---
title: "Scale-Based Monotonicity Analysis in Qualitative Modelling with Flat Segments"
authors:
  - "Martin Brooks"
  - "Yuhong Yan"
  - "Daniel Lemire"
doi: ""
url: "https://ijcai.org/proceedings/2005/102"
pdf: "https://ijcai.org/proceedings/2005/0102.pdf"
venue: "Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence"
year: 2005
pages: "400-404"
track: ""
keywords:
---

# Scale-Based Monotonicity Analysis in Qualitative Modelling with Flat Segments

Martin Brooks, Yuhong Yan, Daniel Lemire

*Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence*, pages 400-404.

## Abstract

Qualitative models are often more suitable than classical quantitative models in tasks such as Model-based Diagnosis (MBD), explaining system behavior, and designing novel devices from first principles. Monotonicity is an important feature to leverage when constructing qualitative models. Detecting monotonic pieces robustly and efficiently from sensor or simulation data remains an open problem. This paper presents scale-based monotonicity: the notion that monotonicity can be defined relative to a scale. Real-valued functions defined on a finite set of reals e.g. sensor data or simulation results, can be partitioned into quasimonotonic segments, i.e. segments monotonic with respect to a scale, in linear time. A novel segmentation algorithm is introduced along with a scalebased definition of “flatness”.