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  1. Roberto Cignoli & Antoni Torrens (2012). Varieties of Commutative Integral Bounded Residuated Lattices Admitting a Boolean Retraction Term. Studia Logica 100 (6):1107-1136.
    Let ${\mathbb{BRL}}$ denote the variety of commutative integral bounded residuated lattices (bounded residuated lattices for short). A Boolean retraction term for a subvariety ${\mathbb{V}}$ of ${\mathbb{BRL}}$ is a unary term t in the language of bounded residuated lattices such that for every ${{\bf A} \in \mathbb{V}, t^{A}}$ , the interpretation of the term on A, defines a retraction from A onto its Boolean skeleton B(A). It is shown that Boolean retraction terms are equationally definable, in the sense that there is (...)
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  2. Manuela Busaniche & Roberto Cignoli (2011). Remarks on an Algebraic Semantics for Paraconsistent Nelson's Logic. Manuscrito 34 (1):99-114.
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  3. Roberto Cignoli (2011). Boolean Skeletons of MV-Algebras and ℓ-Groups. Studia Logica 98 (1-2):141-147.
    Let Γ be Mundici’s functor from the category $${\mathcal{LG}}$$ whose objects are the lattice-ordered abelian groups ( ℓ -groups for short) with a distinguished strong order unit and the morphisms are the unital homomorphisms, onto the category $${\mathcal{MV}}$$ of MV-algebras and homomorphisms. It is shown that for each strong order unit u of an ℓ -group G , the Boolean skeleton of the MV-algebra Γ ( G , u ) is isomorphic to the Boolean algebra of factor congruences of G.
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  4. Roberto Cignoli & Francesc Esteva (2009). Commutative Integral Bounded Residuated Lattices with an Added Involution. Annals of Pure and Applied Logic 161 (2):150-160.
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  5. Roberto Cignoli & Luiz Monteiro (2006). Maximal Subalgebras of MVn-Algebras. A Proof of a Conjecture of A. Monteiro. Studia Logica 84 (3):393 - 405.
    For each integer n ≥ 2, MVn denotes the variety of MV-algebras generated by the MV-chain with n elements. Algebras in MVn are represented as continuous functions from a Boolean space into a n-element chain equipped with the discrete topology. Using these representations, maximal subalgebras of algebras in MVn are characterized, and it is shown that proper subalgebras are intersection of maximal subalgebras. When A ∈ MV3, the mentioned characterization of maximal subalgebras of A can be given in terms of (...)
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  6. Roberto Cignoli & Antoni Torrens Torrell (2006). Free Algebras in Varieties of Glivenko MTL-Algebras Satisfying the Equation 2(X2) = (2x). Studia Logica 83 (1-3):157 - 181.
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  7. Roberto Cignoli & Antoni Torrens Torrell (2006). Free Algebras in Varieties of Glivenko MTL-Algebras Satisfying the Equation 2(X²) = (2x)². Studia Logica 83 (1-3):157 - 181.
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  8. Roberto Cignoli & Antoni Torrens Torrell (2004). Glivenko Like Theorems in Natural Expansions of BCK‐Logic. Mathematical Logic Quarterly 50 (2):111-125.
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  9. Roberto Cignoli & Antoni Torrens (2003). Hájek Basic Fuzzy Logic and Łukasiewicz Infinite-Valued Logic. Archive for Mathematical Logic 42 (4):361-370.
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  10. Xavier Caicedo & Roberto Cignoli (2001). An Algebraic Approach to Intuitionistic Connectives. Journal of Symbolic Logic 66 (4):1620-1636.
    It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...)
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  11. Roberto Cignoli (1999). Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publishers.
    This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as (...)
     
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  12. Roberto Cignoli & Daniele Mundici (1998). An Elementary Presentation of the Equivalence Between MV-Algebras and L-Groups with Strong Unit. Studia Logica 61 (1):49-64.
    Aim of this paper is to provide a self-contained presentation of the natural equivalence between MV-algebras and lattice-ordered abelian groups with strong unit.
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  13. Roberto Cignoli & Daniele Mundici (1997). An Elementary Proof of Chang's Completeness Theorem for the Infinite-Valued Calculus of Lukasiewicz. Studia Logica 58 (1):79-97.
    The interpretation of propositions in Lukasiewicz's infinite-valued calculus as answers in Ulam's game with lies--the Boolean case corresponding to the traditional Twenty Questions game--gives added interest to the completeness theorem. The literature contains several different proofs, but they invariably require technical prerequisites from such areas as model-theory, algebraic geometry, or the theory of ordered groups. The aim of this paper is to provide a self-contained proof, only requiring the rudiments of algebra and convexity in finite-dimensional vector spaces.
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  14. Roberto Cignoli (1996). Free Q-Distributive Lattices. Studia Logica 56 (1-2):23 - 29.
    The dual spaces of the free distributive lattices with a quantifier are constructed, generalizing Halmos' construction of the dual spaces of free monadic Boolean algebras.
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  15. Roberto Cignoli (1991). Complete and Atomic Algebras of the Infinite Valued Łukasiewicz Logic. Studia Logica 50 (3-4):375 - 384.
    The infinite-valued logic of ukasiewicz was originally defined by means of an infinite-valued matrix. ukasiewicz took special forms of negation and implication as basic connectives and proposed an axiom system that he conjectured would be sufficient to derive the valid formulas of the logic; this was eventually verified by M. Wajsberg. The algebraic counterparts of this logic have become know as Wajsberg algebras. In this paper we show that a Wajsberg algebra is complete and atomic (as a lattice) if and (...)
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  16. Roberto Cignoli (1984). An Algebraic Approach to Elementary Theories Based on N‐Valued Lukasiewicz Logics. Mathematical Logic Quarterly 30 (1‐6):87-96.
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  17. Roberto Cignoli (1984). Ayda Ignez Arruda (1936–1983). Studia Logica 43 (1-2):1 - 2.
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  18. Roberto Cignoli (1982). Proper N-Valued Łukasiewicz Algebras as s-Algebras of Łukasiewicz N-Valued Prepositional Calculi. Studia Logica 41 (1):3 - 16.
    Proper n-valued ukasiewicz algebras are obtained by adding some binary operators, fulfilling some simple equations, to the fundamental operations of n-valued ukasiewicz algebras. They are the s-algebras corresponding to an axiomatization of ukasiewicz n-valued propositional calculus that is an extention of the intuitionistic calculus.
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  19. Roberto Cignoli (1979). Coproducts in the Categories of Kleene and Three-Valued Łukasiewicz Algebras. Studia Logica 38 (3):237 - 245.
    It is given an explicit description of coproducts in the category of Kleene algebras in terms of the dual topological spaces. As an application, a description of dual spaces of free Kleene algebras is given. It is also shown that the coproduct of a family of three-valued ukasiewicz algebras in the category of Kleene algebras is the same as the coproduct in the subcategory of three-valued ukasiewicz algebras.
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