#topology

Chapter 15 — Applications

Applications of RelationWorld theory to physics, topology, and combinatorics.

Ontology Neural Network and ORTSF: A Framework for Topological Reasoning and Delay-Robust Control

The advancement of autonomous robotic systems has led to significant capabilities in perception, localization, mapping, and control, yet a critical challenge re

An Axiomatic Framework for Understanding Relations via Gauge-Invariant Cohomology

What does it mean for something to exist within a web of relations? We answer this question by developing a rigorous mathematical framework in which existence e

Ontology Neural Networks for Topologically Conditioned Constraint Satisfaction

Neuro-symbolic reasoning systems face fundamental challenges in maintaining semantic coherence while satisfying physical and logical constraints. Building upon