On Armstrong-compliant logical query languages

Abstract

We present a simple logical query language called RL for expressing different kinds of rules and we study how this language behaves with respect to the well-known Armstrong's axioms. We point out some negative results, e.g. it is undecidable to know whether or not a query from this language is "Armstrong compliant". The main contribution of this paper is to exhibit a restricted form of RL-queries -yet with a good expressive power -for which Armstrong's axioms are sound. From this result, this sublanguage turns out to have structural and computational properties which have been shown to be very useful in data mining, databases and formal concept analysis.

RQL: A Query Language for Rule Discovery in Databases

“…In [5], a slightly different language for rule mining has been proposed. One of the main results was to point out that every query was "Armstrong-compliant", meaning basically that Armstrong axioms are sound and that each query defines a closure system.…”

“…Indeed, the machinery introduced in this paper generalizes the computation of agree sets (a base of the closure system associated with FD) to every RQL query. Moreover, the paper is a major extension of [5,17]: [5] provides a logical view on the ad-hoc language proposed in [6], with some restrictions (e.g. only one relation schema).…”

RQL: A SQL-Like Query Language for Discovering Meaningful Rules

“…From previous works [2], [3], [4], RQL is compliant with Armstrong's axioms, i.e. the language generalizes functional dependencies to a new class of dependencies based on logical implications (if ... then statements).…”