Constructions of Kleene lattices
| Authors | |
|---|---|
| Year of publication | 2022 |
| Type | Article in Proceedings |
| Conference | 2022 IEEE 52ND INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC (ISMVL 2022) |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.ieeecomputersociety.org/10.1109/ISMVL52857.2022.00020 |
| Doi | http://dx.doi.org/10.1109/ISMVL52857.2022.00020 |
| Keywords | Full twist-product; Kleene lattice; representation |
| Description | We present an easy construction producing a Kleene lattice K = (K, (sic), (sic), ') from an arbitrary distributive lattice L = (L, V, Lambda) and a non-empty subset of L. We show that L can be embedded into K and compute vertical bar K vertical bar under certain additional assumptions. We prove that every finite chain considered as a Kleene lattice can be represented in this way and that this construction preserves direct products. Moreover, we demonstrate that certain Kleene lattices that are ordinal sums of distributive lattices are representable. Finally, we prove that not every Kleene lattice is representable. |
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