Quantum Implications in Orthomodular Posets
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Multiple-Valued Logic and Soft Computing |
| MU Faculty or unit | |
| Citation | |
| web | https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-44-number-4-2025/mvlsc-44-4-p-385-405/ |
| Keywords | Multiple-valued implication; classical implication; Kalmbach implication; non-tollens implication; Dishkant implication; Sasaki implication; orthomodular poset; modus ponens rule |
| Description | We show that, for every orthogonal lub-complete poset P, we can introduce multiple-valued implications sharing properties with quantum implications presented by Kalmbach for orthomodular lattices. We call them classical implication, Kalmbach implication, non-tollens implication, Dishkant implication and Sasaki implication. If the classical implication satisfies the order property, then the corresponding orthologic becomes classical and vice versa. If the Kalmbach or non-tollens or Dishkant or Sasaki implication meets the order property, then the corresponding orthologic becomes quantum and vice versa. A related result for the modus ponens rule is obtained. |
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