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  1. Free Three-Valued Closure Łukasiewicz Algebras.M. Abad, J. Varela, L. Rueda & A. Suardiaz - 2006 - Reports on Mathematical Logic 42:3-17.
    In this paper, the structure of finitely generated free objects in the variety of three-valued closure \L ukasiewicz algebras is determined. We describe their indecomposable factors and we give their cardinality.
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  2. An Introduction to Many-Valued Logics.Robert John Ackermann - 1967 - New York: Dover Publications.
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  3. A Note on the Axiomatization of Equational Classes of $N$-Valued Ł Ukasiewicz Algebras.M. E. Adams & R. Cignoli - 1990 - Notre Dame Journal of Formal Logic 31 (2):304-307.
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  4. Two Valued Logic in Ordinary Circumstances.J. Agassi - 1985 - International Logic Review 32:83.
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  5. Finiteness in Infinite-Valued Łukasiewicz Logic.Stefano Aguzzoli & Agata Ciabattoni - 2000 - Journal of Logic, Language and Information 9 (1):5-29.
    In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued ukasiewicz logic to a suitable m-valued ukasiewicz logic m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in if and only if it is also valid in m. We also reduce the notion of logical consequence in to the same (...)
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  6. On the Relations Between Heinrich Scholz and Jan Łukasiewicz.Hans-Christoph Schmidt Am Busch & Kai F. Wehmeier - 2007 - History and Philosophy of Logic 28 (1):67-81.
  7. Review: Atwell R. Turquette, Many-Valued Logics and Systems of Strict Implication. [REVIEW]Alan Ross Anderson - 1957 - Journal of Symbolic Logic 22 (3):328-328.
  8. Review: Ryoichi Takekuma, On a Nine-Valued Propositional Calculus. [REVIEW]Alan Ross Anderson - 1957 - Journal of Symbolic Logic 22 (3):330-330.
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  9. On Axiomatization of Many-Valued Logics Associated with Formalization of Plausible Reasonings.O. M. Anshakov, V. K. Finn & D. P. Skvortsov - 1989 - Studia Logica 48 (4):423 - 447.
    This paper studies a class of infinite-valued predicate logics. A sufficient condition for axiomatizability of logics from that class is given.
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  10. The Strong Completeness of a System Based on Kleene's Strong Three-Valued Logic.Hiroshi Aoyama - 1994 - Notre Dame Journal of Formal Logic 35 (3):355-368.
    The present work, which was inspired by Kripke and McCarthy, is about a non-classical predicate logic system containing a truth predicate symbol. In this system, each sentence A is referred to not by a Gödel number but by its quotation name 'A'.
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  11. Many-Valued Logics. A Mathematical and Computational Introduction.Luis M. Augusto - 2017 - London: College Publications.
    Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and they are (...)
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  12. Lógicas multivalentes. Uma introdução matemática e computacional.Luis M. Augusto - 2016 - Dissertation, Universidade Aberta
    This is a mathematical and computational intro to many-valued logics. The approach is mostly mathematical, namely algebraic (via the notion of logical matrix) and computational (via the satisfiability problem). An automated calculus -- the signed resolution calculus for many-valued logics -- is elaborated on.
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  13. Rough Sets and 3-Valued Logics.A. Avron & B. Konikowska - 2008 - Studia Logica 90 (1):69-92.
    In the paper we explore the idea of describing Pawlak’s rough sets using three-valued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is described using a non-deterministic matrix (Nmatrix). With the strong semantics, where only the value t is (...)
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  14. On an Implication Connective of RM.Arnon Avron - 1986 - Notre Dame Journal of Formal Logic 27 (2):201-209.
  15. Four-Valued Diagnoses for Stratified Knowledge-Bases.Arnon Avron & Arieli Ofer - 1997 - In Dirk van Dalen & Marc Bezem (eds.), Computer Science Logic. Springer. pp. 1-17.
    We present a four-valued approach for recovering consistent data from inconsistent set of assertions. For a common family of knowledge-bases we also provide an e cient algorithm for doing so automaticly. This method is particularly useful for making model-based diagnoses.
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  16. Quantified Propositional Gödel Logics.Matthias Baaz, Agata Ciabattoni & Richard Zach - 2000 - In Andrei Voronkov & Michel Parigot (eds.), Logic for Programming and Automated Reasoning. 7th International Conference, LPAR 2000. Berlin: Springer. pp. 240-256.
    It is shown that Gqp↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp↑ as the intersection of all finite-valued quantified propositional Gödel logics.
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  17. Labeled Calculi and Finite-Valued Logics.Matthias Baaz, Christian G. Fermüller, Gernot Salzer & Richard Zach - 1998 - Studia Logica 61 (1):7-33.
    A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the (...)
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  18. Elimination of Cuts in First-Order Finite-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1994 - Journal of Information Processing and Cybernetics EIK 29 (6):333-355.
    A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.
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  19. Dual Systems of Sequents and Tableaux for Many-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - Bulletin of the EATCS 51:192-197.
    The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and (...)
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  20. Systematic Construction of Natural Deduction Systems for Many-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - In Proceedings of The Twenty-Third International Symposium on Multiple-Valued Logic, 1993. Los Alamitos, CA: IEEE Press. pp. 208-213.
    A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.
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  21. Incompleteness of a First-Order Gödel Logic and Some Temporal Logics of Programs.Matthias Baaz, Alexander Leitsch & Richard Zach - 1996 - In Hans Kleine Büning (ed.), Computer Science Logic. CSL 1995. Selected Papers. Berlin: Springer. pp. 1--15.
    It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal (...)
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  22. Completeness of a Hypersequent Calculus for Some First-Order Gödel Logics with Delta.Matthias Baaz, Norbert Preining & Richard Zach - 2006 - In 36th International Symposium on Multiple-valued Logic. May 2006, Singapore. Proceedings. Los Alamitos: IEEE Press.
    All first-order Gödel logics G_V with globalization operator based on truth value sets V C [0,1] where 0 and 1 lie in the perfect kernel of V are axiomatized by Ciabattoni’s hypersequent calculus HGIF.
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  23. Effective Finite-Valued Approximations of General Propositional Logics.Matthias Baaz & Richard Zach - 2008 - In Arnon Avron, Nachum Dershowitz & Alexander Rabinovich (eds.), Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday. Berlin: Springer. pp. 107–129.
    Propositional logics in general, considered as a set of sentences, can be undecidable even if they have “nice” representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete). On the other hand, finite-valued logics are computationally relatively simple—at worst NP. Moreover, finite-valued semantics are simple, and general methods for theorem proving exist. This raises the question to what extent and under what circumstances propositional logics represented in various ways can (...)
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  24. Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic.Matthias Baaz & Richard Zach - 2000 - In Peter G. Clote & Helmut Schwichtenberg (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Berlin: Springer. pp. 187– 201.
    Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and complete, and (...)
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  25. Compact Propositional Gödel Logics.Matthias Baaz & Richard Zach - 1998 - In 28th IEEE International Symposium on Multiple-Valued Logic, 1998. Proceedings. Los Alamitos: IEEE Press. pp. 108-113.
    Entailment in propositional Gödel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Gödel logics, only one of which is compact. It is also shown that the compact infinite-valued Gödel logic is the only one which interpolates, and the only one with an r.e. entailment relation.
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  26. Approximating Propositional Calculi by Finite-Valued Logics.Matthias Baaz & Richard Zach - 1994 - In 24th International Symposium on Multiple-valued Logic, 1994. Proceedings. Los Alamitos: IEEE Press. pp. 257–263.
    The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) can (...)
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  27. A New Conditional for Naive Truth Theory.Andrew Bacon - 2013 - Notre Dame Journal of Formal Logic 54 (1):87-104.
    In this paper a logic for reasoning disquotationally about truth is presented and shown to have a standard model. This work improves on Hartry Field's recent results establishing consistency and omega-consistency of truth-theories with strong conditional logics. A novel method utilising the Banach fixed point theorem for contracting functions on complete metric spaces is invoked, and the resulting logic is shown to validate a number of principles which existing revision theoretic methods have heretofore failed to provide.
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  28. Curry's Paradox and Omega Inconsistency.Andrew Bacon - 2013 - Studia Logica 101 (1):1-9.
    In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, but (...)
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  29. Non-Classical Metatheory for Non-Classical Logics.Andrew Bacon - 2013 - Journal of Philosophical Logic 42 (2):335-355.
    A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper is (...)
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  30. Carnielli, Walter (ed.). Logic and Philosophy of the Formal Sciences: A Festscrift for Itala M. Loffredo D´ Ottaviano. São Paulo: Centro de Lógica, Epistemología e Historia da Ciência, UNICAMP (Número especial de Manuscrito, Revista Internacional de Filosofia, vol. 28, n. 2, jul-dez.) pp. 191-591.(2005). [REVIEW]Tomás Barrero - 2006 - Ideas Y Valores 55 (132):124-126.
  31. Lógica positiva : plenitude, potencialidade e problemas (do pensar sem negação).Tomás Barrero - 2004 - Dissertation, Universidade Estadual de Campinas
    This work studies some problems connected to the role of negation in logic, treating the positive fragments of propositional calculus in order to deal with two main questions: the proof of the completeness theorems in systems lacking negation, and the puzzle raised by positive paradoxes like the well-known argument of Haskel Curry. We study the constructive com- pleteness method proposed by Leon Henkin for classical fragments endowed with implication, and advance some reasons explaining what makes difficult to extend this constructive (...)
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  32. Tableaux sin refutación.Tomás Barrero & Walter Carnielli - 2005 - Matemáticas: Enseñanza Universitaria 13 (2):81-99.
    Motivated by H. Curry’s well-known objection and by a proposal of L. Henkin, this article introduces the positive tableaux, a form of tableau calculus without refutation based upon the idea of implicational triviality. The completeness of the method is proven, which establishes a new decision procedure for the (classical) positive propositional logic. We also introduce the concept of paratriviality in order to contribute to the question of paradoxes and limitations imposed by the behavior of classical implication.
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  33. On Verification of the Expressions of Many-Valued Sentential Calculi. I.Edward Baŀuka - 1965 - Studia Logica 17 (1):53 - 73.
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  34. On Mixed Inferences and Pluralism About Truth Predicates.J. C. Beall - 2000 - Philosophical Quarterly 50 (200):380-382.
  35. Logic: The Basics (2nd Edition).Jc Beall & Shay A. Logan - 2017 - Routledge.
    Logic: the Basics is an accessible introduction to the core philosophy topic of standard logic. Focussing on traditional Classical Logic the book deals with topics such as mathematical preliminaries, propositional logic, monadic quantified logic, polyadic quantified logic, and English and standard ‘symbolic transitions’. With exercises and sample answers throughout this thoroughly revised new edition not only comprehensively covers the core topics at introductory level but also gives the reader an idea of how they can take their knowledge further and the (...)
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  36. Automated Theorem Proving for Łukasiewicz Logics.Gordon Beavers - 1993 - Studia Logica 52 (2):183 - 195.
    This paper is concerned with decision proceedures for the 0-valued ukasiewicz logics,. It is shown how linear algebra can be used to construct an automated theorem checker. Two decision proceedures are described which depend on a linear programming package. An algorithm is given for the verification of consequence relations in, and a connection is made between theorem checking in two-valued logic and theorem checking in which implies that determing of a -free formula whether it takes the value one is NP-complete (...)
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  37. Extensions of the $\Aleph_0$-Valued Ł Ukasiewicz Propositional Logic.M. G. Beavers - 1993 - Notre Dame Journal of Formal Logic 34 (2):251-262.
  38. Negation on the Australian Plan.Franz Berto & Greg Restall - forthcoming - Journal of Philosophical Logic.
    We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. (...)
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  39. Non Truth-Functional Many-Valuedness.Jean-Yves Beziau - manuscript
    Many-valued logics are standardly defined by logical matrices. They are truth-functional. In this paper non truth-functional many-valued semantics are presented, in a philosophical and mathematical perspective.
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  40. New Dimensions of the Square of Opposition.Jean-Yves Beziau & Stamatios Gerogiorgakis (eds.) - 2017 - Munich: Philosophia.
    The square of opposition is a diagram related to a theory of oppositions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the Aristotelian theory of quantification, but extensions and criticisms of this theory have resulted in various other diagrams. The strength of the theory is that it is at the same time fairly simple and quite rich. The theory of oppositions has recently (...)
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  41. On a Three Valued Calculus and Its Application to the Analysis of Contradictories.D. A. Bochvar - 1939 - Matematicheskii Sbornik 4 (2):287-308.
  42. On a Three-Valued Logical Calculus and its Application to the Analysis of the Paradoxes of the Classical Extended Functional Calculus.D. A. Bochvar & Merrie Bergmann - 1981 - History and Philosophy of Logic 2 (1-2):87-112.
    A three-valued propositional logic is presented, within which the three values are read as ?true?, ?false? and ?nonsense?. A three-valued extended functional calculus, unrestricted by the theory of types, is then developed. Within the latter system, Bochvar analyzes the Russell paradox and the Grelling-Weyl paradox, formally demonstrating the meaninglessness of both.
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  43. Chess Composition as an Art.Miro Brada - manuscript
    The article presents the chess composition as a logical art, with concrete examples. It began with Arabic mansuba, and later evolved to new-strategy designed by Italian Alberto Mari. The redefinition of mate (e.g. mate with a free field) or a theme to quasi-pseudo theme, opens the new space for combinations, and enables to connect it with other fields like computer science. The article was exhibited in Holland Park, W8 6LU, The Ice House between 18. Oct - 3. Nov. 2013.
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  44. Many-Valued Morality.Merav Brodetz - 2000 - Dissertation, City University of New York
    Punishments and rewards are proportionate to actions' degree of wrongness and rightness, which means that gradation is a datum about morality. In my dissertation I argue that this datum cannot be captured by existing---that is, two- and three-valued---moralities, but can be accommodated by a many-valued system. I then develop a many-valued morality and obtain several important results. Among the latter are a pluralist ethics: by contrast to both two- and three-valued moralities, a many-valued framework allows one to always weigh more (...)
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  45. A Conceptual Construction of Complexity Levels Theory in Spacetime Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics and Dynamic Systems. [REVIEW]R. Brown, J. F. Glazebrook & I. C. Baianu - 2007 - Axiomathes 17 (3-4):409-493.
    A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...)
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  46. A Method for Synthesis of Two-Valued Feedback Circuits.W. H. Burkhart - 1954 - Journal of Symbolic Logic 19 (1):56-56.
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  47. A Formal Interpretation of Ł Ukasiewicz' Logics.Michael Byrd - 1979 - Notre Dame Journal of Formal Logic 20 (2):366-368.
  48. Modal and Many-Valued Logics.N. S. C. - 1964 - Review of Metaphysics 18 (1):188-188.
  49. Hybridized Paracomplete and Paraconsistent Logics.Colin R. Caret - 2017 - Australasian Journal of Logic 14 (1):281-325.
    This paper contributes to the study of paracompleteness and paraconsistency. We present two logics that address the following questions in novel ways. How can the paracomplete theorist characterize the formulas that defy excluded middle while maintaining that not all formulas are of this kind? How can the paraconsistent theorist characterize the formulas that obey explosion while still maintaining that there are some formulas not of this kind?
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  50. An algorithm for axiomatizing and theorem proving in finite many - valued propositional logics.W. A. Carnielli - 1985 - Logique Et Analyse 28 (12):363.
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