Undecidability of Finite Model Reasoning in DLFD

Abstract

We resolve an open problem concerning finite logical implication for path functional dependencies (PFDs). This note is an addendum to [4].In this note we show that the finite logical implication for description logics endowed with PFDs is undecidable. This result complements the decidability of the unrestricted problem that is complete for EXPTIME [2,3]. PreliminariesDefinition 1 (Description Logic DLF D) Let F and C be sets of feature names and primitive concept names, respectively. A path expression is defined by the grammar " Pf ::= f. Pf | Id" for f ∈ F . We define derived concept descriptions by a second grammar on the left-hand-side of Figure 1. A concept description obtained by using the final production of this grammar is called a path-functional dependency (PFD).An inclusion dependency C is an expression of the form D ⊑ E. A terminology T consists of a finite set of inclusion dependencies.