Details

Autor(en) / Beteiligte

• Dubut, Jérémy
• Yamada, Akihisa

Titel

Fixed Points Theorems for Non-Transitive Relations

Ist Teil von

• Logical methods in computer science, 2022-02, Vol.18, Issue 1

Ort / Verlag

Logical Methods in Computer Science e.V

Erscheinungsjahr

2022

Link zum Volltext

Quelle

EZB Free E-Journals

Beschreibungen/Notizen

• In this paper, we develop an Isabelle/HOL library of order-theoretic fixed-point theorems. We keep our formalization as general as possible: we reprove several well-known results about complete orders, often with only antisymmetry or attractivity, a mild condition implied by either antisymmetry or transitivity. In particular, we generalize various theorems ensuring the existence of a quasi-fixed point of monotone maps over complete relations, and show that the set of (quasi-)fixed points is itself complete. This result generalizes and strengthens theorems of Knaster-Tarski, Bourbaki-Witt, Kleene, Markowsky, Pataraia, Mashburn, Bhatta-George, and Stouti-Maaden.