Often disgaree with each other sometimes strongly

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Unformatted text preview: n disgaree with each other, sometimes strongly. Logics dealing with inconsistent information are called paraconsistent logics, and were studied in detail by de Costa 7] and Belnap 2]. Blair and Subrahmanian 4] proposed logic programming based on paraconsistent logic and Subrahmanian 22] extended the work to disjunctive deductive databases. In this paper, we present a generalisation of the relational data model. Our model is based on the 4-valued paraconsistent logic of 2] and is capable of manipulating incomplete as well as inconsistent information. The incompleteness is at the tuple level, in that whether or not a particular tuple belongs to a relation may not be known. This notion of incompleteness is di erent from the other null-values related notions mentioned earlier. Similarly, inconsistency is also at the tuple level, in that a particular tuple may be considered to be both in and out of a relation. We introduce paraconsistent relations, which are the fundamental mathematical structures underlying our model. A paraconsistent relation essentially contains two kinds of 2 tuples: ones that de nitely belong to the relation and others that de nitely do not belong to the relation. These structures are strictly more general than ordinary relations, in that for any ordinary relation there is a paraconsistent relation with the same information content, but not vice versa. We de ne algebraic operators over paraconsistent relations that extend the standard operators, such as selection, join, union, over ordinary relations. In addition to answering queries in databases, we show another application of our algebra on paraconsistent relations. We present a bottom-up method to construct the weak well-founded model of general deductive databases; this model was proposed by Fitting in 9]. The rest of the paper is organised as follows. Section 2 introduces paraconsistent relations and two notions of generalising the usual relational operators, such as union, join, projection, for these relations. Section 3 presents some actual generalised algebraic operators for paraconsistent relations. These operators can be used for specifying queries for database systems built on such relations. As another interesting application of these operators, Section 4 gives a method for costructing the weak well-founded model of general deductive databases. An important step in the construction is to translate the database clauses into expressions involving the algebraic operators on paraconsistent relations. Finally, Section 5 contains some concluding remarks and directions for future work. 2 Paraconsistent Relations In this section, we construct a set-theoretic formulation of paraconsistent relations. Unlike ordinary relations that can model worlds in which every tuple is known to either hold a certain underlying predicate or to not hold it, paraconsistent relations provide a framework for incomplete or even inconsistent information about tuples. They naturally model belief systems...
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This note was uploaded on 09/28/2013 for the course CSC 8710 taught by Professor Staff during the Fall '08 term at Georgia State University, Atlanta.

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