### 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 language | English |
---|---|

Pages (from-to) | 18-38 |

Number of pages | 21 |

Journal | Theoretical Computer Science |

Volume | 574 |

DOIs | |

Publication status | Published - Apr 1 2015 |

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### Keywords

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*574*, 18-38. https://doi.org/10.1016/j.tcs.2015.01.032

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

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 574, pp. 18-38. https://doi.org/10.1016/j.tcs.2015.01.032

}

TY - JOUR

T1 - A fixed point theorem for non-monotonic functions

AU - Ésik, Z.

AU - Rondogiannis, Panos

PY - 2015/4/1

Y1 - 2015/4/1

N2 - 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.

AB - 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.

KW - Fixed point theory

KW - Non-monotonicity

KW - Semantics of logic programming

UR - http://www.scopus.com/inward/record.url?scp=84943606122&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84943606122&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2015.01.032

DO - 10.1016/j.tcs.2015.01.032

M3 - Article

AN - SCOPUS:84943606122

VL - 574

SP - 18

EP - 38

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -