Modality and interrupts

We suggest that modal operators, in addition to their well-understood semantic role in declarative systems, also mark points at which these systems can be interrupted. We use this idea to describe an interruptible declarative system that gradually refines its responses to queries. Although initial responses may be in error, a correct answer will be provided if arbitrarily large computational resources are available. The ideas presented generalize existing work on stratification of logic programs and the treatment of floundered subgoals.