Multi Dimensional CTL and Stratified Datalog

In this work we define Multi Dimensional CTL (MD-CTL in short) by extending CTL which is the dominant temporal specification language in practice. The need for Multi Dimensional CTL is mainly due to the advent of semi-structured data. The common path nature of CTL and XPath which provides a suitable model for semi-structured data, has caused the emergence of work on specifying a relation among them aiming at exploiting the nice properties of CTL. Although the advantages of such an approach have already been noticed [36, 26, 5], no formal definition of MD-CTL has been given. The goal of this work is twofold; a) we define MD-CTL and prove that the “nice” properties of CTL (linear model checking and bounded model property) transfer also to MD-CTL, b) we establish new results on stratified Datalog. In particular, we define a fragment of stratified Datalog called Multi Branching Temporal (MBT in short) programs that has the same expressive power as MD-CTL. We prove that by devising a linear translation between MBT and MD-CTL. We actually give the exact translation rules for both directions. We further build on this relation to prove that query evaluation is linear and checking satisfiability, containment and equivalence are EXPTIME–complete for MBT programs. The class MBT is the largest fragment of stratified Datalog for which such results exist in the literature.