A fixed point theorem for non-monotonic functions

Z. Ésik, Panos Rondogiannis

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)18-38
Number of pages21
JournalTheoretical Computer Science
Volume574
DOIs
Publication statusPublished - Apr 1 2015

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Fixed point theorem
Logic programming
Logic Programming
Theorem
Monotonic Function
Complete Lattice
Semantics
Fixed point

Keywords

  • Fixed point theory
  • Non-monotonicity
  • Semantics of logic programming

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

A fixed point theorem for non-monotonic functions. / Ésik, Z.; Rondogiannis, Panos.

In: Theoretical Computer Science, Vol. 574, 01.04.2015, p. 18-38.

Research output: Contribution to journalArticle

Ésik, Z. ; Rondogiannis, Panos. / A fixed point theorem for non-monotonic functions. In: Theoretical Computer Science. 2015 ; Vol. 574. pp. 18-38.
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