In this paper we propose an extension of a Horn-rule sublogic of PLFC (a first-order Possibilistic logic programmming language dealing with fuzzy constants and fuzzily restricted quantifiers) with similarity-based unification of object constants. At the semantic level, we equip each sort with a fuzzy similarity relation, and at the syntactic level, we replace each precise object constant in the antecedent of a Horn-rule by a variable weight fuzzily 'enlarged' by menas of a fuzzy similarity relation.