“The Nonexistence of Unicorns and Many-Sorted Löwenheim-Skolem Theorems” by Benjamin Przybocki, Guilherme Toledo, Yoni Zohar, and Clark Barrett. In Proceedings of the 26^th International Symposium on Formal Methods (FM '24), Part I, (André Platzer, Kristin Yvonne Rozier, Matteo Pradella, and Matteo Rossi, eds.), Sep. 2024, pp. 658-675. Milan, Italy.
Stable infiniteness, strong finite witnessability, and smoothness are model-theoretic properties relevant to theory combination in satisfiability modulo theories. Theories that are strongly finitely witnessable and smooth are called strongly polite and can be effectively combined with other theories. Toledo, Zohar, and Barrett conjectured that stably infinite and strongly finitely witnessable theories are smooth and therefore strongly polite. They called counterexamples to this conjecture unicorn theories, as their existence seemed unlikely. We prove that, indeed, unicorns do not exist. We also prove versions of the Löwenheim-Skolem theorem and the \Lo-Vaught test for many-sorted logic.
BibTeX entry:
@inproceedings{PTZ+24,
author = {Benjamin Przybocki and Guilherme Toledo and Yoni Zohar and
Clark Barrett},
editor = {Andr{\'e} Platzer and Kristin Yvonne Rozier and Matteo
Pradella and Matteo Rossi},
title = {The Nonexistence of Unicorns and Many-Sorted
L{\"o}wenheim--Skolem Theorems},
booktitle = {Proceedings of the {\it 26^{th}} International Symposium
on Formal Methods (FM '24), Part I},
series = {Lecture Notes in Computer Science},
volume = {14933},
pages = {658--675},
publisher = {Springer Nature Switzerland},
month = sep,
year = {2024},
doi = {10.1007/978-3-031-71162-6_34},
note = {Milan, Italy},
url = {https://link.springer.com/chapter/10.1007/978-3-031-71162-6_34}
}
(This webpage was created with bibtex2web.)