中文摘要：

已有的量子逻辑存在只适合于刻画封闭量子系统以及无法形式化量子测量算子等问题。为了描述开放量子系统,本文基于量子测量给出一种逻辑语言。首先,将经典命题公式作为逻辑语言的局部公式,以量子测量算子作为项公式;然后,将项公式的比较式和封闭量子子系统作为逻辑语言的原子命题,并定义一组量子联结词;最后,按结构归纳方式给出逻辑语言的全局公式。通过比较、分析已有的逻辑语言,说明量子测量逻辑的表达能力。作为公理化系统,给出量子测量逻辑的推理规则、元定理等相关理论。

英文摘要：

At present,several problems exist in quantum logics such as only being suitable for closed quantum systems and the inability to formalize quantum measurement operators.In order to model and reason about open quantum systems,a logical language is proposed based on quantum measurement.Firstly,classical propositional formulas are taken as initial and local formulas,and term formulas are interpreted as quantum measurement operators.Secondly,the comparative formulas between quantum measurement operators and closed quantum sub-systems are logically defined as atomic propositions. Meanwhile,a set of quantum connectives are introduced.Finally,global formulas of our logic are inductively built.By comparison and analysis about several logics,the expression power of our logic is illustrated.As an axiomatic system,the related deduction theories are studied such as the inference rule and meta-theorems.