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  1. Edwin Mares & Francesco Paoli (2014). Logical Consequence and the Paradoxes. Journal of Philosophical Logic 43 (2-3):439-469.
    We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, (...)
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  2. Francesco Paoli (2014). Logic: The Laws of Truth by Nicholas J. J. Smith. [REVIEW] History and Philosophy of Logic 35 (3):306-8.
     
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  3. Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) (2013). Paraconsistency: Logic and Applications. Springer.
    A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...)
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  4. Francesco Paoli (2013). A Paraconsistent and Substructural Conditional Logic. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. 173--198.
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  5. Tomasz Kowalski, Francesco Paoli & Matthew Spinks (2011). Quasi-Subtractive Varieties. Journal of Symbolic Logic 76 (4):1261-1286.
    Varieties like groups, rings, or Boolean algebras have the property that, in any of their members, the lattice of congruences is isomorphic to a lattice of more manageable objects, for example normal subgroups of groups, two-sided ideals of rings, filters (or ideals) of Boolean algebras.algebraic logic can explain these phenomena at a rather satisfactory level of generality: in every member A of a τ-regular variety the lattice of congruences of A is isomorphic to the lattice of deductive filters on (...)
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  6. Francesco Paoli (2011). Comments on 'Fuzzy Logic and Higher-Order Vagueness' by Nicholas J.J. Smith. In Petr Cintula, Christian G. Fermüller, Lluis Godo & Petr Hájek (eds.), Understanding Vagueness: Logical, Philosophical and Linguistic Perspectives. College Publications. 33-5.
     
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  7. Koji Tanaka, Francesco Berto, Edwin Mares & Francesco Paoli (2010). Guest Editors' Introduction. Logic and Logical Philosophy 19 (1-2):5-6.
    A logic is said to be paraconsistent if it doesn’t license you to infer everything from a contradiction. To be precise, let |= be a relation of logical consequence. We call |= explosive if it validates the inference rule: {A,¬A} |= B for every A and B. Classical logic and most other standard logics, including intuitionist logic, are explosive. Instead of licensing you to infer everything from a contradiction, paraconsistent logic allows you to sensibly deal with the contradiction.
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  8. Francesco Paoli, Antonio Ledda, Roberto Giuntini & Hector Freytes (2009). On Some Properties of Quasi-MV Algebras and $\Sqrt{^{\Prime }}$ Quasi-MV Algebras. Reports on Mathematical Logic:31-63.
    We investigate some properties of two varieties of algebras arising from quantum computation - quasi-MV algebras and $\sqrt{^{\prime }}$ quasi-MV algebras - first introduced in \cite{Ledda et al. 2006}, \cite{Giuntini et al. 200+} and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of $\sqrt{^{\prime }}$ quasi-MV algebras; we give a representation of semisimple $\sqrt{^{\prime }}$ quasi-MV algebras in terms of algebras of functions; (...)
     
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  9. Francesco Paoli, Matthew Spinks & Robert Veroff (2008). Abelian Logic and the Logics of Pointed Lattice-Ordered Varieties. Logica Universalis 2 (2):209-233.
    We consider the class of pointed varieties of algebras having a lattice term reduct and we show that each such variety gives rise in a natural way, and according to a regular pattern, to at least three interesting logics. Although the mentioned class includes several logically and algebraically significant examples (e.g. Boolean algebras, MV algebras, Boolean algebras with operators, residuated lattices and their subvarieties, algebras from quantum logic or from depth relevant logic), we consider here in greater detail Abelian ℓ-groups, (...)
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  10. Roberto Giuntini, Antonio Ledda & Francesco Paoli (2007). Expanding Quasi-MV Algebras by a Quantum Operator. Studia Logica 87 (1):99 - 128.
    We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety of such quasi-MV algebras has a subquasivariety whose members—called cartesian—can be obtained in an appropriate way out of MV algebras. After showing that cartesian . quasi-MV algebras generate ,we prove a standard completeness theorem for w.r.t. an algebra over the complex numbers.
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  11. Francesco Paoli (2007). Implicational Paradoxes and the Meaning of Logical Constants. Australasian Journal of Philosophy 85 (4):553 – 579.
    I discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. I argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads me to select as a plausible candidate LL, a fragment of linear logic that differs from R in that it rejects both contraction and distribution.
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  12. Antonio Ledda, Martinvaldo Konig, Francesco Paoli & Roberto Giuntini (2006). MV-Algebras and Quantum Computation. Studia Logica 82 (2):245 - 270.
    We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers.
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  13. Francesco Paoli (2005). ★-Autonomous Lattices. Studia Logica 79 (2):283 - 304.
    -autonomous lattices are the algebraic exponentials and without additive constants. In this paper, we investigate the structure theory of this variety and some of its subvarieties, as well as its relationships with other classes of algebras.
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  14. Francesco Paoli (2005). The Ambiguity of Quantifiers. Philosophical Studies 124 (3):313 - 330.
    In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.
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  15. Greg Restall & Francesco Paoli (2005). The Geometry of Non-Distributive Logics. Journal of Symbolic Logic 70 (4):1108 - 1126.
    In this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems (...)
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  16. Francesco Paoli (2004). Logic and Groups. Logic and Logical Philosophy 9:109.
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  17. Francesco Paoli (2003). A Really Fuzzy Approach to the Sorites Paradox. Synthese 134 (3):363 - 387.
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  18. Francesco Paoli (2003). Quine and Slater on Paraconsistency and Deviance. Journal of Philosophical Logic 32 (5):531-548.
    In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant *c* in a given logic: its operational meaning, given by the operational rules for *c* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing *c* which can be proved in the same calculus. Subsequently, we use the (...)
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  19. Francesco Paoli (2002). On the Algebraic Structure of Linear, Relevance, and Fuzzy Logics. Archive for Mathematical Logic 41 (2):107-121.
    Substructural logics are obtained from the sequent calculi for classical or intuitionistic logic by suitably restricting or deleting some or all of the structural rules (Restall, 2000; Ono, 1998). Recently, this field of research has come to encompass a number of logics - e.g. many fuzzy or paraconsistent logics - which had been originally introduced out of different, possibly semantical, motivations. A finer proof-theoretical analysis of such logics, in fact, revealed that it was possible to subsume them under the previous (...)
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  20. Kazumi Nakamatsu, Marek Nasieniewski, Volodymyr Navrotskiy, Sergey Pavlovich Odintsov, Carlos Oiler, Mieczyslaw Omyla, Hiroakira Ono, Ewa Orlowska, Katarzyna Palasihska & Francesco Paoli (2001). List of Participants 17 Robert K. Meyer (Camberra, Australia) Barbara Morawska (Gdansk, Poland) Daniele Mundici (Milan, Italy). Logic and Logical Philosophy 7:16.
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  21. Francesco Paoli (2000). A Common Abstraction of MV-Algebras and Abelian L-Groups. Studia Logica 65 (3):355-366.
    We investigate the class of strongly distributive pregroups, a common abstraction of MV-algebras and Abelian l-groups which was introduced by E.Casari. The main result of the paper is a representation theorem which yields both Chang's representation of MV-algebras and Clifford's representation of Abelian l-groups as immediate corollaries.
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  22. Francesco Paoli (1998). Simplified Affine Phase Structures. Reports on Mathematical Logic:21-34.
    Phase models for affine linear logic were independently devised by Lafont [10] and Piazza [15], although foreshadowed by Ono [14]. However, the existing semantics either contain no explicit directions for the construction of models in the general case, or else are forced to resort to additional conditions extending Girard's semantics . We dispense with these extra postulates - at least for the subexponential fragment of this logic - considering structures where the set of antiphases is concretely constructed. Moreover, we show (...)
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  23. Francesco Paoli (1996). On Strong Comparative Logic. Logique Et Analyse 155 (156):271-283.
     
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  24. Francesco Paoli (1996). S Is Constructively Complete. Reports on Mathematical Logic:31-47.
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  25. Francesco Paoli (1993). Semantics For First Degree Relatedness Logic. Reports on Mathematical Logic:81-94.
    In this paper, we axiomatize the first-degree entailments of relatedness logic, and introduce both tabular and algebraic semantics for such a fragment. Thereby, we partly answer the problems referred to as P1 and P28 in the Problem Section of this journal.Back to Main Menu.
     
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  26. Francesco Paoli (1991). Bolzano e le dimostrazioni matematiche. Rivista di Filosofia 82 (2):221-242.
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