17 found
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  1.  19
    The Poset of All Logics III: Finitely Presentable Logics.Ramon Jansana & Tommaso Moraschini - 2020 - Studia Logica 109 (3):539-580.
    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 (...)
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  2.  9
    Singly generated quasivarieties and residuated structures.Tommaso Moraschini, James G. Raftery & Johann J. Wannenburg - 2020 - Mathematical Logic Quarterly 66 (2):150-172.
    A quasivariety of algebras has the joint embedding property (JEP) if and only if it is generated by a single algebra A. It is structurally complete if and only if the free ℵ0‐generated algebra in can serve as A. A consequence of this demand, called ‘passive structural completeness’ (PSC), is that the nontrivial members of all satisfy the same existential positive sentences. We prove that if is PSC then it still has the JEP, and if it has the JEP and (...)
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  3.  13
    A study of truth predicates in matrix semantics.Tommaso Moraschini - 2018 - Review of Symbolic Logic 11 (4):780-804.
  4.  34
    On the complexity of the Leibniz hierarchy.Tommaso Moraschini - 2019 - Annals of Pure and Applied Logic 170 (7):805-824.
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  5.  4
    The algebraic significance of weak excluded middle laws.Tomáš Lávička, Tommaso Moraschini & James G. Raftery - 2022 - Mathematical Logic Quarterly 68 (1):79-94.
    For (finitary) deductive systems, we formulate a signature‐independent abstraction of the weak excluded middle law (WEML), which strengthens the existing general notion of an inconsistency lemma (IL). Of special interest is the case where a quasivariety algebraizes a deductive system ⊢. We prove that, in this case, if ⊢ has a WEML (in the general sense) then every relatively subdirectly irreducible member of has a greatest proper ‐congruence; the converse holds if ⊢ has an inconsistency lemma. The result extends, in (...)
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  6.  17
    A computational glimpse at the Leibniz and Frege hierarchies.Tommaso Moraschini - 2018 - Annals of Pure and Applied Logic 169 (1):1-20.
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  7.  15
    A logical and algebraic characterization of adjunctions between generalized quasi-varieties.Tommaso Moraschini - 2018 - Journal of Symbolic Logic 83 (3):899-919.
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  8.  6
    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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  9.  7
    Hereditarily Structurally Complete Intermediate Logics: Citkin’s Theorem Via Duality.Nick Bezhanishvili & Tommaso Moraschini - 2023 - Studia Logica 111 (2):147-186.
    A deductive system is said to be structurally complete if its admissible rules are derivable. In addition, it is called hereditarily structurally complete if all its extensions are structurally complete. Citkin (1978) proved that an intermediate logic is hereditarily structurally complete if and only if the variety of Heyting algebras associated with it omits five finite algebras. Despite its importance in the theory of admissible rules, a direct proof of Citkin’s theorem is not widely accessible. In this paper we offer (...)
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  10.  85
    M-Sets and the Representation Problem.Josep Maria Font & Tommaso Moraschini - 2015 - Studia Logica 103 (1):21-51.
    The “representation problem” in abstract algebraic logic is that of finding necessary and sufficient conditions for a structure, on a well defined abstract framework, to have the following property: that for every structural closure operator on it, every structural embedding of the expanded lattice of its closed sets into that of the closed sets of another structural closure operator on another similar structure is induced by a structural transformer between the base structures. This question arose from Blok and Jónsson abstract (...)
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  11.  29
    An Abstract Approach to Consequence Relations.Petr Cintula, José Gil-férez, Tommaso Moraschini & Francesco Paoli - 2019 - Review of Symbolic Logic 12 (2):331-371.
    We generalise the Blok–Jónsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and Jónsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariablyaggregatedvia set-theoretical union. Our approach is more general in that nonidempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, are considered. (...)
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  12.  38
    The semantic isomorphism theorem in abstract algebraic logic.Tommaso Moraschini - 2016 - Annals of Pure and Applied Logic 167 (12):1298-1331.
  13.  10
    Varieties of positive modal algebras and structural completeness.Tommaso Moraschini - 2019 - Review of Symbolic Logic 12 (3):557-588.
    Positive modal algebras are the$$\left\langle { \wedge, \vee,\diamondsuit,\square,0,1} \right\rangle $$-subreducts of modal algebras. We prove that the variety of positive S4-algebras is not locally finite. On the other hand, the free one-generated positive S4-algebra is shown to be finite. Moreover, we describe the bottom part of the lattice of varieties of positive S4-algebras. Building on this, we characterize structurally complete varieties of positive K4-algebras.
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  14.  7
    Positive modal logic beyond distributivity.Nick Bezhanishvili, Anna Dmitrieva, Jim de Groot & Tommaso Moraschini - 2024 - Annals of Pure and Applied Logic 175 (2):103374.
  15.  14
    Structural Completeness in Many-Valued Logics with Rational Constants.Joan Gispert, Zuzana Haniková, Tommaso Moraschini & Michał Stronkowski - 2022 - Notre Dame Journal of Formal Logic 63 (3):261-299.
    The logics RŁ, RP, and RG have been obtained by expanding Łukasiewicz logic Ł, product logic P, and Gödel–Dummett logic G with rational constants. We study the lattices of extensions and structural completeness of these three expansions, obtaining results that stand in contrast to the known situation in Ł, P, and G. Namely, RŁ is hereditarily structurally complete. RP is algebraized by the variety of rational product algebras that we show to be Q-universal. We provide a base of admissible rules (...)
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  16.  3
    Intuitionistic Sahlqvist Theory for Deductive Systems.Damiano Fornasiere & Tommaso Moraschini - forthcoming - Journal of Symbolic Logic:1-59.
    Sahlqvist theory is extended to the fragments of the intuitionistic propositional calculus that include the conjunction connective. This allows us to introduce a Sahlqvist theory of intuitionistic character amenable to arbitrary protoalgebraic deductive systems. As an application, we obtain a Sahlqvist theorem for the fragments of the intuitionistic propositional calculus that include the implication connective and for the extensions of the intuitionistic linear logic.
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  17.  3
    Elementary Equivalence in Positive Logic Via Prime Products.Tommaso Moraschini, Johann J. Wannenburg & Kentaro Yamamoto - forthcoming - Journal of Symbolic Logic:1-18.
    We introduce prime products as a generalization of ultraproducts for positive logic. Prime products are shown to satisfy a version of Łoś’s Theorem restricted to positive formulas, as well as the following variant of the Keisler Isomorphism Theorem: under the generalized continuum hypothesis, two models have the same positive theory if and only if they have isomorphic prime powers of ultrapowers.
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