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  1. The Poset of All Logics I: Interpretations and Lattice Structure.R. Jansana & T. Moraschini - 2021 - Journal of Symbolic Logic 86 (3):935-964.
    A notion of interpretation between arbitrary logics is introduced, and the poset$\mathsf {Log}$of all logics ordered under interpretability is studied. It is shown that in$\mathsf {Log}$infima of arbitrarily large sets exist, but binary suprema in general do not. On the other hand, the existence of suprema of sets of equivalential logics is established. The relations between$\mathsf {Log}$and the lattice of interpretability types of varieties are investigated.
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  • On Equational Completeness Theorems.Tommaso Moraschini - 2022 - Journal of Symbolic Logic 87 (4):1522-1575.
    A logic is said to admit an equational completeness theorem when it can be interpreted into the equational consequence relative to some class of algebras. We characterize logics admitting an equational completeness theorem that are either locally tabular or have some tautology. In particular, it is shown that a protoalgebraic logic admits an equational completeness theorem precisely when it has two distinct logically equivalent formulas. While the problem of determining whether a logic admits an equational completeness theorem is shown to (...)
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