Logic of Fuzzy Paths
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915961972457472 |
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| author | Grover, Kush Gupta, Pratham Křetínský, Jan |
| author_facet | Grover, Kush Gupta, Pratham Křetínský, Jan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24907 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Logic of Fuzzy Paths Grover, Kush Gupta, Pratham Křetínský, Jan Logic in Computer Science Robotics 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. |
| title | Logic of Fuzzy Paths |
| topic | Logic in Computer Science Robotics |
| url | https://arxiv.org/abs/2604.24907 |