We present an overview on Temporal Logic Programming under the perspective of its application for Knowledge Representation and declarative problem solving. Such programs are the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). We focus on recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL, but performs a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). We obtain a proper extension of the stable models semantics for the general case of arbitrary temporal formulas. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between infinite and finite traces. We also provide other useful results, such as the translation into other formalisms like Quantified Equilibrium Logic or Second-order LTL, and some techniques for computing temporal stable models based on automata. In a second part, we focus on practical aspects, defining a syntactic fragment called temporal logic programs closer to ASP, and explain how this has been exploited in the construction of the solver TELINGO.
翻译:我们从应用“知识代表性”和“宣示性解决方案”的角度概述了“时间逻辑编程”的概况。这种程序是将常规规则与时间模式操作者相结合的结果,如在“线性时时逻辑”(LTL)中。我们侧重于“时间平衡逻辑(TEL)”这一非流动形式主义的最新结果,它被界定为“时间平衡逻辑”(TEL)的全部语法,但根据“平衡逻辑”这一众所周知的“回答系统编程”的逻辑逻辑特征(ASP)执行一个示范选择标准。我们获得了任意时间公式一般情况下的稳定模型语义的适当扩展。我们回顾TEL及其单调基础的基本定义,即“时间平衡逻辑(TTHT)”的时空逻辑,并研究无限和有限痕迹之间的差别。我们还提供了其他有用的结果,例如将“平衡逻辑”或“第二顺序”“LTLP”等翻译为其他形式,以及一些基于“自动模型”计算时间稳定模型的技术。在第二部分中,我们注重“技术”及其单调基础的基本定义,我们更密切地解释了“时间-空间”的逻辑,我们如何利用“时间”的逻辑。