Constructive Preference Relations: Navigating Undecidability in Rational LTL Contraction

2026-06-15

AI Summary

This work addresses the fundamental challenge of constructing preference relations in Linear Temporal Logic (LTL) that satisfy rational contraction postulates, a task rendered inherently difficult by the undecidability of core decision problems. To overcome this barrier within the conventional automata-theoretic framework, the paper proposes a constructive approach based on a non-classical generalization of Dalal’s distance measure and a multi-layered preference aggregation mechanism. By integrating Büchi automata-based semantic modeling of LTL with formal belief contraction theory, the authors develop a rich and computable family of preference relations. These relations not only enable effective belief contraction in LTL but also substantially extend the expressive power and applicability of rational preference models beyond classical logic.

Abstract

We study the computational aspects of epistemic preference relations in non-classical logics, particularly linear temporal logic (LTL). Epistemic preferences form the backbone of belief contraction operators, which describe how to rationally relinquish obsolete beliefs. These preference relations have to satisfy certain innocuous conditions; and constructing such relations is usually assumed to be a trivial process. However, in the case of LTL, where relations are represented with Büchi automata, we show that this is a challenging task: the core condition, which guarantees the success of contraction, is in fact undecidable. Towards achieving effective LTL belief contraction, we then propose several concrete constructions of novel preference relations that satisfy the required conditions by design. These constructions include, among others, (1) generalisations of distance measures (e.g. Dalal) beyond the classical setting, as well as (2) the ability to hierarchically compose different preference relations. Our results not only provide rich families of preference relations for LTL, but also generalise the limited pool of concrete preference relations for the classical cases, allowing us to go beyond Dalal to achieve full rationality.

Problem

• Preference Relations
• Belief Contraction
• Linear Temporal Logic
• Undecidability
• Epistemic Preferences

Innovation

• Preference Relations
• LTL Contraction
• Undecidability
• Belief Revision
• Büchi Automata