A universal model of a database D and a set Σ of integrity constraints is a database that extends D, satisfies Σ, and is most general in the sense that it contains sound and complete information. Universal models have a number of applications including answering conjunctive queries, and deciding containment of conjunctive queries, with respect to databases with integrity constraints. Furthermore, they are used in slightly modified form as solutions in data exchange. In general, it is undecidable whether a database possesses a universal model, but in the past few years researchers identified various settings where this problem is decidable, and even efficiently solvable. This paper focuses on computing universal models under finite sets of guarded TGDs, non-conflicting keys, and negative constraints. Such constraints generalize inclusion dependencies, and were recently shown to be expressive enough to capture certain members of the DL-Lite family of description logics. The main ...