Humans are good at understanding subjective or vague statements which, however, are hard to express in classical logic. Fuzzy logic is an evolution of classical logic that can cope with vague terms by handling degrees of truth and not just the crisp values true and false. Logic is the formal basis of computing, enabling the formal design of systems supported by tools such as model checkers and theorem provers.This paper shows how a model checker such as Alloy can evolve to handle both classical and fuzzy logic, enabling the specification of high-level quantitative relational models in the fuzzy domain. In particular, the paper showcases how QAlloy-F (a conservative, general-purpose quantitative extension to standard Alloy) can be used to tackle fuzzy problems, namely in the context of validating the design of fuzzy controllers. The evaluation of QAlloy-F against examples taken from various classes of fuzzy case studies shows the approach to be feasible.
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% BibTex
@inproceedings{SilvaCMO24,
author = {Pedro Silva and
Alcino Cunha and
Nuno Macedo and
Jos{\'{e}} N. Oliveira},
editor = {Silvia Bonfanti and
Angelo Gargantini and
Michael Leuschel and
Elvinia Riccobene and
Patrizia Scandurra},
title = {Alloy Goes Fuzzy},
booktitle = {Rigorous State-Based Methods - 10th International Conference, {ABZ}
2024, Bergamo, Italy, June 25-28, 2024, Proceedings},
series = {Lecture Notes in Computer Science},
volume = {14759},
pages = {61--79},
publisher = {Springer},
year = {2024},
url = {https://doi.org/10.1007/978-3-031-63790-2\_4},
doi = {10.1007/978-3-031-63790-2\_4},
timestamp = {Fri, 19 Jul 2024 23:15:46 +0200},
biburl = {https://dblp.org/rec/conf/zum/SilvaCMO24.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}