Kalmbach implication in orthomodular posets

• Autoři: EMIR Kadir; PASEKA Jan
• Rok publikování: 2023
• Druh: Článek ve sborníku
• Konference: 53rd International Symposium on Multiple-Valued Logic (ISMVL 2023)
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: http://dx.doi.org/10.1109/ismvl57333.2023.00015
• Doi: http://dx.doi.org/10.1109/ISMVL57333.2023.00015
• Klíčová slova: multiple-valued implication; classical implication; Kalmbach implication; non-tolens implication; orthomodular poset; modus ponens rule
• Popis: We show that for every orthogonal lub-complete poset P = (P,?,', 0, 1), we can introduce multiple-valued implications sharing properties with quantum implications presented for orthomodular lattices by Kalmbach. We call them classical implication, Kalmbach implication, and non-tolens implication.If the classical implication satisfies the order property, then the corresponding orthologic becomes classical and vice versa. If the Kalmbach or non-tolens implication meets the order property, then the corresponding orthologic becomes quantum and vice versa. A related result for the modus ponens rule is obtained.

Související projekty

• Ortomodularita z různých pohledů
• Specifický výzkum v odborné a učitelské matematice 2023