  Order-Sorted Feature (OSF) logic is a knowledge representation and reasoning
language based on function-denoting feature symbols and set-denoting sort
symbols ordered in a subsumption lattice. OSF logic allows the construction of
record-like terms that represent classes of entities and that are themselves
ordered in a subsumption relation. The unification algorithm for such
structures provides an efficient calculus of type subsumption, which has been
applied in computational linguistics and implemented in constraint logic
programming languages such as LOGIN and LIFE and automated reasoners such as
CEDAR. This work generalizes OSF logic to a fuzzy setting. We give a flexible
definition of a fuzzy subsumption relation which generalizes Zadeh's inclusion
between fuzzy sets. Based on this definition we define a fuzzy semantics of OSF
logic where sort symbols and OSF terms denote fuzzy sets. We extend the
subsumption relation to OSF terms and prove that it constitutes a fuzzy partial
order with the property that two OSF terms are subsumed by one another in the
crisp sense if and only if their subsumption degree is greater than 0. We show
how to find the greatest lower bound of two OSF terms by unifying them and how
to compute the subsumption degree between two OSF terms, and we provide the
complexity of these operations.
