Semantics for a useful fragment of the situation calculus

In a recent paper, we presented a new logic called ES for reasoning about the knowledge, action, and perception of an agent. Although formulated using modal operators, we argued that the language was in fact a dialect of the situation calculus but with the situation terms suppressed. This allowed us to develop a clean and workable semantics for the language without piggybacking on the generic Tarski semantics for first-order logic. In this paper, we reconsider the relation between ES and the situation calculus and show how to map sentences of ES into the situation calculus. We argue that the fragment of the situation calculus represented by ES is rich enough to handle the basic action theories defined by Reiter as well as Golog. Finally, we show that in the full second-order version of ES, almost all of the situation calculus can be accommodated.