An algebraic construction of the well-founded model

An algebraic method for the construction of the well-founded model of general deductive databases is presented. The method adopts paraconsistent relations as the semantic objects associated with the predicate symbols of the database. Paraconsistent relations are a generalization of ordinary relations in that they allow manipulation of incomplete as well as inconsistent information. Algebraic operators, such as union, join, selection, are defined for paraconsistent relations. The first step in the model construction method is to transform the database clauses into paraconsistent relation definitions involving these operators. The second step is to build the well-founded model iteratively. Algorithms for both steps along with arguments for their termination and correctness are presented.