Logic of Fuzzy Paths

2026-04-27

AI Summary

Traditional temporal logics struggle to intuitively capture human intent and are ill-suited for learning task specifications from demonstration data. This work proposes a novel fuzzy path logic that treats paths as first-class entities, decoupling geometric and logical concerns. By integrating fuzzy logic, time-varying signal constraints, and path semantics, the approach extends Signal Temporal Logic (STL) into a specification language capable of expressing behavioral preferences. The authors develop a corresponding learning algorithm and prototype system that automatically infer task specifications from demonstrations. Empirical evaluation across multiple motion planning scenarios demonstrates the logic’s advantages in conciseness, interpretability, and flexibility, enabling preliminary applications in specification learning, model checking, and runtime monitoring.

Abstract

We introduce a new family of temporal logics intended for specifications in motion planning (MP). It builds upon the signal temporal logic (STL), which is a linear-time logic over real-valued signals that possess quantitative semantics and thus became popular in the areas of cyber-physical systems, robotics, and specifically robot MP. However, in contrast to STL, the proposed logic works with paths as first-class citizens, separating the concerns of geometry and of logic. This in turn leads to simpler and more understandable formulae, and a more refined notion of satisfaction being able to reflect also preferences over behaviours. Technically, the logic is built on fuzzy, time-varying signal constraints. As a consequence of this expressivity, it is (i) more usable for human-given specifications in MP and (ii) more amenable to learning specifications from demonstrations than other logics. The former is important for the traditional style of verification in robot MP; the latter is becoming recognized as crucial for mining data-given tasks and controller synthesis in human-aware MP. We expose the advantages of our proposed logic on examples and show the versatility and flexibility of the framework on a number of scenarios. Finally, we give a learning algorithm with a prototype implementation and discuss the possibilities of model checking and monitoring.

Problem

• motion planning
• temporal logic
• specification learning
• fuzzy paths
• human-aware robotics

Innovation

• fuzzy paths
• temporal logic
• motion planning
• specification learning
• signal temporal logic