Work

Fixed Points Theorems for Non-Transitive Relations

Year: 2022

Type: article

Abstract: 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.

Source: Logical Methods in Computer Science

DOI: 10.46298/lmcs-18(1:30)2022

Authors: Jérémy Dubut, Akihisa Yamada

Institutions: National Institute of Informatics, National Institute of Advanced Industrial Science and Technology

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Japan Society for the Promotion of Science, Exploratory Research for Advanced Technology

Awards: Synthesising directed structures in Computer Science using Directed Algebraic Topology, G5913768863