Only knowing in the situation calculus

Actions depend crucially on what an agent knows and does not know. For example, an action may have a precondition that requires knowing the referent of a term, which is generally referred to as knowing who or knowing what. Alternatively, executing a sense action may be the result of realizing that the referent of a term is not known yet. The latter requires an agent to reason about all it knows about the world. This concept, also called only knowing, has been studied using possible-world semantics, yet only in the static case. One of the best understood action formalisms is the situation calculus. Moreover, it also comes equipped with a possible-world model of knowledge, which has led to deep insights into the relationship between action and knowledge. Adding only knowing to the situation calculus, which is the topic of this paper, turns out to be much more problematic than in the case of adding knowledge. It requires a reconstruction of the situation calculus itself by first developing a possible-world model of action and then interpreting situations explicitly as possible worlds. The properties of the situation calculus, which normally need to be stipulated axiomatically, are shown to be valid formulas in our model. More importantly, only knowing is fully integrated into the action formalism.