In the present paper we use the approach of height functions to defining a semi-distance measure between Horn clauses. This appraoch is already discussed elsewhere in the framework of
propositional and sim- ple first order languages (atoms). Hereafter we prove its applicability for Horn clauses. We use some
basic results from lattice theory and introduce a family of language independent coverage-based height functions.Then we show
how these results apply to Horn clauses. We also show an exam- ple of conceptual clustering of first order atoms, where the
hypotheses are Horn clauses.