LOGICAL PROGRAM AND ITS MATHEMATICAL FOUNDATION

逻辑规划的研究是当代规划理论的重要研究领域之一。在本研究项目中，研究者在分析语义和分析等价理论的基础上，开发了几种用于逻辑和程序程序的验证形式，即SOFA、包络理论和时态算法。这些是分析和验证程序，控制离散的某些连续的物理或其他外部系统。每种形式都描述了从观察时间对下一个动作的唤醒时间的分析。我们得到了下一个动作上升时的实际合理时间值，使验证更容易、更精确。研究人员还将音乐信息处理作为实时和高智能程序系统的一个例子进行了研究。他们开发并试验了实时控制性能系统。这些系统的设计本质上是困难的，因为实时性和人类独舞者的物理动作和反应的本质到目前为止还没有被很好地理解。此外，特别是原声三角钢琴有0.5[秒。]每次MIDI事件输入后物理声音（即对应键的动作）的延迟，使得程序在涉及钢琴的伴奏系统中必须预测人的表现，这是使设计更加复杂和困难的另一个因素。为了应对这些情况和解决现代软件技术带来的各种问题，他们逻辑地表示了这些系统的规范，并使用这些形式化来验证这些规范的正确性。

A study of logical programs are one of the most important fields for contemporary program theory. In this research project, the investigators have developed several verification formalisms for logical and procedural programs, named SOFA, the envelope theory and the tense arithmetic, based on the analytical semantics and the analytical equivalence theory. These are to analyze and verify programs that controls discretely certain continuously physical or other external system. Each formalism describes analysis of the wake-up time of the next action from an observation time. We obtain the actual rational time value when the next action will rise, so that verification can be easier and more precise.The investigators have also researched music information processing as one of the examples of the realtime and highly intelligent program systems. They have developed and experimented realtime controlled performance systems. The design of these systems is essentially difficult because of the realtimeness and the fact that the nature of physical action and reaction by human soloists has not been understood well so far. Besides, especially, the acoustic grand piano has 0.5[sec.] delay of physical sound (i.e., the action of the corresponding key) after each input of MIDI event, so that the program must forecast human's performance in the accompaniment systems involving piano, which is another factor to make the design more complex and difficult. In order to cope with these situations and to solve various problems incurred upon with modern software techniques, they have represented specifications of these systems logically and verify these correctness using these formalisms.