Action Theories over Generalized Databases with Equality Constraints

Situation calculus action theories allow full first-order expressiveness but, typically, restricted cases are studied such that projection or progression become decidable or first-order, respectively, and computationally feasible. In this work we focus on KBs that are specified as generalized databases with equality constraints, thus able to finitely represent complete information over possibly infinite number of objects. First, we show that this form characterizes the class of definitional KBs and provide a transformation for putting KBs in this form that we call generalized fluent DB. Then we show that for action theories over such KBs, the KBs are closed under progression, and discuss how this view exposes some differences with existing progression methods compared to DB update. We also look into the temporal projection problem and show how queries over these theories can be decided based on an induced transition system and evaluation of local conditions over states. In particular, we look into a wide class of generalized projection queries that include quantification over situations and prove that it is decidable under a practical restriction. The proposed action theories are to date the most expressive ones for which there are known decidable methods for computing both progression and generalized projection.