Temporal logic and annotated constraint logic programming

Abstract

We introduce a family of logic programming languages for representing and reasoning about time. The family is conceptually simple while covering substantial parts of temporal logic. Given a logic in our framework, there is a systematic way to make it executable as a constraint logic program. Thus we can study and compare various temporal logics and their executable fragments. Our approach allows for different models of time, different temporal operators, and temporal variables for both time points and time periods. Formulas can be labeled with temporal information using annotations. In this way we avoid the proliferation of variables and quantifiers as encountered in first order approaches. Unlike temporal logic, both qualitative and quantitative (metric) temporal reasoning with time points (instants) and periods (temporal intervals) are supported. A Horn clause fragment of our temporal logic can be seen as annotated constraint logic programming language. This class of languages can be implemented by translation into a standard constraint programming language. Thus we can make our temporal logic executable.