogous semantical interpretation was proposed by Kripke [3] for the in? tuitionistic logic. In the intuitionistic model the relation R is subjected to the con? dition of transitivity, stronger than Rl. Here the transition from T to T** is always possible, or: the knowledge obtained in many steps of cognition may be obtained