Reasoning about soft constraints and conditional preferences: complexity results and approximation techniques

TL;DR

This paper introduces a unified framework combining CP-nets and soft constraints to handle hard constraints, soft constraints, and conditional preferences efficiently, analyzing their complexity and proposing approximation methods.

Contribution

It presents a novel formalism that unifies different preference and constraint types and studies their computational complexity and approximation techniques.

Findings

Testing preference consistency is computationally complex.

Soft constraints can approximate conditional preferences effectively.

The framework improves computational efficiency in preference reasoning.

Abstract

Many real life optimization problems contain both hard and soft constraints, as well as qualitative conditional preferences. However, there is no single formalism to specify all three kinds of information. We therefore propose a framework, based on both CP-nets and soft constraints, that handles both hard and soft constraints as well as conditional preferences efficiently and uniformly. We study the complexity of testing the consistency of preference statements, and show how soft constraints can faithfully approximate the semantics of conditional preference statements whilst improving the computational complexity