Motivated by the need to extend features of semantic matchmaking between request and offer descriptions, a model is presented that exploits recently proposed non-standard inference services in Description Logics. The model allows to manage negotiable and strict constraints of a request (equivalently of an offer) while performing a matchmaking process, even if both the request and the offer are incompatible -some part of one description is in conflict with the other- and some constraints in one description are not specified in the other one. An algorithm is presented to compute both which part of the request should be retracted and which part of the offer has to be refined in order to make them completely satisfiable with each other
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