We present a preliminary framework for reasoning with possibilistic description logics ontologies with disjunctive assertions (PDLDA ontologies for short). PDLDA ontologies are composed of a terminology as well as an assertional box that allows to declare three kinds of assertional statements: an individual is a member of one concept, two individuals are related through a role, an individual is a member of the union of two or more concepts or two individuals are related through the union of two or more roles. Each axiom in the ontologies has a certainty degree as is usual in possibilistic logics. For reasoning with PDLDA ontologies, we interpret them in terms of a adaptation of Bodanza's Suppositional Argumentation System. Our framework allows to reason with modus ponens and constructive dilemmas. We use it for determining the membership of individuals to concepts when there is doubt to exactly which one of the concepts in the union the individual belongs. We think that our approach will be of use for implementers of reasoning systems in the Semantic Web where uncertainty of membership of individuals to concepts or roles is present.XVI Workshop Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI
