In the present study, we provide conditions for the existence of pushouts of signature morphisms in constructor-based order-sorted algebra, and then we prove that reducibility and termination of term rewriting systems are closed under pushouts. Under the termination assumption, reducibility is equivalent to sufficient-completeness, which is crucial for proving several important properties in computing for constructor-based logics such as completeness, existence of initial models and interpolation. In logic frameworks that are not based on constructors, sufficient-completeness is essential to establish the soundness of the induction schemes which are based on some methodological constructor operators. We discuss the application of our results to the instantiation of parameterized specifications.

在本研究中，我们为基于构造函数的有序排序代数中特征词素推出的存在提供了条件，然后我们证明了在推出下封闭了术语重写系统的可约性和终止。在终止假设下，可归约性等于充分完整性，这对于证明基于构造函数的逻辑的计算中的几个重要属性（例如完整性，初始模型的存在和内插）至关重要。在不基于构造函数的逻辑框架中，充分的完整性对于建立基于某些方法构造函数运算符的归纳方案的健全性至关重要。我们讨论了将结果应用于参数化规范的实例化的问题。