A Linear Temporal Logic of Frequencies on Series of Events

2026-04-12

AI Summary

This work addresses the challenge of formally expressing and reasoning about frequency properties in event sequences to bridge the gap between logical inference and empirical observation. It introduces LTLF, a novel extension of linear temporal logic that incorporates measure-sensitive explicit modal quantifiers within the standard Kripke semantics, thereby embedding frequency information directly into the logical framework for the first time. LTLF enables a unified characterization of the relationship between empirically observed frequencies and idealized distributions, supporting rigorous evaluation of event frequencies and prediction of future behaviors. By providing a verifiable logical foundation and associated reasoning tools, LTLF facilitates the monitoring and control of quantitative systems—such as machine learning classifiers—where precise frequency-aware guarantees are essential.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Machine Learning: Statistical Relational/Logic Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• 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

Abstract

This paper introduces LTLF, a temporal logic designed to express the frequency properties of event series in a natural but rigorous manner. By introducing novel, measure-sensitive operators, LTLF allows for the evaluation of frequencies and the prediction of future occurrences, thus providing a formal framework to monitor and control quantitative systems, such as machine learning classifiers. The core novelty lies in the introduction of original modal quantifiers associated with a standard Kripke-style semantics. These quantifiers enable the explicit formalization of event series properties and the investigation of the relationship between actual observed frequencies and ideal distributions within a single logical structure. This framework bridges the gap between formal logical reasoning and empirical observation.

Problem

• Linear Temporal Logic
• frequency properties
• event series
• modal quantifiers
• formal reasoning

Innovation

• Linear Temporal Logic
• frequency properties
• measure-sensitive operators
• modal quantifiers
• Kripke semantics