Relevance implication and orthomodular posets
| Authors | |
|---|---|
| Year of publication | 2024 |
| Type | Article in Proceedings |
| Conference | 2024 IEEE 54th International Symposium on Multiple-Valued Logic (ISMVL) |
| MU Faculty or unit | |
| Citation | |
| web | https://ieeexplore.ieee.org/document/10628568 |
| Doi | http://dx.doi.org/10.1109/ISMVL60454.2024.00026 |
| Keywords | multiple-valued implication; Kalmbach implication; non-tollens implication; Dishkant implication; Sasaki implication; relevance implication; classical implication; orthomodular poset; modus ponens rule |
| Description | We establish five distinct multiple-valued quantum implications for orthogonal 2-lub-complete posets, encompassing Kalmbach implication, non-tollens implication, Dishkant implication, Sasaki implication, and relevance implication. We demonstrate that if any of these implications adhere to the order property, the corresponding poset transforms into a quantum logic, and vice versa. Additionally, we obtain a corresponding result for the modus ponens rule. |
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