Logic of Fuzzy Paths

• URL: http://arxiv.org/abs/2604.24907v1
• Date: Mon, 27 Apr 2026 18:40:05 GMT
• Title: Logic of Fuzzy Paths
• Abstract summary: We introduce a new family of temporal logics intended for specifications in motion planning (MP)<n>It builds upon the signal temporal logic (STL), which is a linear-time logic over real-valued signals.<n>We show the advantages of our proposed logic on examples and show the versatility and flexibility of the framework on a number of scenarios.
• Score: 0.5161531917413708
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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