Ontology mappings are often assigned a weight or confidence factor by matchers. Nonetheless, few semantic accounts have been given so far for such weights. This paper presents a formal semantics for weighted mappings between different ontologies. It is based on a classificational interpretation of mappings: if O1 and O2 are two ontologies used to classify a common set X, then mappings between O1 and O2 are interpreted to encode how elements of X classified in the concepts of O1 are re-classified in the concepts of O2, and weights are inter- preted to measure how precise and complete re-classifications are. This semantics is justifiable by extensional practice of ontology matching. It is a conservative ex- tension of a semantics of crisp mappings. The paper also includes properties that relate mapping entailment with description logic constructors.