Knowledge Equivalence in Combined Action Theories

We investigate the relationship between two accountsof knowledge and action in the situation calculus: the Scherl and Levesque (SL) approach that models knowledge with possible worlds, and the Demolombe and Pozos Parra (DP) approach that models knowledge by a set of “knowledge fluents.” We construct combined action theories:basic action theories that encode a correspondence between an SL and a DP theory. We prove, subject to certain restrictions, that knowledge of fluent literals are provably the same after a sequence of actions. Moreover, this knowledge equivalence extends to a rich class of formulae. These results allow us to translate certain SL theories into equivalent DP theories that avoid the computational drawbacks of possible world reasoning.They also enable us to prove the correctness of the DP treatment of knowledge and action in terms of a possible world specification.