A general modal framework for the event calculus and its skeptical and credulous variants

We propose a general and uniform modal framework for the Event Calculus (EC) and its skeptical and credulous variants. The resulting temporal formalism, called the Generalized Modal Event Calculus (GMEC), extends considerably the expressive power of EC when information about the ordering of events is incomplete. It provides means of inquiring about the evolution of the maximal validity intervals of properties relative to all possible refinements of the ordering data by allowing a free mix of propositional connectives and modal operators. We first give a semantic definition of GMEC and relate it to known systems of modal logic; then, we propose a declarative encoding of GMEC in the language of hereditary Harrop formulas and prove the soundness and completeness of the resulting logic programs.