Relevant S is Undecidable. Knudstorp, S. B. In Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science, of LICS '24, New York, NY, USA, 2024. Association for Computing Machinery.
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Since the introduction of the semilattice relevant logic S by [Urquhart 1972, 1973], its decision problem has persisted as an open problem.[Urquhart 1984] showed that many relevant logics are undecidable, yet S eluded these techniques. Eventually, this led experts, including [Urquhart 2016], to conjecture that S is decidable. Contrary to this conjecture, by interpreting a tiling problem, we show that S is undecidable.
@inproceedings{10.1145/3661814.3662128,
author = {Knudstorp, S\o{}ren Brinck},
title = {Relevant S is Undecidable},
year = {2024},
isbn = {9798400706608},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3661814.3662128},
doi = {10.1145/3661814.3662128},
abstract = {Since the introduction of the semilattice relevant logic S by [Urquhart 1972, 1973], its decision problem has persisted as an open problem.[Urquhart 1984] showed that many relevant logics are undecidable, yet S eluded these techniques. Eventually, this led experts, including [Urquhart 2016], to conjecture that S is decidable. Contrary to this conjecture, by interpreting a tiling problem, we show that S is undecidable.},
booktitle = {Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science},
articleno = {51},
numpages = {8},
keywords = {relevant logic, undecidability, finite model property, tiling, semilattice},
location = {Tallinn, Estonia},
series = {LICS '24}
}

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