Kowalski and Sergot's Event Calculus (EC) is a simple temporal formalism that, given a set of event occurrences, allows the derivation of the maximal validity intervals (MVIs) over which properties initiated or terminated by those events hold. The limited expressive power of EC is notably augmented by permitting events to initiate or terminate a property only if a given set of preconditions hold at their occurrence time. We define a semantic formalization of the Event Calculus with Preconditions. We gain further expressiveness by considering modal variants of this formalism, and show how to adapt our semantic characterization to encompass the additional operators. We discuss the complexity of MVI validation and describe examples showing that modal event calculi with preconditions can be successfully exploited to deal with real-world applications.
