On Armstrong-compliant logical query languages

We present a simple logical query language called R£ 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 R£-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.