7 found
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  1.  22
    On Paraconsistent Weak Kleene Logic: Axiomatisation and Algebraic Analysis.Stefano Bonzio, José Gil-Férez, Francesco Paoli & Luisa Peruzzi - 2017 - Studia Logica 105 (2):253-297.
    Paraconsistent Weak Kleene logic is the 3-valued logic with two designated values defined through the weak Kleene tables. This paper is a first attempt to investigate PWK within the perspective and methods of abstract algebraic logic. We give a Hilbert-style system for PWK and prove a normal form theorem. We examine some algebraic structures for PWK, called involutive bisemilattices, showing that they are distributive as bisemilattices and that they form a variety, \, generated by the 3-element algebra WK; we also (...)
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  2.  80
    Representations of Structural Closure Operators.José Gil-Férez - 2011 - Archive for Mathematical Logic 50 (1-2):45-73.
    We continue the work of Blok and Jónsson by developing the theory of structural closure operators and introducing the notion of a representation between them. Similarities and equivalences of Blok-Jónsson turn out to be bijective representations and bijective structural representations, respectively. We obtain a characterization for representations induced by a transformer. In order to obtain a similar characterization for structural representations we introduce the notions of a graduation and a graded variable of an M-set. We show that several deductive systems, (...)
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  3.  4
    Join-Completions of Partially Ordered Algebras.José Gil-Férez, Luca Spada, Constantine Tsinakis & Hongjun Zhou - 2020 - Annals of Pure and Applied Logic 171 (10):102842.
    We present a systematic study of join-extensions and join-completions of partially ordered algebras, which naturally leads to a refined and simplified treatment of fundamental results and constructions in the theory of ordered structures ranging from properties of the Dedekind–MacNeille completion to the proof of the finite embeddability property for a number of varieties of lattice-ordered algebras.
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  4.  15
    Leibniz Interpolation Properties.Leonardo Cabrer & José Gil-Férez - 2014 - Annals of Pure and Applied Logic 165 (4):933-962.
    We introduce a family of notions of interpolation for sentential logics. These concepts generalize the ones for substructural logics introduced in [5]. We show algebraic characterizations of these notions for the case of equivalential logics and study the relation between them and the usual concepts of Deductive, Robinson, and Maehara interpolation properties.
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  5.  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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  6.  5
    Integrally Closed Residuated Lattices.José Gil-Férez, Frederik Möllerström Lauridsen & George Metcalfe - 2020 - Studia Logica 108 (5):1063-1086.
    A residuated lattice is said to be integrally closed if it satisfies the quasiequations \ and \, or equivalently, the equations \ and \. Every integral, cancellative, or divisible residuated lattice is integrally closed, and, conversely, every bounded integrally closed residuated lattice is integral. It is proved that the mapping \\backslash {\mathrm {e}}\) on any integrally closed residuated lattice is a homomorphism onto a lattice-ordered group. A Glivenko-style property is then established for varieties of integrally closed residuated lattices with respect (...)
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  7.  6
    Multi‐Term Π‐Institutions and Their Equivalence.José Gil-Férez - 2006 - Mathematical Logic Quarterly 52 (5):505-526.
    The notion of a multi-term π-institution is introduced and a criterion for the equivalence of two multi-term π-institutions in terms of their categories of theories is proved. Moreover, a counterexample that shows that this criterion is false for arbitrary π-institutions is given.
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