Temporal Stream Logic (TSL) is a temporal logic that extends LTL with updates and predicates over arbitrary function terms. This allows for specifying data-intensive systems for which LTL is not expressive enough. In TSL, functions and predicates are uninterpreted. In this paper, we investigate the satisfiability problem of TSL both with respect to the standard underlying theory of uninterpreted functions and with respect to other theories such as Presburger arithmetic. We present an algorithm for checking the satisfiability of a TSL formula in the theory of uninterpreted functions and evaluate it on different benchmarks: It scales well and is able to validate assumptions in a real-world system design. The algorithm is not guaranteed to terminate. In fact, we show that TSL satisfiability is highly undecidable in the theories of uninterpreted functions, equality, and Presburger arithmetic, proving that no complete algorithm exists. However, we identify three fragments of TSL for which the satisfiability problem is (semi-)decidable in the theory of uninterpreted functions.

中文翻译：

---

时间流逻辑模理论

时态流逻辑（TSL）是一种时态逻辑，可通过更新和谓词扩展任意功能项来扩展LTL。这允许指定LTL表现力不足的数据密集型系统。在TSL中，未解释函数和谓词。在本文中，我们针对未解释函数的标准基础理论以及诸如Presburger算术之类的其他理论，研究了TSL的可满足性问题。我们提出了一种算法，用于在未解释函数的理论中检查TSL公式的可满足性，并在不同的基准上对其进行评估：它具有良好的伸缩性，并且能够验证实际系统设计中的假设。不保证算法会终止。实际上，我们表明，在未解释函数，等式和Presburger算术的理论中，TSL的可满足性是高度不确定的，证明不存在完整的算法。但是，我们确定了TSL的三个片段，在未解释的功能理论中，它们的可满足性问题是（半）可确定的。