One of the main issue in formalizing the Data Integration Systems (DIS) is the semantic characterization of its global schema and the mappings with its source databases. Each DIS must be robust enough in order to take in account the incomplete and inconsistent information of its source databases, typical in Web applications: the extension of source databases change in an unpredictable way so that in different time instances we pass from a consistent to inconsistent DIS and viceversa. Thus, DIS will generally have possibly infinite number of consistent repairs and their models and, consequently, query answering in such DISs is very complex and time consuming. The current systems adopt the two extreme solutions for a query-answering: certain answers (true in all models of a given DIS) or all possible answers (true at any model). The first solution is to much strong requirement and practically non applicable in real situations, the second one is less meaningful (not all possible Skolem-based completions of an incomplete logical theory are plausible for users) and time/space consuming (they may be infinite also). In this paper we propose the middle solution between these two extremes based on the plausible nonmonotonic query-answering inference.