Publication details
Foulis m-semilattices and their modules
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Proceedings |
| Conference | 2025 IEEE 55th International Symposium on Multiple-Valued Logic (ISMVL) |
| MU Faculty or unit | |
| Citation | |
| web | https://www.computer.org/csdl/proceedings-article/ismvl/2025/074400a196/27EbG45NrGw |
| Doi | https://doi.org/10.1109/ISMVL64713.2025.00044 |
| Keywords | quantale; quantale module; orthomodular lattice; linear map; Sasaki projection; Foulis m-semilattice; msemilattice module |
| Description | Building upon results of Jacobs, we show that the category OMLatLin of orthomodular lattices and linear maps forms a dagger category. For each orthomodular lattice X, we construct a Foulis m-semilattice Lin(X) composed of endomorphisms of X. This m-semilattice acts as a quantale, enabling us to regard X as a left Lin(X)-module. Our novel approach introduces a fuzzy-theoretic dimension to the theory of orthomodular lattices. |
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