Chajda, I., Fazio, D., Länger, H., Ledda, A., & Paseka, J. (2024). Implication in sharply paraorthomodular and relatively paraorthomodular posets. In J. Malinowski & R. Palczewski (Eds.), Janusz Czelakowski on Logical Consequence (Vol. 27, pp. 419–446). Springer. https://doi.org/10.1007/978-3-031-44490-6
In this paper we show that several classes of partially ordered structures having paraorthomodular reducts, or whose sections may be regarded as paraorthomodular posets, admit a quite natural notion of implication, that admits a suitable notion of adjointness. Within this framework, we propose a smooth generalization of celebrated Greechie’s theorems on amalgams of finite Boolean algebras to the realm of Kleene lattices.
