A fixed point theorem for non-monotonic functions

We present a fixed point theorem for a class of (potentially) non-monotonic functions over specially structured complete lattices. The theorem has as a special case the Knaster–Tarski fixed point theorem when restricted to the case of monotonic functions and Kleene's theorem when the functions...

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Bibliographic Details
Published in:Theoretical computer science Vol. 574; pp. 18 - 38
Main Authors: Ésik, Zoltán, Rondogiannis, Panos
Format: Journal Article
Language:English
Published: Elsevier B.V 01.04.2015
Subjects:
Fixed point theory
Fixed points (mathematics)
Lattices
Logic programming
Mathematical analysis
Mathematical models
Non-monotonicity
Proving
Semantics
Semantics of logic programming
Theorems
Non-monotonicity
Fixed point theory
Semantics of logic programming
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:We present a fixed point theorem for a class of (potentially) non-monotonic functions over specially structured complete lattices. The theorem has as a special case the Knaster–Tarski fixed point theorem when restricted to the case of monotonic functions and Kleene's theorem when the functions are additionally continuous. From the practical side, the theorem has direct applications in the semantics of negation in logic programming. In particular, it leads to a more direct and elegant proof of the least fixed point result of [12]. Moreover, the theorem appears to have potential for possible applications outside the logic programming domain.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2015.01.032