Constructing Models for Continuous-Time and Continuous-Change Event Calculus

Extensive research in the field of reasoning about actions and discrete changes led to many different logic-based formalisms such as Action Languages E and C+, Fluent Calculus, Temporal Action Logics, Situation Calculus, and Event Calculus. Some of these formalisms, Situation Calculus and Event Calculus for example, were extended to reason about continuous changes described as functions of time, and in some cases, Event Calculus for example, also via systems of ordinary differential equations. However, there are no reasoners, for any type of reasoning tasks, for the latter formalisms. Here we present a model-builder for Miller and Shanahan’s (1996) Event Calculus formalism which constructs models for given, numerical, and finite domains, given an initial state and narratives about exogenous action occurrences. The models are constructed by alternatively performing logical reasoning and solving ordinary differential and other equations. In order to make such a separation possible, and to make construction of models more tractable, we (syntactically) derive new axioms from given Event Calculus descriptions and introduce some axiomatically defined restrictions to the Event Calculus. Taking lead from Kim, Lee, and Palla (2009) we use answer-set solvers for logical reasoning. Specifically, we use Eiter et al.’s (2005) HEX-programs, which extends answer-set programs with external computations, required for real number arithmetic and comparisons. And, we use Mathematica for solving ordinary differential and other equations, and other real number computations.