On Partial Features in the DLF Dialects of Description Logic with Inverse Features

The DLF dialects of description logic are fragments of first order logic with underlying signatures based on unary predicate symbols and on unary function symbols interpreted as total functions. In earlier work, we have shown how computational properties of logical consequence for dialects of this family without inverse features are preserved when unary function symbols are interpreted instead as partial functions, and when a “∃f” concept constructor for feature value existence is added that can be used to enforce function totality. In this paper, we resolve a number of open problems mentioned in this earlier work that concerns DLF dialects with inverse features. Our main result shows how the dialect CFDI∀− nc can be extended with a limited form of conjunction on left-hand-sides of inclusion dependencies that enables a straightforward simulation of partial functions together with the ∃f concept constructor.