The Complexity of Model Checking in Modal Event Calculi with Quantifiers

Kowalski and Sergot’s Event Calculus (EC ) is a simple temporal formalism that, given a set of event occurrences, derives the maximal validity intervals (MVIs) over which properties initiated or terminated by these events hold. It does so in polynomial time with respect to the number of events. Extensions of its query language with Boolean connectives and operators from modal logic have been shown to improve substantially its scarce expressiveness, although at the cost of an increase in computational complexity. However, significant sublanguages are still tractable. In this paper, we further extend EC queries by admitting arbitrary event quantification. We demonstrate the added expressive power by encoding a hardware diagnosis problem in the resulting calculus. We conduct a detailed complexity analysis of this formalism and several sublanguages that restrict the way modalities, connectives, and quantifiers can be interleaved. We also describe an implementation in the higher-order logic programming language λProlog.