Technology Category
Knowledge Representation and Reasoning: Description LogicsMachine Learning: Statistical Relational/Logic LearningReasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
A Linear Temporal Logic of Frequencies on Series of Events
🤖 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
Application Category
📝 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
Research questions and friction points this paper is trying to address.
Linear Temporal Logic
frequency properties
event series
modal quantifiers
formal reasoning
Innovation
Methods, ideas, or system contributions that make the work stand out.
Linear Temporal Logic
frequency properties
measure-sensitive operators
modal quantifiers
Kripke semantics
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