Integrating Qualitative and Quantitative Reasoning in Knowledge Representation Systems

Title: Integrating Qualitative and Quantitative Reasoning in Knowledge Representation Systems

Abstract: This research aims to develop a knowledge representation system that can integrate both qualitative and quantitative reasoning. The system is designed to provide a more flexible, cognitively plausible, and computationally efficient way to represent knowledge from various sources. The study integrates Frank's cone-shaped and projection-based calculi of cardinal direction relations, which are well-known in qualitative spatial reasoning (QSR). The general form of a constraint in the system is a disjunction of convex constraints, which allows for the representation of both qualitative and quantitative knowledge. The research presents an effective solution search algorithm for the Spatial Constraint Satisfaction Problem (SCSP), which uses constraint propagation and the Simplex algorithm for completeness. This approach is particularly suitable for large-scale high-level vision applications, such as satellite surveillance.

Main Research Question: How can we develop a knowledge representation system that integrates both qualitative and quantitative reasoning, providing a more flexible, cognitively plausible, and computationally efficient way to represent knowledge?

Methodology: The study integrates Frank's cone-shaped and projection-based calculi of cardinal direction relations into a more general language based on convex constraints. The general form of a constraint in the system is a disjunction of convex constraints, allowing for the representation of both qualitative and quantitative knowledge. The research presents an effective solution search algorithm for the SCSP, which uses constraint propagation and the Simplex algorithm for completeness.

Results: The research demonstrates that the proposed system can effectively represent both qualitative and quantitative knowledge. The SCSP algorithm provides an efficient way to search for solutions, ensuring completeness and providing better computational performance.

Implications: The development of a knowledge representation system that integrates both qualitative and quantitative reasoning can provide a more flexible and cognitively plausible way to represent knowledge. This can lead to improved performance in various applications, such as high-level vision systems, where the ability to reason about both qualitative and quantitative information is essential.

Link to Article: https://arxiv.org/abs/0311051v1 Authors: arXiv ID: 0311051v1