Constraint-Generating Dependencies

Abstract

These are a generalization of equality-generating dependencies where equality requirements are replaced by constraints on an interpreted domain. The main technical results in the paper are a general decision procedure for the implication and consistency problems for constraint-generating dependencies and complexity results for specific classes of such dependencies over given domains. The decision procedure proceeds by reducing the dependency problem to a decision problem for the constraint theory of interest and is applicable as soon as the underlying constraint theory is decidable. The complexity results are, in some cases, directly lifted from the constraint theory; in other cases, optimal complexity bounds are obtained by taking into account the specific form of the constraint decision problem obtained by reducing the dependency implication problem.

Unifying logic rules and machine learning for entity enhancing

“…• Lower bound. Consider constraint-generating dependencies with equality and ordering [40], denoted by CGDs. CGDs are REEs of the form R 1 (t 1 ) ∧ .…”

“…, l m , l are predicates of the form t.A ⊕ c or t.A ⊕ t ′ .B, and ⊕ is one of =, =, <, . It is known that the satisfiability problem is NP-complete for CGDs with a fixed number of atom formulas [40]; hence so is the problem for REEs.…”

RQL: A Query Language for Rule Discovery in Databases

“…Many dependencies different from functional dependencies have been studied such as implications in formal concept analysis (FCA) [38,42,9], conditional FDs [14], sequential dependencies [27], metric FDs [35], denial constraints [19] or constraint-generating dependencies [10]. They can partially be represented with RQL (cf.…”

“…The relational database management systems (DBMS) market is already huge and continues to grow since it is expected to nearly double by 2016 [41]. As a trivial consequence for the data mining community, it makes sense -more 10 SPEN C01 FINANCE 18 F 52750 500 4220 20 20 THOMP -MANAGER 18 M 41250 800 3300 -30 KWAN -FINANCE 20 F 38250 500 3060 10 50 GEYER -MANAGER 16 M 40175 800 3214 20 60 STERN D21 SALE 14 M 32250 500 2580 30 70 PULASKI D21 SALE 16 F 36170 700 2893 100 90 HENDER D21 SALE 17 F 29750 500 2380 10 100 SPEN C01 FINANCE 18 M 26150 800 2092 20 Figure 1: Running example than ever -to query the data in-place when using state of the art database technologies. While a lot of techniques have been proposed over the last 20 years for pattern mining, only a few of them are tightly coupled with a DBMS.…”

Data exchange with arithmetic operations

“…In [23], constrained tuple-generating dependencies (ctgds) were first introduced as a generalization of tuple-generating dependencies, constrained functional dependencies [22], and constraint-generating dependencies [6]. These ctgds are defined in [23] relative to a given constraint domain, which is a pair (D, L), where D is a structure and L is a fragment of first-order logic.…”