Action theories over generalized databases with equality constraints

In this work we focus on situation calculus action theories over generalized databases with equality constraints, here called GFDBs, which are able to finitely represent complete information over a possibly infinite number of objects. We contribute with the following: i) we show that GFDBs characterize the class of definitional KBs and that they are closed under progression; ii) we show that temporal projection queries are decidable for theories with an initial KB expressed as a GFDB, which we call GFDB-BATs; iii) we extend the notion of boundedness to allow for infinite objects in the extensions of fluents and prove that a wide class of generalized projection queries is decidable for GFDB-BAT under a restriction we call C-boundedness; iv) we show that checking whether C-boundedness holds for a given bound is decidable. The proposed action theories are to date the most expressive ones for which there are decidable methods for computing both progression and generalized projection.