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  1. Structurally complete finitary extensions of positive Łukasiewicz logic.Paolo Aglianò & Francesco Manfucci - forthcoming - Logic Journal of the IGPL.
    In this paper we study |$\mathcal{M}\mathcal{V}^{+}$|⁠, i.e. the positive fragment of Łukasiewicz infinite-valued Logic |$\mathcal{M}\mathcal{V}$|⁠. Using mainly algebraic techniques we characterize all the finitary extensions of |$\mathcal{M}\mathcal{V}^{+}$| that are structurally complete and those that are hereditarily structurally complete.
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  • Free Constructions in Hoops via $$\ell $$-Groups.Valeria Giustarini, Francesco Manfucci & Sara Ugolini - forthcoming - Studia Logica:1-49.
    Lattice-ordered abelian groups, or abelian$$\ell $$ ℓ -groups in what follows, are categorically equivalent to two classes of 0-bounded hoops that are relevant in the realm of the equivalent algebraic semantics of many-valued logics: liftings of cancellative hoops and perfect MV-algebras. The former generate the variety of product algebras, and the latter the subvariety of MV-algebras generated by perfect MV-algebras, that we shall call $$\textsf{DLMV}$$ DLMV. In this work we focus on these two varieties and their relation to the structures (...)
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  • On the Structure of Bochvar Algebras.Stefano Bonzio & Michele Pra Baldi - forthcoming - Review of Symbolic Logic:1-27.
    Bochvar algebras consist of the quasivariety $\mathsf {BCA}$ playing the role of equivalent algebraic semantics for Bochvar (external) logic, a logical formalism introduced by Bochvar [4] in the realm of (weak) Kleene logics. In this paper, we provide an algebraic investigation of the structure of Bochvar algebras. In particular, we prove a representation theorem based on Płonka sums and investigate the lattice of subquasivarieties, showing that Bochvar (external) logic has only one proper extension (apart from classical logic), algebraized by the (...)
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