Characterizing LTL Formulas by Examples

2026-04-23

AI Summary

This study investigates whether Linear Temporal Logic (LTL) formulas can be uniquely characterized by finite labeled examples, a capability essential for example-based specification, debugging, and learning. Through formal analysis, the work provides the first complete characterization of the fragment of LTL that is uniquely identifiable from finite words. It further substantially extends this identifiability by introducing two enriched forms of examples: transfinite words and patterned examples. Transfinite words enable the finite unique characterization of a broad class of monotonic LTL formulas, while patterned examples overcome the expressive limitations inherent in traditional finite samples. Collectively, this work establishes a systematic theoretical framework for the characterizability of LTL formulas under varying assumptions on the form and structure of available examples.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Statistical Relational/Logic Learning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We investigate the extent to which Linear Temporal Logic (LTL) formulas can be uniquely characterized by a finite set of labeled examples. We consider different types of examples, ranging from finite words to transfinite words, as well as schematic examples. In the finite-word setting, we provide a complete classification of basis-restricted LTL fragments that admit such unique characterizations. Next, we show that allowing transfinite words as examples enables finite unique characterizations for large monotone fragments of LTL. Finally, we introduce schematic examples, i.e., patterns that compactly represent a family of finite words, and we show that these enable unique characterization results in the finite setting that were not possible with ordinary finite examples alone. Overall, the work provides a foundational account of the descriptive power of different example types for example-driven specification, debugging, and learning of temporal properties.

Problem

• LTL
• unique characterization
• finite words
• transfinite words
• schematic examples

Innovation

• Linear Temporal Logic
• unique characterization
• schematic examples
• transfinite words
• example-driven specification