Manuel Atencia, Alexander Borgida, Jérôme Euzenat, Chiara Ghidini, Luciano Serafini, A formal semantics for weighted ontology mappings, in: Proc. 11th conference on International semantic web conference (ISWC), Boston (MA US), (Philippe Cudré-Mauroux, Jeff Heflin, Evren Sirin, Tania Tudorache, Jérôme Euzenat, Manfred Hauswirth, Josiane Xavier Parreira, James Hendler, Guus Schreiber, Abraham Bernstein, Eva Blomqvist (eds), The semantic web (Proc. 11th conference on International semantic web conference (ISWC)), Lecture notes in computer science 7649, 2012), pp17-33, 2012
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 interpreted to measure how precise and complete re-classifications are. This semantics is justifiable by extensional practice of ontology matching. It is a conservative extension of a semantics of crisp mappings. The paper also includes properties that relate mapping entailment with description logic constructors.