Efficient Inference and Computation of Optimal Alternatives for Preference Languages Based On Lexicographic Models

TL;DR

This paper introduces efficient algorithms for inference and optimality testing in lexicographic preference languages, demonstrating polynomial complexity for a broad class of preference statements and validating with experimental results.

Contribution

It identifies strong compositionality enabling greedy algorithms for consistency checking and establishes polynomial-time methods for inference and optimal set computation in lexicographic models.

Findings

Consistency testing is polynomial for language LpqT.

Optimal set computation is polynomial.

Experimental results support the efficiency of proposed algorithms.

Abstract

We analyse preference inference, through consistency, for general preference languages based on lexicographic models. We identify a property, which we call strong compositionality, that applies for many natural kinds of preference statement, and that allows a greedy algorithm for determining consistency of a set of preference statements. We also consider different natural definitions of optimality, and their relations to each other, for general preference languages based on lexicographic models. Based on our framework, we show that testing consistency, and thus inference, is polynomial for a specific preference language LpqT, which allows strict and non-strict statements, comparisons between outcomes and between partial tuples, both ceteris paribus and strong statements, and their combination. Computing different kinds of optimal sets is also shown to be polynomial; this is backed up by our experimental results.