Incomplete causal laws in the situation calculus using free fluents

We propose a simple relaxation of Reiter's basic action theories, based on fluents without successor state axioms, that accommodates incompleteness beyond the initial database. We prove that fundamental results about basic action theories can be fully recovered and that the generalized framework allows for natural specifications of various forms of incomplete causal laws. We illustrate this by showing how the evolution of incomplete databases, guarded action theories, and non-deterministic actions can be conveniently specified.