Abstract
We prove several lattice theoretical fixpoint theorems based on the classical theorem of Knaster and Tarski. These theorems give sufficient conditions for a system of generally nonmonotonic functions on a complete lattice to define a unique minimal fixpoint. The primary objective of this paper is to develop a domain theoretic framework to study the semantics of logic programs as well as various rule-based systems where the rules define generally nonmonotonic functions on lattices.
Work supported in part by the US Department of Navy, Space and Naval Warfare Systems Command and Defense Advance Research Projects agency under contract N00039-88-@-0163.
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Zhou, Y., Muller, R. (1990). Domain theory for nonmonotonic functions. In: Kirchner, H., Wechler, W. (eds) Algebraic and Logic Programming. ALP 1990. Lecture Notes in Computer Science, vol 463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53162-9_36
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DOI: https://doi.org/10.1007/3-540-53162-9_36
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