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A study of truth predicates in matrix semantics

Tommaso Moraschini

Review of Symbolic Logic 11 (4):780-804 (2018)

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The Suszko operator relative to truth‐equational logics.Hugo Albuquerque - 2021 - Mathematical Logic Quarterly 67 (2):226-240.details This note presents some new results from [1] about the Suszko operator and truth‐equational logics, following the works of Czelakowski [11] and Raftery [17]. It is proved that the Suszko operator relative to a truth‐equational logic preserves suprema and commutes with endomorphisms. Together with injectivity, proved by Raftery in [17], the Suszko operator relative to a truth‐equational logic is a structural representation, as defined in [15]. Furthermore, if is a quasivariety, then the Suszko operator relative to a truth‐equational logic is (...) Download Export citation Bookmark
On the complexity of the Leibniz hierarchy.Tommaso Moraschini - 2019 - Annals of Pure and Applied Logic 170 (7):805-824.details Download Export citation Bookmark 4 citations
On Equational Completeness Theorems.Tommaso Moraschini - 2022 - Journal of Symbolic Logic 87 (4):1522-1575.details 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 (...) Download Export citation Bookmark 1 citation
The Poset of All Logics III: Finitely Presentable Logics.Ramon Jansana & Tommaso Moraschini - 2020 - Studia Logica 109 (3):539-580.details A logic in a finite language is said to be finitely presentable if it is axiomatized by finitely many finite rules. It is proved that binary non-indexed products of logics that are both finitely presentable and finitely equivalential are essentially finitely presentable. This result does not extend to binary non-indexed products of arbitrary finitely presentable logics, as shown by a counterexample. Finitely presentable logics are then exploited to introduce finitely presentable Leibniz classes, and to draw a parallel between the Leibniz (...) and the Maltsev hierarchies. (shrink) Download Export citation Bookmark 6 citations
The Poset of All Logics I: Interpretations and Lattice Structure.R. Jansana & T. Moraschini - 2021 - Journal of Symbolic Logic 86 (3):935-964.details 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. Download Export citation Bookmark 2 citations
The Poset of All Logics II: Leibniz Classes and Hierarchy.R. Jansana & T. Moraschini - 2023 - Journal of Symbolic Logic 88 (1):324-362.details A Leibniz class is a class of logics closed under the formation of term-equivalent logics, compatible expansions, and non-indexed products of sets of logics. We study the complete lattice of all Leibniz classes, called the Leibniz hierarchy. In particular, it is proved that the classes of truth-equational and assertional logics are meet-prime in the Leibniz hierarchy, while the classes of protoalgebraic and equivalential logics are meet-reducible. However, the last two classes are shown to be determined by Leibniz conditions consisting of (...) meet-prime logics only. (shrink) Download Export citation Bookmark 2 citations

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