Augmenting concept languages by transitive closure of roles : an alternative to terminological cycles
Franz Baader · 1990
In Baader (1990a,1990b), we have considered different types of semantics for terminologicial cycles in the concept language FL0 which allows only conjunction of concepts and value restrictions. It turned out that greatest fixed-point semantics (gfp-semantics) seems to be most appropriate for cycles in this language. In the present paper we shall show that the concept defining facilities of FL0 with cyclic definitions and gfp-semantics can also be obtained in a different way. One may replace cycles by role definitions involving union, composition, and transitive closure of roles. This proposes a way of retaining, in an extended language, the pleasant features of gfp-semantics for FL0 with cyclic definitions without running into the troubles caused by cycles in larger languages. Starting with the language ALC of Schmidt- Schauß