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Unformatted text preview: th the same information content, but not vice versa. Since paraconsistent relations are capable of containing contradictory information, these structures model belief systems more naturally than knowledge systems. We developed two notions of generalising operators on ordinary relations for paraconsistent relations. Of these, the stronger notion guarantees that any generalised operator is \well-behaved" for paraconsistent relation operands that contain consistent information. For some well-known operators on ordinary relations, such as union, join, projection, we introduced generalised operators on paraconsistent relations. These generalised operators maintain the belief system intuition behind paraconsistent relations, and are shown to be \well-behaved" in the sense mentioned above. Our data model can be used to represent relational information that may be incomplete or inconsistent. As usual, the algebraic operators can be used to construct queries to any database systems for retrieving paraconsistent information. As another application of paraconsistent relations and the algebra on them, we presented a method for constructing the weak well-founded model for general deductive databases 9]. This method requires translating the clauses of the database into expressions involving the generalised operators introduced earlier. A minor modi cation to this method can tailor it for constructing the well-founded model for such databases 25]. Recently there has been some interest in studying extended logic programs in which the head of clauses can have one or more literals 19]. This leads to two notions of negation: implicit negation (corresponding to negative literals in the body) and explicit negation (corresponding to negative literals in the head). One possible direction for further research is to extend the paraconsistent relational model presented in this paper to include disjunctive tuples as in 16], thereby providing a framework under which the semantics of extended logic programs could be constructed in a bottom-up manner. Allowing explicit negation in a disjunctive deductive database/logic program usually cuts down on the number of minimal models, sometimes quite drastically, and as a consequence increases the e ciency of query processing. This will be one of the main motivations in exploring the possibility of paraconsistent relations with disjunctive tuples. 18 References 1] R. Bagai, M. Bezem, and M. H. van Emden. On downward closure ordinals of logic programs. Fundamenta Informaticae, XIII(1):67{83, 1990. 2] N. D. Belnap. A useful four-valued logic. In G. Eppstein and J. M. Dunn, editors, Modern Uses of Many-valued Logic, pages 8{37. Reidel, Dordrecht, 1977. 3] J. Biskup. A foundation of Codd's relational maybe-operations. ACM Transactions on Database Systems, 8(4):608{636, December 1983. 4] H. A. Blair and V. S. Subrahmanian. Paraconsistent logic programming. Theoretical Computer Science, 68:135{154, 1989. 5] E. F. Codd. A relational mo...
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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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