CRL is syntactically defined as a base language and a surface language. The base language is characterized by the following aspects:

• its three major predicates  Holds ,  Occurs , and  Occlude , which provide coherence when the language is extended;

• its reportoire of categorial functions, which is augmented when additional expressiveness is required in the language.

The surface language provides additional notational convenience, and is defined by translation to the base language.

The range of expressivity includes actions with duration, nondeterministic actions, actions in hybrid worlds with piecewise continuous fluents, some forms of ramification and causation, imprecise sensors and actuators, action failure, and some aspects of goal-directed agent behavior.

Entailment methods are functions that map scenario descriptions to sets of intended models. They are defined using a reportoire of set-theoretic operations on sets of formulas and sets of models, including but not restricted to minimizing a set of models with respect to a preference relation.

A progression of underlying semantics is defined, beginning with the partial state-transition semantics and its immediate generalization, the trajectory semantics. These underlying semantics are used for the formal analysis of the range of applicability of various entailment methods, including both those proposed by the others in this research, and those that developed in the course of the present work.

The present reference article summarizes notation and definitions, so that forthcoming articles can refer to it for that purpose. It does not report on the results that have been obtained with the present approach, except insofar as it is needed for putting the notation into perspective.