A new notion of generalized rewrite theory suitable for symbolic reasoning and generalizing the standard notion in [19] is motivated and defined. Also, new requirements for symbolic executability of generalized rewrite theories that extend those in [33] for standard rewrite theories, including a generalized notion of coherence, are given. Symbolic executability, including coherence, is both ensured and made available for a wide class of such theories by automatable theory transformations. Using these foundations, several symbolic reasoning methods using generalized rewrite theories are studied, including: (i) symbolic description of sets of terms by pattern predicates; (ii) reasoning about universal reachability properties by generalized rewriting; (iii) reasoning about existential reachability properties by constrained narrowing; and (iv) symbolic verification of safety properties such as invariants and stability properties.

提出并定义了一种新的广义重写理论概念，该理论适用于符号推理并推广[19]中的标准概念。此外，还给出了对通用重写理论的符号可执行性的新要求，这些要求扩展了[33]中的标准重写理论的要求，其中包括广义的一致性概念。可以通过自动化的理论转换来确保符号可执行性（包括连贯性），并且可以使这类可执行性适用于广泛的此类理论。利用这些基础，研究了几种使用广义重写理论的符号推理方法，包括：（i）通过模式谓词对术语集进行符号描述; （ii）通过广义重写对通用可达性进行推理；（iii）通过约束变窄对存在的可达性进行推理；（iv）对安全特性（如不变性和稳定性）进行符号验证。