Titlebook: Algebraic Perspectives on Substructural Logics; Davide Fazio,Antonio Ledda,Francesco Paoli Book 2021 Springer Nature Switzerland AG 2021 S

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Editorial Introduction,After providing an overview of the algebraic investigations into substructural logics in a historical perspective, with a special focus on their relationships with quantum logics, we summarise the contents of the subsequent chapters of this volume.

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978-3-030-52165-3Springer Nature Switzerland AG 2021

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https://doi.org/10.1007/978-3-642-20904-8e try to introduce an implication in these lattices which can be easily axiomatized and which yields a nice lattice structure. As shown in the paper, this can be realized in several different ways. Moreover, we reveal the connection of weakly and dually weakly orthomodular lattices to residuated str

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https://doi.org/10.1007/978-3-642-20904-8hen these operators are transformed into lattice terms and the poset . is completed to its Dedekind–MacNeille completion . then the complete lattice . becomes a residuated lattice with respect to these transformed terms. It is shown that this holds in particular for Boolean posets and for relatively

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https://doi.org/10.1007/978-3-642-20904-8ttices and Kleene algebras with an extra unary operation. We study in the framework of PBZ.–lattices two constructions—the ordinal sum construction and the horizontal sum construction—that have been widely used in the investigation of both quantum structures and residuated structures. We provide axi

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