Results for 'Boolean algebra'

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  1. Deontic Logics Based on Boolean Algebra.Pablo F. Castro & Piotr Kulicki - forthcoming - In Robert Trypuz (ed.), Krister Segerberg on Logic of Actions. Springer.
    Deontic logic is devoted to the study of logical properties of normative predicates such as permission, obligation and prohibition. Since it is usual to apply these predicates to actions, many deontic logicians have proposed formalisms where actions and action combinators are present. Some standard action combinators are action conjunction, choice between actions and not doing a given action. These combinators resemble boolean operators, and therefore the theory of boolean algebra offers a well-known athematical framework to study the (...)
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  2.  10
    The Spectrum of Partitions of a Boolean Algebra.J. Donald Monk - 2001 - Archive for Mathematical Logic 40 (4):243-254.
    The main notion dealt with in this article is where A is a Boolean algebra. A partition of 1 is a family ofnonzero pairwise disjoint elements with sum 1. One of the main reasons for interest in this notion is from investigations about maximal almost disjoint families of subsets of sets X, especially X=ω. We begin the paper with a few results about this set-theoretical notion.Some of the main results of the paper are:• (1) If there is a (...)
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  3.  3
    A Superatomic Boolean Algebra with Few Automorphisms.Matatyahu Rubin & Sabine Koppelberg - 2001 - Archive for Mathematical Logic 40 (2):125-129.
    Assuming GCH, we prove that for every successor cardinal μ > ω1, there is a superatomic Boolean algebra B such that |B| = 2μ and |Aut B| = μ. Under ◊ω1, the same holds for μ = ω1. This answers Monk's Question 80 in [Mo].
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  4. Ones and Zeros Understanding Boolean Algebra, Digital Circuits, and the Logic of Sets.John Gregg - 1998
     
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  5.  24
    A Systematics of Deontic Action Logics Based on Boolean Algebra.Robert Trypuz & Piotr Kulicki - 2009 - Logic and Logical Philosophy 18 (3-4):253-270.
    Within the scope of interest of deontic logic, systems in which names of actions are arguments of deontic operators (deontic action logic) have attracted less interest than purely propositional systems. However, in our opinion, they are even more interesting from both theoretical and practical point of view. The fundament for contemporary research was established by K. Segerberg, who introduced his systems of basic deontic logic of urn model actions in early 1980s. Nowadays such logics are considered mainly within propositional dynamic (...)
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  6.  5
    A Model in Which Every Boolean Algebra has Many Subalgebras.James Cummings & Saharon Shelah - 1995 - Journal of Symbolic Logic 60 (3):992-1004.
    We show that it is consistent with ZFC (relative to large cardinals) that every infinite Boolean algebra B has an irredundant subset A such that 2 |A| = 2 |B| . This implies in particular that B has 2 |B| subalgebras. We also discuss some more general problems about subalgebras and free subsets of an algebra. The result on the number of subalgebras in a Boolean algebra solves a question of Monk from [6]. The paper (...)
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  7.  3
    On the Homogeneous Countable Boolean Contact Algebra.Ivo Düntsch & Sanjiang Li - 2013 - Logic and Logical Philosophy 22 (2):213-251.
    In a recent paper, we have shown that the class of Boolean contact algebras (BCAs) has the hereditary property, the joint embedding property and the amalgamation property. By Fraïssé’s theorem, this shows that there is a unique countable homogeneous BCA. This paper investigates this algebra and the relation algebra generated by its contact relation. We first show that the algebra can be partitioned into four sets {0}, {1}, K, and L, which are the only orbits of (...)
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  8. The Existence of Countable Totally Nonconstructive Extensions of the Countable Atomless Boolean Algebra.E. W. Madison - 1983 - Journal of Symbolic Logic 48 (1):167-170.
    Our results concern the existence of a countable extension U of the countable atomless Boolean algebra B such that U is a "nonconstructive" extension of B. It is known that for any fixed admissible indexing φ of B there is a countable nonconstructive extension U of B (relative to φ). The main theorem here shows that there exists an extension U of B such that for any admissible indexing φ of B, U is nonconstructive (relative to φ). Thus, (...)
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  9.  69
    Boolean Algebra and Syllogism.V. A. Bocharov - 1986 - Synthese 66 (1):35 - 54.
    This article contains the proof of equivalence boolean algebra and syllogistics arc2. The system arc2 is obtained as a superstructure above the propositional calculus. Subjects and predicates of syllogistic functors a, E, J, O may be complex terms, Which are formed using operations of intersection, Union and complement. In contrast to negative sentences the interpretation of affirmative sentences suggests non-Empty terms. To prove the corresponding theorem we demonstrate that boolean algebra is included into syllogistics arc2 and (...)
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  10. Negative Theology, Coincidentia Oppositorum, and Boolean Algebra.Uwe Meixner - 1998 - Logical Analysis and History of Philosophy 1:75-89.
    In Plato's Parmenides we find on the one hand that the One is denied every property , and on the other hand that the One is attributed every property . In the course of the history of Platonism , these assertions - probably meant by Plato as ontological statements of an entirely formal nature - were repeatedly made the starting points of metaphysical speculations. In the Mystical Theology of the Pseudo-Dionysius they became principles of Christian mysticism and negative theology. I (...)
     
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  11.  25
    Concerning Axiomatizability of the Quasivariety Generated by a Finite Heyting or Topological Boolean Algebra.Wlesław Dziobiak - 1982 - Studia Logica 41 (4):415 - 428.
    In classes of algebras such as lattices, groups, and rings, there are finite algebras which individually generate quasivarieties which are not finitely axiomatizable (see [2], [3], [8]). We show here that this kind of algebras also exist in Heyting algebras as well as in topological Boolean algebras. Moreover, we show that the lattice join of two finitely axiomatizable quasivarieties, each generated by a finite Heyting or topological Boolean algebra, respectively, need not be finitely axiomatizable. Finally, we solve (...)
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  12.  15
    Combinatorial and Recursive Aspects of the Automorphism Group of the Countable Atomless Boolean Algebra.E. W. Madison & B. Zimmermann-Huisgen - 1986 - Journal of Symbolic Logic 51 (2):292-301.
    Given an admissible indexing φ of the countable atomless Boolean algebra B, an automorphism F of B is said to be recursively presented (relative to φ) if there exists a recursive function $p \in \operatorname{Sym}(\omega)$ such that F ⚬ φ = φ ⚬ p. Our key result on recursiveness: Both the subset of $\operatorname{Aut}(\mathscr{B})$ consisting of all those automorphisms which are recursively presented relative to some indexing, and its complement, the set of all "totally nonrecursive" automorphisms, are uncountable. (...)
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  13.  5
    The Spectrum of Maximal Independent Subsets of a Boolean Algebra.J. Donald Monk - 2004 - Annals of Pure and Applied Logic 126 (1-3):335-348.
    Recall that a subset X of a Boolean algebra A is independent if for any two finite disjoint subsets F , G of X we have ∏ x∈F x ∏ y∈G −y≠0. The independence of a BA A , denoted by Ind, is the supremum of cardinalities of its independent subsets. We can also consider the maximal independent subsets. The smallest size of an infinite maximal independent subset is the cardinal invariant i , well known in the case (...)
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  14.  10
    Augustus De Morgan's Boolean Algebra.Daniel D. Merrill - 2005 - History and Philosophy of Logic 26 (2):75-91.
    De Morgan's Formal Logic, which was published on virtually the same day in 1847 as Boole's The Mathematical Analysis of Logic, contains a logic of complex terms (LCT) which has been sadly neglected. It is surprising to find that LCT contains almost a full theory of Boolean algebra. This paper will: (1) provide some background to LCT; (2) outline its main features; (3) point out some gaps in it; (4) compare it with Boole's algebra; (5) show that (...)
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  15.  5
    Rumely Domains with Atomic Constructible Boolean Algebra. An Effective Viewpoint.Claude Sureson - 2007 - Notre Dame Journal of Formal Logic 48 (3):399-423.
    The archetypal Rumely domain is the ring \widetildeZ of algebraic integers. Its constructible Boolean algebra is atomless. We study here the opposite situation: Rumely domains whose constructible Boolean algebra is atomic. Recursive models (which are rings of algebraic numbers) are proposed; effective model-completeness and decidability of the corresponding theory are proved.
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  16. Logic and Algebra.Aldo Ursini, Paolo Aglianò, Roberto Magari & International Conference on Logic and Algebra - 1996
     
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  17.  1
    Boolean Valued and Stone Algebra Valued Measure Theories.Hirokazu Nishimura - 1994 - Mathematical Logic Quarterly 40 (1):69-75.
    In conventional generalization of the main results of classical measure theory to Stone algebra valued measures, the values that measures and functions can take are Booleanized, while the classical notion of a σ-field is retained. The main purpose of this paper is to show by abundace of illustrations that if we agree to Booleanize the notion of a σ-field as well, then all the glorious legacy of classical measure theory is preserved completely.
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  18.  8
    The Boolean Algebra of Formulas of First-Order Logic.Don H. Faust - 1982 - Annals of Mathematical Logic 23 (1):27-53.
    The algebraic recursive structure of countable languages of classical first-order logic with equality is analysed. all languages of finite undecidable similarity type are shown to be algebraically and recursively equivalent in the following sense: their boolean algebras of formulas are, after trivial factors involving the one element models of the languages have been excepted, recursively isomorphic by a map which preserves the degree of recursiveness of their models.
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  19. On Deontic Action Logics Based on Boolean Algebra.Robert Trypuz & Piotr Kulicki - forthcoming - Journal of Logic and Computation.
     
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  20.  16
    On the Number of Ultrafilters of an Infinite Boolean Algebra.D. C. Makinson - 1969 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15 (7-12):121-122.
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  21.  3
    Every Recursive Boolean Algebra is Isomorphic to One with Incomplete Atoms.Rod Downey - 1993 - Annals of Pure and Applied Logic 60 (3):193-206.
    The theorem of the title is proven, solving an old question of Remmel. The method of proof uses an algebraic technique of Remmel-Vaught combined with a complex tree of strategies argument where the true path is needed to figure out the final isomorphism.
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  22.  23
    Application of Bi-Elemental Boolean Algebra to Electronic Circuits.Henryk Greniewski, Krystyn Bochenek & Romuald Marczyński - 1955 - Studia Logica 2 (1):7-75.
  23.  21
    Theory and Problems of Boolean Algebra and Switching Circuits.Elliott Mendelson - 1974 - Journal of Symbolic Logic 39 (3):615-615.
  24.  33
    Relation of Leśniewski's Mereology to Boolean Algebra.Robert E. Clay - 1974 - Journal of Symbolic Logic 39 (4):638-648.
  25.  16
    The Boolean Algebra of Predicates.Martin Kühnrich - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (22-24):355-360.
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  26.  14
    Some Ramsey Theory in Boolean Algebra for Complexity Classes.Gregory L. McColm - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):293-298.
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  27.  13
    Boolean Algebra and its Extra-Logical Sources: The Testimony of Mary Everest Boole.Luis M. Laita - 1980 - History and Philosophy of Logic 1 (1-2):37-60.
    Mary Everest, Boole's wife, claimed after the death of her husband that his logic had a psychological, pedagogical, and religious origin and aim rather than the mathematico-logical ones assigned to it by critics and scientists. It is the purpose of this paper to examine the validity of such a claim. The first section consists of an exposition of the claim without discussing its truthfulness; the discussion is left for the sections 2?4, in which some arguments provided by the examination of (...)
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  28.  13
    Representation Theorem for Distributive Pseudo-Boolean Algebra.Cecylis Rauszer & Bogdan Sabalski - 1974 - Bulletin of the Section of Logic 3 (3/4):17-21.
  29.  2
    On the Number of Ultrafilters of an Infinite Boolean Algebra.D. C. Makinson - 1969 - Mathematical Logic Quarterly 15 (7‐12):121-122.
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  30.  17
    Is a Set B with Boolean Operations a∨ B (Join), a∧ B (Meet) and− a (Complement), Partial Ordering a≤ B Defined by a∧ B= a and the Smallest and Greatest Element, 0 and 1. By Stone's Representation Theorem, Every Boolean Algebra is Isomorphic to an Algebra of Subsets of Some Nonempty Set S, Under Operations a∪ B, a∩ B, S− a, Ordered by Inclusion, with 0=∅. [REVIEW]Mystery Of Measurability - 2006 - Bulletin of Symbolic Logic 12 (2).
  31. Logic Machines, Diagrams and Boolean Algebra.Martin Gardner - 1958 - New York: Dover Publications.
     
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  32.  1
    Review: Albert Whiteman, Postulates for Boolean Algebra in Terms of Ternary Rejection. [REVIEW]Alonzo Church - 1937 - Journal of Symbolic Logic 2 (2):91-91.
  33.  8
    The Boolean Algebra of Objectives.Bogus law Wolniewicz - 1981 - Bulletin of the Section of Logic 10 (1):17-22.
  34.  17
    Boolean Algebra and the Propositional Calculus.Hugues Leblanc - 1962 - Mind 71 (283):383-386.
  35. Review: Franz E. Hohn, Applied Boolean Algebra. An Elementary Introduction. [REVIEW]J. Kuntzmann - 1968 - Journal of Symbolic Logic 33 (2):304-304.
  36.  7
    Review: D. E. Muller, Application of Boolean Algebra to Switching Circuit Design and to Error Detection. [REVIEW]Raymond J. Nelson - 1955 - Journal of Symbolic Logic 20 (2):195-195.
  37.  2
    Abbott J. C.. Semi-Boolean Algebra. Matematički Vesnik, Vol. 4 , Pp. 177–198.G. Grätzer - 1972 - Journal of Symbolic Logic 37 (1):191.
  38.  5
    Relation of Leśniewski's Mereology to Boolean Algebra.Robert E. Clay - 1984 - In Jan T. J. Srzednicki, V. F. Rickey & J. Czelakowski (eds.), Journal of Symbolic Logic. Distributors for the United States and Canada, Kluwer Boston. pp. 241--252.
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  39.  32
    Canonical Expressions in Boolean Algebra.Archie Blake - 1938 - University of Chicago Press.
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  40.  13
    Corrections to Canonical Expressions in Boolean Algebra.Archie Blake - 1938 - Journal of Symbolic Logic 3 (3):112-113.
  41.  3
    Implicative Boolean Algebra.Arthur H. Copeland - 1951 - Journal of Symbolic Logic 16 (2):151-152.
  42.  9
    Studies in the Axiomatic Foundations of Boolean Algebra. I.Czesław Lejewski - 1960 - Notre Dame Journal of Formal Logic 1 (1-2):23-47.
  43.  5
    The Boolean Algebra of Objectives.Boguslaw Wolniewicz - 1981 - Bulletin of the Section of Logic 10 (1):17-22.
    This is the fth and last installment in series dealing with the Wittgen- steinian notion of a situation . All proofs and most lemmas have been omitted. They are contained in a comprehensive paper on the ontol- ogy of situations to be submitted to Studia Logica.
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  44. Review: Flora Dinkines, Elementary Concepts of Modern Mathematics; L. R. Sjoblom, Application of Boolean Algebra to Switching Networks. [REVIEW]Alfons Borgers - 1967 - Journal of Symbolic Logic 32 (3):422-423.
  45. Review: Arthur H. Copeland, Frank Harary, The Extension of an Arbitrary Boolean Algebra to an Implicative Boolean Algebra[REVIEW]K. E. Aubert - 1959 - Journal of Symbolic Logic 24 (3):254-254.
  46.  3
    Review: David Sachs, The Lattice of Subalgebras of a Boolean Algebra[REVIEW]G. Gratzer - 1972 - Journal of Symbolic Logic 37 (1):190-191.
  47.  1
    Vaidyanathaswamy R.. On the Group-Operations of a Boolean Algebra. The Journal of the Indian Mathematical Society, N.S. Vol. 2 , Pp. 250–254. [REVIEW]Albert A. Bennett - 1937 - Journal of Symbolic Logic 2 (3):142.
  48.  1
    Hohn Franz E.. Applied Boolean Algebra. An Elementary Introduction. Deuxième Édition, Revue Et Augmentée, de XXVII 104. The Macmillan Company, New York, Et Collier-Macmillan Limited, Londres, 1966, Xiii + 273 P. [REVIEW]J. Kuntzmann - 1968 - Journal of Symbolic Logic 33 (2):304.
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  49.  1
    Muller D. E.. Application of Boolean Algebra to Switching Circuit Design and to Error Detection. Transactions of the Institute of Radio Engineers Professional Group on Electronic Computers, Vol. EC-3 , Pp. 6–12. [REVIEW]Raymond J. Nelson - 1955 - Journal of Symbolic Logic 20 (2):195.
  50.  1
    Federal Electric Corporation. Boolean Algebra. A Self-Instructional Programed Manual. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1966, Ix + 246 Pp. [REVIEW]Ann M. Singleterry - 1967 - Journal of Symbolic Logic 32 (1):133-134.
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