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  1. On Free Annotated Algebras.Renato A. Lewin, Irene F. Mikenberg & Marı́a G. Schwarze - 2001 - Annals of Pure and Applied Logic 108 (1-3):249-259.
    In Lewin et al. 359–386) the authors proved that certain systems of annotated logics are algebraizable in the sense of Block and Rigozzi 396). Later in Lewin et al. the study of the associated quasi-varieties of annotated algebras is initiated. In this paper we continue the study of the these classes of algebras, in particular, we report some recent results about the free annotated algebras.
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  2. M. Abad Varieties of Three-Valued.A. M. Suardiaz A. Quantifier - forthcoming - Studia Logica.
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  3. On Three-Valued Moisil Algebras.M. Abad & L. Monteiro - 1984 - Logique Et Analyse 27 (8):407-414.
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  4. Varieties of Three-Values Heyting Algebras with a Quantifier.Manuel Abad, J. P. Diaz Varela & L. A. Rueda - 2000 - Studia Logica 65 (2):181-198.
    This paper is devoted to the study of some subvarieties of the variety Q of Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q subscript 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Q is far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q subscript 3 and we construct (...)
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  5. Orthoimplication Algebras.J. C. Abbott - 1976 - Studia Logica 35 (2):173 - 177.
    Orthologic is defined by weakening the axioms and rules of inference of the classical propositional calculus. The resulting Lindenbaum-Tarski quotient algebra is an orthoimplication algebra which generalizes the author's implication algebra. The associated order structure is a semi-orthomodular lattice. The theory of orthomodular lattices is obtained by adjoining a falsity symbol to the underlying orthologic or a least element to the orthoimplication algebra.
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  6. A Note On Curry Algebras.Jair Abe - 1987 - Bulletin of the Section of Logic 16 (4):151-156.
    In one of its possible formulations, the principle of the excluded middle says that, from two propositions A and ¬A , one is true. A paracomplete logic is a logic which can be the basis of theories in which there are propositions A such that A and ¬A are both false. So, we may assert that in a paracomplete logic the law of the excluded middle fails. For a discussion of such kind of logic, as well as for the study (...)
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  7. Annotated Logics Qt and Ultraproducts.Jair Minoro Abe & Seiki Akama - 1997 - Logique Et Analyse 160:335-343.
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  8. Minimal "Sum of Products of Sums" Expressions of Boolean Functions.Shreeram Abhyankar - 1959 - Journal of Symbolic Logic 24 (3):254-255.
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  9. Domain Theory in Logical Form.Samson Abramsky - 1991 - Annals of Pure and Applied Logic 51 (1-2):1-77.
    Abramsky, S., Domain theory in logical form, Annals of Pure and Applied Logic 51 1–77. The mathematical framework of Stone duality is used to synthesise a number of hitherto separate developments in theoretical computer science.• Domain theory, the mathematical theory of computation introduced by Scott as a foundation for detonational semantics• The theory of concurrency and systems behaviour developed by Milner, Hennesy based on operational semantics.• Logics of programsStone duality provides a junction between semantics and logics . Moreover, the underlying (...)
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  10. Some Uses of Dilators in Combinatorial Problems. II.Abrusci V. Michele, Girard Jean-Yves & Wiele Jacques Van De - 1990 - Journal of Symbolic Logic 55 (1):32 - 40.
    We study increasing F-sequences, where F is a dilator: an increasing F-sequence is a sequence (indexed by ordinal numbers) of ordinal numbers, starting with 0 and terminating at the first step x where F(x) is reached (at every step x + 1 we use the same process as in decreasing F-sequences, cf. [2], but with "+ 1" instead of "- 1"). By induction on dilators, we shall prove that every increasing F-sequence terminates and moreover we can determine for every dilator (...)
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  11. A Comparison Between Lambek Syntactic Calculus and Intuitionistic Linear Propositional Logic.V. Michele Abrusci - 1990 - Mathematical Logic Quarterly 36 (1):11-15.
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  12. Non‐Commutative Intuitionistic Linear Logic.V. Michele Abrusci - 1990 - Mathematical Logic Quarterly 36 (4):297-318.
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  13. Review: Toshio Umezawa, On Intermediate Many-Valued Logics. [REVIEW]W. Ackermann - 1959 - Journal of Symbolic Logic 24 (3):250-250.
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  14. Umezawa Toshio. On Intermediate Many-Valued Logics. Journal of the Mathematical Society of Japan, Bd. 11 Heft 2 , S. 116–128. [REVIEW]W. Ackermann - 1959 - Journal of Symbolic Logic 24 (3):250.
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  15. Review: Robert Stanley, An Extended Procedure in Quantificational Logic. [REVIEW]Wilhelm Ackermann - 1956 - Journal of Symbolic Logic 21 (2):197-197.
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  16. Review: Yoemon Sampei, On the Orthogonal Expansion of the Boolean Polynomial and Its Applications I; Yoemon Sampei, On the Orthogonal Expansion of the Boolean Polynomial and Its Applications. [REVIEW]Wilhelm Ackermann - 1956 - Journal of Symbolic Logic 21 (4):401-402.
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  17. Stanley Robert. An Extended Procedure in Quantificational Logic.Wilhelm Ackermann - 1956 - Journal of Symbolic Logic 21 (2):197.
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  18. Sampei Yoemon. On the Orthogonal Expansion of the Boolean Polynomial and its Applications I. Journal of the Faculty of Science, Hokkaido University, Series I, Bd. 11 Heft 3 , S. 113–125.Sampei Yoemon. On the Orthogonal Expansion of the Boolean Polynomial and its Applications II. Commentarii Mathematici Universitatis Sancti Pauli, Bd. 1 Heft 2 , S. 51–57. [REVIEW]Wilhelm Ackermann - 1956 - Journal of Symbolic Logic 21 (4):401-402.
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  19. Dienes Paul. On Ternary Logic.Wilhelm Ackermann - 1950 - Journal of Symbolic Logic 15 (3):225.
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  20. Review: Paul Dienes, On Ternary Logic. [REVIEW]Wilhelm Ackermann - 1950 - Journal of Symbolic Logic 15 (3):225-225.
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  21. Review: F.I. Andon, Ob Odnom Podhode K Minimizacii Sistem Buleoyh Funkcij (On One Approach to the Minimization of Systems of Boolean Functions); F. I. Andon, Algoritm Uproscenia D.N.F. Bulevyh Funckij (A Simplification Alogorithm of a Disjunctive Normal Form of the Boolean Functions). [REVIEW]A. Adam - 1970 - Journal of Symbolic Logic 35 (2):330-330.
  22. Review: G. N. Povarov, On the Group Invariance of Boolean Functions. [REVIEW]A. Adam - 1970 - Journal of Symbolic Logic 35 (1):161-162.
  23. Review: U. I. Zuravlev, Set-Theoretical Methods in the Algebra of Logic. [REVIEW]A. Adam - 1970 - Journal of Symbolic Logic 35 (1):162-162.
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  24. Review: V. V. Vojtišék, Ob Odnom Podhode K Klassifikacii Bulevyh Funkcij (On an Approach to the Classification of Boolean Functions). [REVIEW]A. Ádám - 1970 - Journal of Symbolic Logic 35 (4):593-593.
  25. Set-Theoretical Methods in the Algebra of Logic.A. Adam & U. I. Zuravlev - 1970 - Journal of Symbolic Logic 35 (1):162.
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  26. On the Logic of High Probability.Ernest W. Adams - 1986 - Journal of Philosophical Logic 15 (3):255 - 279.
  27. Richard Routley Postscript: Some Setbacks on the Choice and Descriptions Adventure.Descriptions Adventure - 1974 - In Edgar Morscher, Johannes Czermak & Paul Weingartner (eds.), Problems in Logic and Ontology. Akadem. Druck- U. Verlagsanst.. pp. 223.
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  28. Two Valued Logic in Ordinary Circumstances.J. Agassi - 1985 - International Logic Review 32:83.
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  29. Basic Hoops: An Algebraic Study of Continuous T -Norms.P. Aglianò, I. M. A. Ferreirim & F. Montagna - 2007 - Studia Logica 87 (1):73 - 98.
    A continuoxis t- norm is a continuous map * from [0, 1]² into [0,1] such that ([ 0,1], *, 1) is a commutative totally ordered monoid. Since the natural ordering on [0,1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and ([ 0,1], *, →, 1) becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras ([ 0,1], *, →, 1), where (...)
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  30. Basic Hoops: An Algebraic Study of Continuous T-Norms.P. Aglianò, I. M. A. Ferreirim & F. Montagna - 2007 - Studia Logica 87 (1):73-98.
    A continuoxis t- norm is a continuous map * from [0, 1]² into [0,1] such that is a commutative totally ordered monoid. Since the natural ordering on [0,1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras, where * is a continuous t-norm. In this paper we investigate the structure of the (...)
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  31. On Polynomial Semantics for Propositional Logics.Juan C. Agudelo-Agudelo, Carlos A. Agudelo-González & Oscar E. García-Quintero - 2016 - Journal of Applied Non-Classical Logics 26 (2):103-125.
    Some properties and an algorithm for solving systems of multivariate polynomial equations over finite fields are presented. It is then shown how formulas of propositional logics can be translated into polynomials over finite fields in such a way that several logic problems are expressed in terms of algebraic problems. Consequently, algebraic properties and algorithms can be used to solve the algebraically-represented logic problems. The methods described herein combine and generalise those of various previous works.
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  32. The Free N-Generated BL-Algebra.Stefano Aguzzoli & Simone Bova - 2010 - Annals of Pure and Applied Logic 161 (9):1144-1170.
    For each integer n≥0, we provide an explicit functional characterization of the free n-generated BL-algebra, together with an explicit construction of the corresponding normal forms.
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  33. Probability Measures in the Logic of Nilpotent Minimum.Stefano Aguzzoli & Brunella Gerla - 2010 - Studia Logica 94 (2):151-176.
    We axiomatize the notion of state over finitely generated free NM-algebras, the Lindenbaum algebras of pure Nilpotent Minimum logic. We show that states over the free n -generated NM-algebra exactly correspond to integrals of elements of with respect to Borel probability measures.
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  34. De Finetti's No-Dutch-Book Criterion for Gödel Logic.Stefano Aguzzoli, Brunella Gerla & Vincenzo Marra - 2008 - Studia Logica 90 (1):25 - 41.
    We extend de Finetti’s No-Dutch-Book Criterion to Gödel infinite-valued propositional logic.
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  35. On the Interpretation of Attitude Logics.Tuomo Aho - 1994 - In Dag Prawitz & Dag Westerståhl (eds.), Logic and Philosophy of Science in Uppsala. Kluwer Academic Publishers. pp. 1--11.
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  36. Logic for Physical Space: From Antiquity to Present Days.Marco Aiello, Guram Bezhanishvili, Isabelle Bloch & Valentin Goranko - 2012 - Synthese 186 (3):619-632.
    Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major milestones (...)
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  37. Handbook of Spatial Logics.Marco Aiello, Ian E. Pratt-Hartmann & Johan van Benthem (eds.) - 2007 - Springer Verlag.
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  38. 1. Infon Logic Based On Constructive Logic.Seiki Akama - 2006 - Logique Et Analyse 49.
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  39. Subformula Semantics for Strong Negation Systems.Seiki Akama - 1990 - Journal of Philosophical Logic 19 (2):217 - 226.
    We present a semantics for strong negation systems on the basis of the subformula property of the sequent calculus. The new models, called subformula models, are constructed as a special class of canonical Kripke models for providing the way from the cut-elimination theorem to model-theoretic results. This semantics is more intuitive than the standard Kripke semantics for strong negation systems.
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  40. Three-Valued Temporal Logic Q T and Future Contingents.Seiki Akama, Yasunori Nagata & Chikatoshi Yamada - 2008 - Studia Logica 88 (2):215-231.
    Prior's three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic $Q_t $ and give its axiomatization and semantics. We also argue that $Q_t $ provides a smooth solution to the problem of future contingents.
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  41. A Truth Table Method for the Synthesis of Combinational Logic.Sheldon B. Akers - 1963 - Journal of Symbolic Logic 28 (4):290-290.
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  42. Monadic Bounded Algebras.Galym Akishev & Robert Goldblatt - 2010 - Studia Logica 96 (1):1 - 40.
    We introduce the equational notion of a monadic bounded algebra (MBA), intended to capture algebraic properties of bounded quantification. The variety of all MBA's is shown to be generated by certain algebras of two-valued propositional functions that correspond to models of monadic free logic with an existence predicate. Every MBA is a subdirect product of such functional algebras, a fact that can be seen as an algebraic counterpart to semantic completeness for monadic free logic. The analysis involves the representation of (...)
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  43. A Short Note on the Free Implication Algebra Over a Poset.Figallo-Orellano Aldo - 2016 - SOUTH AMERICAN JOURNAL OF LOGIC 2 (1):91-100.
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  44. Functional Dependencies Between Variables.Natasha Alechina - 2000 - Studia Logica 66 (2):273-283.
    We consider a predicate logic Lfd where not all assignments of values to individual variables are possible. Some variables are functionally dependent on other variables. This makes sense if the models of logic are assumed to correspond to databases or states. We show that Lfd is undecidable but has a complete and sound sequent calculus formalisation.
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  45. Hypotheses Testing in Adaptive Logics: An Application to Medical Diagnosis.A. Aliseda & L. Leonides - 2013 - Logic Journal of the IGPL 21 (6):915-930.
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  46. On the Linear Lindenbaum Algebra of Basic Propositional Logic.M. Alizadeh & M. Ardeshir - 2004 - Mathematical Logic Quarterly 50 (1):65.
    We study the linear Lindenbaum algebra of Basic Propositional Calculus, called linear basic algebra.
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  47. Amalgamation Property for the Class of Basic Algebras and Some of its Natural Subclasses.Majid Alizadeh & Mohammad Ardeshir - 2006 - Archive for Mathematical Logic 45 (8):913-930.
    We study Basic algebra, the algebraic structure associated with basic propositional calculus, and some of its natural extensions. Among other things, we prove the amalgamation property for the class of Basic algebras, faithful Basic algebras and linear faithful Basic algebras. We also show that a faithful theory has the interpolation property if and only if its correspondence class of algebras has the amalgamation property.
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  48. On Löb Algebras.Majid Alizadeh & Mohammad Ardeshir - 2006 - Mathematical Logic Quarterly 52 (1):95-105.
    We study the variety of Löb algebras , the algebraic structures associated with formal propositional calculus. Among other things, we prove a completeness theorem for formal propositional logic with respect to the variety of Löb algebras. We show that the variety of Löb algebras has the weak amalgamation property. Some interesting subclasses of the variety of Löb algebras, e.g. linear, faithful and strongly linear Löb algebras are introduced.
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  49. Review: P. H. Nowell-Smith, E. J. Lemmon, Escapism: The Logical Basis of Ethics. [REVIEW]Layman E. Allen - 1968 - Journal of Symbolic Logic 33 (4):611-612.
  50. A Generalization of the Łukasiewicz Algebras.Almada Teresa & Carvalho Júlia Vaz de - 2001 - Studia Logica 69 (3):329 - 338.
    We introduce the variety $\scr{L}_{n}^{m}$ , m ≥ 1 and n ≥ 2, of m-generalized Łukasiewicz algebras of order n and characterize its subdirectly irreducible algebras. The variety $\scr{L}_{n}^{m}$ is semisimple, locally finite and has equationally definable principal congruences. Furthermore, the variety $\scr{L}_{n}^{m}$ contains the variety of Łukasiewicz algebras of order n.
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