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      Multivalued Mappings, Fixed-Point Theorems and Disjunctive Databases

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      3rd Irish Workshop on Formal Methods (IWFM)

      Formal Methods

      1st - 2nd July 1999

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          Abstract

          In this paper, we discuss the semantics of disjunctive programs and databases and show how multivalued mappings and their fixed points arise naturally within this context. A number of fixed-point theorems for multivalued mappings are considered, some of which are already known and some of which are new. The notion of a normal derivative of a disjunctive program is introduced. Normal derivatives are normal logic programs which are determined by the disjunctive program. Thus, the well-known single-step operator associated with a normal derivative is single-valued, and its fixed points can be found by well-established means. It is shown how fixed points of the multivalued mapping determined by a disjunctive program relate to the fixed points of the single-step operators coming from its normal derivatives. This procedure has potential for simplifying the construction of models of disjunctive databases, and this point is discussed.

          Most of the results for multivalued mappings rest on corresponding, known results concerning fixed points of single-valued mappings. Since the latter results are frequently referred to, they have been collected together for convenience in a survey which should be of independent interest as well as being preparatory for the later results. Finally, a number of problems and issues raised by this work are discussed.

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          Most cited references 7

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          Classical negation in logic programs and disjunctive databases

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            A kripke-kleene semantics for logic programs*

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              On the Declarative Semantics of Deductive Databases and Logic Programs

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                Author and article information

                Contributors
                Conference
                July 1999
                July 1999
                : 1-18
                Affiliations
                Department of Mathematics, National University of Ireland - Cork

                Cork, Ireland
                Article
                10.14236/ewic/IWFM1999.8
                © Pascal Hitzler et al. Published by BCS Learning and Development Ltd. 3rd Irish Workshop on Formal Methods

                This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

                3rd Irish Workshop on Formal Methods
                IWFM
                3
                Galway, Ireland
                1st - 2nd July 1999
                Electronic Workshops in Computing (eWiC)
                Formal Methods
                Product
                Product Information: 1477-9358BCS Learning & Development
                Self URI (journal page): https://ewic.bcs.org/
                Categories
                Electronic Workshops in Computing

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