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arXiv · 2604.10669

A Linear Temporal Logic of Frequencies on Series of Events

Melissa Antonelli·Leonardo Ceragioli·Alessandro Giuseppe Buda·Giuseppe Primiero
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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.

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Melissa Antonelli, Leonardo Ceragioli, Alessandro Giuseppe Buda, Giuseppe Primiero. 2026-04-12. A Linear Temporal Logic of Frequencies on Series of Events. https://arxiv.org/abs/2604.10669

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