Search results for 'Boolean algebra' (try it on Scholar)

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  1. Pablo F. Castro & Piotr Kulicki (forthcoming). Deontic Logics Based on Boolean Algebra. In Robert Trypuz (ed.), Krister Segerberg on Logic of Actions. Springer.score: 240.0
    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. J. Donald Monk (2001). The Spectrum of Partitions of a Boolean Algebra. Archive for Mathematical Logic 40 (4):243-254.score: 240.0
    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. Matatyahu Rubin & Sabine Koppelberg (2001). A Superatomic Boolean Algebra with Few Automorphisms. Archive for Mathematical Logic 40 (2):125-129.score: 240.0
    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. James Cummings & Saharon Shelah (1995). A Model in Which Every Boolean Algebra has Many Subalgebras. Journal of Symbolic Logic 60 (3):992-1004.score: 208.0
    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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  5. Lei-Bo Wang (2010). Congruences on a Balanced Pseudocomplemented Ockham Algebra Whose Quotient Algebras Are Boolean. Studia Logica 96 (3):421-431.score: 192.0
    In this note we shall describe the lattice of the congruences on a balanced Ockham algebra with the pseudocomplementation whose quotient algebras are boolean. This is an extension of the result obtained by Rodrigues and Silva who gave a description of the lattice of congruences on an Ockham algebra whose quotient algebras are boolean.
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  6. Robert Trypuz & Piotr Kulicki (2010). A Systematics of Deontic Action Logics Based on Boolean Algebra. Logic and Logical Philosophy 18 (3-4):253-270.score: 192.0
    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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  7. Ivo Düntsch & Sanjiang Li (2013). On the Homogeneous Countable Boolean Contact Algebra. Logic and Logical Philosophy 22 (2):213-251.score: 192.0
    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. V. A. Bocharov (1986). Boolean Algebra and Syllogism. Synthese 66 (1):35 - 54.score: 180.0
    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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  9. Wlesław Dziobiak (1982). Concerning Axiomatizability of the Quasivariety Generated by a Finite Heyting or Topological Boolean Algebra. Studia Logica 41 (4):415 - 428.score: 180.0
    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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  10. E. W. Madison & B. Zimmermann-Huisgen (1986). Combinatorial and Recursive Aspects of the Automorphism Group of the Countable Atomless Boolean Algebra. Journal of Symbolic Logic 51 (2):292-301.score: 180.0
    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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  11. Daniel D. Merrill (2005). Augustus De Morgan's Boolean Algebra. History and Philosophy of Logic 26 (2):75-91.score: 180.0
    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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  12. E. W. Madison (1983). The Existence of Countable Totally Nonconstructive Extensions of the Countable Atomless Boolean Algebra. Journal of Symbolic Logic 48 (1):167-170.score: 180.0
    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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  13. Boguslaw Wolniewicz (forthcoming). The Boolean Algebra of Objectives. Bulletin of the Section of Logic.score: 180.0
    This concludes a series of papers constructing a semantics for propositional languages based on the notion of a possible "situation". objectives of propositions are the situations described by them. the set of objectives is defined and shown to be a boolean algebra isomorphic to that formed by sets of possible worlds.
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  14. Claude Sureson (2007). Rumely Domains with Atomic Constructible Boolean Algebra. An Effective Viewpoint. Notre Dame Journal of Formal Logic 48 (3):399-423.score: 180.0
    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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  15. Hirokazu Nishimura (1994). Boolean Valued and Stone Algebra Valued Measure Theories. Mathematical Logic Quarterly 40 (1):69-75.score: 168.0
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  16. Don H. Faust (1982). The Boolean Algebra of Formulas of First-Order Logic. Annals of Mathematical Logic 23 (1):27-53.score: 164.0
    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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  17. Thomas Jech & Saharon Shelah (1996). On Countably Closed Complete Boolean Algebras. Journal of Symbolic Logic 61 (4):1380-1386.score: 160.0
    It is unprovable that every complete subalgebra of a countably closed complete Boolean algebra is countably closed.
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  18. V. Yu Shavrukov (2010). Effectively Inseparable Boolean Algebras in Lattices of Sentences. Archive for Mathematical Logic 49 (1):69-89.score: 160.0
    We show the non-arithmeticity of 1st order theories of lattices of Σ n sentences modulo provable equivalence in a formal theory, of diagonalizable algebras of a wider class of arithmetic theories than has been previously known, and of the lattice of degrees of interpretability over PA. The first two results are applications of Nies’ theorem on the non-arithmeticity of the 1st order theory of the lattice of r.e. ideals on any effectively dense r.e. Boolean algebra. The theorem on (...)
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  19. Anastasis Kamburelis (1989). Iterations of Boolean Algebras with Measure. Archive for Mathematical Logic 29 (1):21-28.score: 156.0
    We consider a classM of Boolean algebras with strictly positive, finitely additive measures. It is shown thatM is closed under iterations with finite support and that the forcing via such an algebra does not destroy the Lebesgue measure structure from the ground model. Also, we deduce a simple characterization of Martin's Axiom reduced to the classM.
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  20. Robert E. Clay (1974). Relation of Leśniewski's Mereology to Boolean Algebra. Journal of Symbolic Logic 39 (4):638-648.score: 150.0
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  21. Hugues Leblanc (1962). Boolean Algebra and the Propositional Calculus. Mind 71 (283):383-386.score: 150.0
  22. Archie Blake (1938). Corrections to Canonical Expressions in Boolean Algebra. Journal of Symbolic Logic 3 (3):112-113.score: 150.0
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  23. Luis M. Laita (1980). Boolean Algebra and its Extra-Logical Sources: The Testimony of Mary Everest Boole. History and Philosophy of Logic 1 (1-2):37-60.score: 150.0
    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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  24. Henryk Greniewski, Krystyn Bochenek & Romuald Marczyński (1955). Application of Bi-Elemental Boolean Algebra to Electronic Circuits. Studia Logica 2 (1):7 - 76.score: 150.0
  25. Edward V. Huntington (1933). A Simplification of Lewis and Langford's Postulates for Boolean Algebra. Mind 42 (166):203-207.score: 150.0
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  26. J. Donald Monk, The Mathematics of Boolean Algebra. Stanford Encyclopedia of Philosophy.score: 150.0
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  27. J. Donald Monk (2004). The Spectrum of Maximal Independent Subsets of a Boolean Algebra. Annals of Pure and Applied Logic 126 (1-3):335-348.score: 150.0
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  28. Czesław Lejewski (1960). Studies in the Axiomatic Foundations of Boolean Algebra. I. Notre Dame Journal of Formal Logic 1 (1-2):23-47.score: 150.0
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  29. Czesław Lejewski (1960). Studies in the Axiomatic Foundations of Boolean Algebra. II. Notre Dame Journal of Formal Logic 1 (3):91-106.score: 150.0
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  30. Czesław Lejewski (1961). Studies in the Axiomatic Foundations of Boolean Algebra. III. Notre Dame Journal of Formal Logic 2 (2):79-93.score: 150.0
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  31. G. Gratzer (1972). Review: David Sachs, The Lattice of Subalgebras of a Boolean Algebra. [REVIEW] Journal of Symbolic Logic 37 (1):190-191.score: 150.0
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  32. Paul Henle (1937). Review: Tang Tsao-Chen, The Theorem "$P Qldot = Ldot Pq = P$" and Huntington's Relation Between Lewis's Strict Implication and Boolean Algebra; Tang Tsao-Chen, A Paradox of Lewis's Strict Implication. [REVIEW] Journal of Symbolic Logic 2 (1):58-58.score: 150.0
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  33. D. C. Makinson (1969). On the Number of Ultrafilters of an Infinite Boolean Algebra. Mathematical Logic Quarterly 15 (7‐12):121-122.score: 150.0
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  34. Raymond J. Nelson (1955). Review: D. E. Muller, Application of Boolean Algebra to Switching Circuit Design and to Error Detection. [REVIEW] Journal of Symbolic Logic 20 (2):195-195.score: 150.0
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  35. Diane Resek (1981). Review: Kathleen Levitz, Hilbert Levitz, Logic and Boolean Algebra. [REVIEW] Journal of Symbolic Logic 46 (2):420-421.score: 150.0
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  36. Albert A. Bennett (1937). Review: S. Pankajam, On Symmetric Functions of $N$ Elements in a Boolean Algebra. [REVIEW] Journal of Symbolic Logic 2 (4):173-173.score: 150.0
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  37. Alfons Borgers (1967). Review: Flora Dinkines, Elementary Concepts of Modern Mathematics; L. R. Sjoblom, Application of Boolean Algebra to Switching Networks. [REVIEW] Journal of Symbolic Logic 32 (3):422-423.score: 150.0
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  38. Alonzo Church (1937). Review: Albert Whiteman, Postulates for Boolean Algebra in Terms of Ternary Rejection. [REVIEW] Journal of Symbolic Logic 2 (2):91-91.score: 150.0
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  39. Alonzo Church (1938). Review: Edmund C. Berkeley, Boolean Algebra (The Technique for Manipulating "and," "or," "Not," and Conditions) and Applications to Insurance. [REVIEW] Journal of Symbolic Logic 3 (2):90-90.score: 150.0
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  40. Alonzo Church (1954). Review: Robert Serrell, Elements of Boolean Algebra for the Study of Information-Handling Systems. [REVIEW] Journal of Symbolic Logic 19 (2):142-142.score: 150.0
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  41. Robert E. Clay (1984). Relation of Leśniewski's Mereology to Boolean Algebra. In Jan T. J. Srzednicki, V. F. Rickey & J. Czelakowski (eds.), Leśniewski's Systems. Distributors for the United States and Canada, Kluwer Boston. 241--252.score: 150.0
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  42. H. B. Enderton (1976). Review: H. C. Torng, Introduction to the Logical Design of Switching Systems; Basil Zacharov, Digital Systems Logic and Circuits; Ray Ryan, Basic Digital Electronics--Understanding Number Systems, Boolean Algebra, & Logic Circuits. [REVIEW] Journal of Symbolic Logic 41 (2):549-550.score: 150.0
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  43. William E. Gould (1974). Review: Elliott Mendelson, Theory and Problems of Boolean Algebra and Switching Circuits. [REVIEW] Journal of Symbolic Logic 39 (3):615-615.score: 150.0
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  44. Theodore Hailperin (1964). Review: B. H. Arnold, Logic and Boolean Algebra. [REVIEW] Journal of Symbolic Logic 29 (2):95-96.score: 150.0
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  45. J. C. C. McKinsey (1938). Review: Archie Blake, Canonical Expressions in Boolean Algebra. [REVIEW] Journal of Symbolic Logic 3 (2):93-93.score: 150.0
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  46. Mystery Of Measurability (2006). 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] Bulletin of Symbolic Logic 12 (2).score: 150.0
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  47. Thomas H. Mott (1962). Review: J. Eldon Whitesitt, Boolean Algebra and Its Applications. [REVIEW] Journal of Symbolic Logic 27 (1):103-104.score: 150.0
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  48. Ann M. Singleterry (1967). Review: Allan Lytel, ABC's of Boolean Algebra. [REVIEW] Journal of Symbolic Logic 32 (1):133-133.score: 150.0
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  49. F. M. Yaqub (1970). Review: M. J. Maczynski, T. Traczyk, The $Mathfrak{M}$-Amalgamation Property for $Mathfrak{M}$-Distributive Boolean Algebra. [REVIEW] Journal of Symbolic Logic 35 (2):346-347.score: 150.0
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  50. K. E. Aubert (1959). Review: Arthur H. Copeland, Frank Harary, The Extension of an Arbitrary Boolean Algebra to an Implicative Boolean Algebra. [REVIEW] Journal of Symbolic Logic 24 (3):254-254.score: 150.0
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