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Tommaso Moraschini [11]T. Moraschini [5]
  1.  27
    On the Complexity of the Leibniz Hierarchy.Tommaso Moraschini - 2019 - Annals of Pure and Applied Logic 170 (7):805-824.
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  2.  8
    Logics of Left Variable Inclusion and Płonka Sums of Matrices.S. Bonzio, T. Moraschini & M. Pra Baldi - 2020 - Archive for Mathematical Logic (1-2):49-76.
    The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic \. We prove that the description of the algebraic counterpart of the left variable inclusion companion of a given logic \ is related to the construction of Płonka sums of the matrix models of \. This observation allows to obtain a Hilbert-style axiomatization of the logics of left variable inclusion, to describe the structure of their reduced models, and to locate (...)
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  3.  79
    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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  4.  11
    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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  5.  16
    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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  6.  3
    The Poset of All Logics III: Finitely Presentable Logics.Ramon Jansana & Tommaso Moraschini - forthcoming - Studia Logica:1-42.
    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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  7.  9
    A Study of Truth Predicates in Matrix Semantics.Tommaso Moraschini - 2018 - Review of Symbolic Logic 11 (4):780-804.
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  8.  4
    Varieties of de Morgan Monoids: Covers of Atoms.T. Moraschini, J. G. Raftery & J. J. Wannenburg - 2020 - Review of Symbolic Logic 13 (2):338-374.
    The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De Morgan monoids may (...)
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  9.  6
    Epimorphisms, Definability and Cardinalities.T. Moraschini, J. G. Raftery & J. J. Wannenburg - 2020 - Studia Logica 108 (2):255-275.
    We characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures. This allows us to strengthen a result of Bacsich, as follows: in any prevariety having at most \ non-logical symbols and an axiomatization requiring at most \ variables, if the epimorphisms into structures with at most \ elements are surjective, then so are all of the epimorphisms. Using these facts, we formulate and prove manageable ‘bridge theorems’, matching the surjectivity of all epimorphisms in (...)
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  10.  32
    The Semantic Isomorphism Theorem in Abstract Algebraic Logic.Tommaso Moraschini - 2016 - Annals of Pure and Applied Logic 167 (12):1298-1331.
  11.  4
    Logics of Varieties, Logics of Semilattices and Conjunction.J. M. Font & T. Moraschini - 2014 - Logic Journal of the IGPL 22 (6):818-843.
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  12.  19
    An Abstract Approach to Consequence Relations.Petr Cintula, José Gil-férez, Tommaso Moraschini & Francesco Paoli - 2019 - Review of Symbolic Logic 12 (2):331-371.
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  13.  7
    Epimorphism Surjectivity in Varieties of Heyting Algebras.T. Moraschini & J. J. Wannenburg - 2020 - Annals of Pure and Applied Logic 171 (9):102824.
    It was shown recently that epimorphisms need not be surjective in a variety K of Heyting algebras, but only one counter-example was exhibited in the literature until now. Here, a continuum of such examples is identified, viz. the variety generated by the Rieger-Nishimura lattice, and all of its (locally finite) subvarieties that contain the original counter-example K . It is known that, whenever a variety of Heyting algebras has finite depth, then it has surjective epimorphisms. In contrast, we show that (...)
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  14. Singly Generated Quasivarieties and Residuated Structures.Tommaso Moraschini, James G. Raftery & Johann J. Wannenburg - 2020 - Mathematical Logic Quarterly 66 (2):150-172.
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  15.  8
    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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