Results for ' Algebra'

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  1.  47
    Introduction to Model Theory and to the Metamathematics of Algebra.Abraham Robinson - 1963 - Elsevier Publishing Company.
  2.  33
    A cylindrical algebra based on the Boolean ring.Jerzy Kotas & August Pieczkowski - 1967 - Studia Logica 21 (1):71 - 80.
  3. Kant on arithmetic, algebra, and the theory of proportions.Daniel Sutherland - 2006 - Journal of the History of Philosophy 44 (4):533-558.
    Daniel Sutherland - Kant on Arithmetic, Algebra, and the Theory of Proportions - Journal of the History of Philosophy 44:4 Journal of the History of Philosophy 44.4 533-558 Muse Search Journals This Journal Contents Kant on Arithmetic, Algebra, and the Theory of Proportions Daniel Sutherland Kant's philosophy of mathematics has both enthralled and exercised philosophers since the appearance of the Critique of Pure Reason. Neither the Critique nor any other work provides a sustained and focused account of his (...)
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  4. 10. Lógica y Computabilidad.Sergio Celani, Daniela Montangie & Álgebras de Hilbert Modales - 2001 - Journal of Symbolic Logic 66:1620-1636.
     
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  5.  24
    Byrne Lee. Boolean algebra in terms of inclusion. American journal of mathematics, vol. 70 , pp. 139–143.H. E. Vaughan - 1948 - Journal of Symbolic Logic 13 (3):159-159.
  6. NeutroAlgebra is a Generalization of Partial Algebra.Florentin Smarandache - 2020 - International Journal of Neutrosophic Science 2 (1):8-17.
    In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let <A> be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to <A> and <antiA>, and one corresponding to neutral (indeterminate) <neutA> (also denoted <neutroA>) between the opposites}, which may (...)
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  7.  9
    Geometric and Cognitive Differences between Logical Diagrams for the Boolean Algebra B_4.Lorenz6 Demey & Hans5 Smessaert - 2018 - Annals of Mathematics and Artificial Intelligence 83 (2):185-208.
    © 2018, Springer International Publishing AG, part of Springer Nature. Aristotelian diagrams are used extensively in contemporary research in artificial intelligence. The present paper investigates the geometric and cognitive differences between two types of Aristotelian diagrams for the Boolean algebra B4. Within the class of 3D visualizations, the main geometric distinction is that between the cube-based diagrams and the tetrahedron-based diagrams. Geometric properties such as collinearity, central symmetry and distance are examined from a cognitive perspective, focusing on diagram design (...)
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  8.  24
    Oh the Algebra of Logic.C. S. Peirce - 1880 - American Journal of Mathematics 3 (1):15-57.
  9.  44
    The mathematical origins of nineteenth-century algebra of logic.Volker Peckhaus - 2011 - In Leila Haaparanta (ed.), The development of modern logic. New York: Oxford University Press. pp. 159.
    This chapter discusses the complex conditions for the emergence of 19th-century symbolic logic. The main scope will be on the mathematical motives leading to the interest in logic; the philosophical context will be dealt with only in passing. The main object of study will be the algebra of logic in its British and German versions. Special emphasis will be laid on the systems of George Boole and above all of his German follower Ernst Schröder.
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  10. Table Des matieres editorial preface 3.Jair Minoro Abe, Curry Algebras Pt, Paraconsistent Logic, Newton Ca da Costa, Otavio Bueno, Jacek Pasniczek, Beyond Consistent, Complete Possible Worlds, Vm Popov & Inverse Negation - 1998 - Logique Et Analyse 41:1.
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  11.  20
    Model theoretic algebra.G. L. Cherlin - 1976 - Journal of Symbolic Logic 41 (2):537-545.
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  12.  1
    Tagmemic analysis of elementary algebra.Vern S. Poythress - 1976 - Semiotica 17 (2).
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  13. 30 treatise on universal algebra (gif images).Alfred North Whitehead - unknown
     
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  14.  35
    Using computer algebra to determine rate constants in biochemistry.M. Bayram, J. P. Bennett & M. C. Dewar - 1993 - Acta Biotheoretica 41 (1-2):53-62.
    In earlier work we have described how computer algebra may be used to derive composite rate laws for complete systems of equations, using the mathematical technique of Gröbner Bases (Bennett, Davenport and Sauro, 1988). Such composite rate laws may then be fitted to experimental data to yield estimates of kinetic parameters.Recently we have been investigating the practical application of this methodology to the estimation of kinetic parameters for the closed two enzyme system of aspartate aminotransferase (AAT) and malate dehydrogenase (...)
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  15. Descartes' unification of algebra and geometry.Emily R. Grosholz - 1980 - In Stephen Gaukroger (ed.), Descartes: philosophy, mathematics and physics. Totowa, N.J.: Barnes & Noble. pp. 156--68.
  16. O papel da abstração na instanciação da álgebra nas Regulae ad Directionem Ingenii.Érico Andrade - 2011 - Analytica (Rio) 15 (1):145-172.
    In this essay I will defend three points, the first being that Descartes- unlike the aristotelian traditon- maintained that abstraction is not a operation in which the intellect builds the mathematical object resorting to sensible ob- jects. Secondly I will demonstrate that, according to cartesian philosophy, the faculty of understanding has the ability to instatiate- within the process of abstraction- mathematical symbols that represent the relation between quantities, whether magnitude or multitude.And finally I will advocate that the lack of onthological (...)
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  17.  16
    Concerning some cylindric algebra versions of the downward Löwenheim-Skolem theorem.Ildikó Sain - 1988 - Notre Dame Journal of Formal Logic 29 (3):332-344.
  18.  64
    An Einstein addition law for nonparallel boosts using the geometric algebra of space-time.B. Tom King - 1995 - Foundations of Physics 25 (12):1741-1755.
    The modern use of algebra to describe geometric ideas is discussed with particular reference to the constructions of Grassmann and Hamilton and the subsequent algebras due to Clifford. An Einstein addition law for nonparallel boosts is shown to follow naturally from the use of the representation-independent form of the geometric algebra of space-time.
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  19. A new algebra of implications and some consequences.C. I. Lewis - 1913 - Journal of Philosophy, Psychology and Scientific Methods 10 (16):428-438.
  20.  83
    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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  21. Vectors and Beyond: Geometric Algebra and its Philosophical Significance.Peter Simons - 2009 - Dialectica 63 (4):381-395.
  22.  11
    On models of exponentiation. Identities in the HSI-algebra of posets.Gurgen Asatryan - 2008 - Mathematical Logic Quarterly 54 (3):280-287.
    We prove that Wilkie's identity holds in those natural HSI-algebras where each element has finite decomposition into components.Further, we construct a bunch of HSI-algebras that satisfy all the identities of the set of positive integers ℕ. Then, based on the constructed algebras, we prove that the identities of ℕ hold in the HSI-algebra of finite posets when the value of each variable is a poset having an isolated point.
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  23. A Survey of Geometric Algebra and Geometric Calculus.Alan Macdonald - 2017 - Advances in Applied Clifford Algebras 27:853-891.
    The paper is an introduction to geometric algebra and geometric calculus for those with a knowledge of undergraduate mathematics. No knowledge of physics is required. The section Further Study lists many papers available on the web.
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  24.  41
    A New Game Equivalence, its Logic and Algebra.Johan van Benthem, Nick Bezhanishvili & Sebastian Enqvist - 2019 - Journal of Philosophical Logic 48 (4):649-684.
    We present a new notion of game equivalence that captures basic powers of interacting players. We provide a representation theorem, a complete logic, and a new game algebra for basic powers. In doing so, we establish connections with imperfect information games and epistemic logic. We also identify some new open problems concerning logic and games.
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  25.  2
    The Boolean Algebra of Predicates.Martin Kühnrich - 1980 - Mathematical Logic Quarterly 26 (22‐24):355-360.
  26.  17
    On substitutive algebra and its syntax.Karl Menger - 1964 - Mathematical Logic Quarterly 10 (6‐7):81-104.
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  27.  55
    Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks.I. C. Baianu, R. Brown, G. Georgescu & J. F. Glazebrook - 2006 - Axiomathes 16 (1):65-122.
    A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a (...)
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  28.  20
    B. Tsaban, Algebra, selections and additive Ramsey theory. Fundamenta Mathematicae, , no. 240, pp. 81–104.Rodrigo R. Dias - 2018 - Bulletin of Symbolic Logic 24 (2):179-180.
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  29. Evolución del Álgebra: Categorías.Enrique Góngora - 1969 - Revista de Filosofía de la Universidad de Costa Rica 25:179-182.
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  30.  88
    Completeness of S4 for the Lebesgue Measure Algebra.Tamar Lando - 2012 - Journal of Philosophical Logic 41 (2):287-316.
    We prove completeness of the propositional modal logic S 4 for the measure algebra based on the Lebesgue-measurable subsets of the unit interval, [0, 1]. In recent talks, Dana Scott introduced a new measure-based semantics for the standard propositional modal language with Boolean connectives and necessity and possibility operators, and . Propositional modal formulae are assigned to Lebesgue-measurable subsets of the real interval [0, 1], modulo sets of measure zero. Equivalence classes of Lebesgue-measurable subsets form a measure algebra, (...)
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  31.  54
    Dual Choice and Iteration in an Abstract Algebra of Action.Kim Solin - 2012 - Studia Logica 100 (3):607-630.
    This paper presents an abstract-algebraic formulation of action facilitating reasoning about two opposing agents. Two dual nondeterministic choice operators are formulated abstract-algebraically: angelic (or user) choice and demonic (or system) choice. Iteration operators are also defined. As an application, Hoare-style correctness rules are established by means of the algebra. A negation operator is also discussed.
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  32.  19
    Complexity-theoretic algebra II: Boolean algebras.A. Nerode & J. B. Remmel - 1989 - Annals of Pure and Applied Logic 44 (1-2):71-99.
  33.  22
    On the Metamathematics of Algebra.Abraham Robinson - 1952 - Journal of Symbolic Logic 17 (3):205-207.
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  34.  33
    The lindenbaum fixed point algebra is undecidable.V. Yu Shavrukov - 1991 - Studia Logica 50 (1):143-147.
    We prove that the first order theory of the fixed point algebra corresponding to an r.e. consistent theory containing arithmetic is hereditarily undecidable.
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  35.  17
    Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra.Michalis Sialaros & Jean Christianidis - 2016 - Science in Context 29 (2):129-150.
    ArgumentThe aim of this paper is to employ the newly contextualized historiographical category of “premodern algebra” in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on “geometrical algebra.” Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related (...)
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  36. Principles of the Algebra of Logic.Alexander Macfarlane - 1879 - Mind 4 (16):580-582.
     
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  37.  43
    The shuffle Hopf algebra and noncommutative full completeness.R. F. Blute & P. J. Scott - 1998 - Journal of Symbolic Logic 63 (4):1413-1436.
    We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformations being equivariant under certain actions of a noncocommutative Hopf algebra called the shuffie algebra. Multiplicative sequents are assigned a vector space of such dinaturals, and we show that this space has as a basis the denotations of cut-free (...)
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  38.  9
    Some Interconnections Between Modern Algebra and Mathematical Logic.Leon Henkin - 1955 - Journal of Symbolic Logic 20 (2):183-184.
  39.  34
    The algebra of logic.Victor Sanchez Valencia - 2004 - In Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the history of logic. Boston: Elsevier. pp. 389-544.
  40.  23
    Multi-modal meaning – An empirically-founded process algebra approach.Hannes Rieser & Insa Lawler - 2020 - Semantics and Pragmatics 13 (8):1-48.
    Humans communicate with different modalities. We offer an account of multi-modal meaning coordination, taking speech-gesture meaning coordination as a prototypical case. We argue that temporal synchrony (plus prosody) does not determine how to coordinate speech meaning and gesture meaning. Challenging cases are asynchrony and broadcasting cases, which are illustrated with empirical data. We propose that a process algebra account satisfies the desiderata. It models gesture and speech as independent but concurrent processes that can communicate flexibly with each other and (...)
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  41.  27
    On the algebra of classes of formulae of Jaśkowski's discussive system.Jerzy Kotas - 1971 - Studia Logica 27 (1):81-90.
  42.  12
    Corry, L.: Modern Algebra and the Rise of Mathematical Structures, Birkhäuser, Basel, 1996, 460 págs.Carlos Ortiz de Landázuri - 1999 - Anuario Filosófico:847-848.
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  43.  4
    Before the “Language of Calculation”: Writing the Operations in Pierre de La Ramée’s Algebra.François Loget - 2018 - Philosophia Scientiae 22:81-113.
    Dans son Algebra de 1560, Pierre de La Ramée (1515-1572) emploie une manière originale de poser les opérations de l’algèbre sous la forme de ce que j’appellerai des « schémas de calcul ». Ces schémas constituent un aspect singulier de l’écriture mathématique de Pierre de La Ramée par rapport à celle de ses contemporains. Avec ses « schémas de calcul », La Ramée contribue à l’invention, pour les mathématiques de la modernité, d’une langue propre. Leur étude conduit donc à (...)
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  44. A Treatise on Universal Algebra, with Applications. Vol. 1.Alfred North Whitehead - 1900 - Revue de Métaphysique et de Morale 8 (3):323-362.
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  45. 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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  46.  16
    El álgebra de proposiciones y la lógica del descubrimiento.Miguel Ángel Quintanilla Fisac - 1979 - Cuadernos Salmantinos de Filosofía 6:187-196.
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  47.  35
    Some remarks on the algebra of Eddington'sE numbers.Nikos Salingaros - 1985 - Foundations of Physics 15 (6):683-691.
    This paper reviews the algebra of Eddington'sE numbers and identifies those points where Eddington anticipated results of current interest. He discovered the Majorana spinors, and was responsible for the standard γ 5 notation as well as the notion of chirality. Furthermore, Eddington defined Clifford algebras in eight and nine dimensions which are now appearing in grand unified gauge and supersymmetric theories. A point which Eddington cleared up, yet is still misunderstood, is that the Dirac algebra corresponds to afive-dimensional (...)
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  48.  46
    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 A= (...)
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  49.  20
    Constructive version of Boolean algebra.F. Ciraulo, M. E. Maietti & P. Toto - 2013 - Logic Journal of the IGPL 21 (1):44-62.
  50. Deontic Logics based on Boolean Algebra.Pablo F. Castro & Piotr Kulicki - 2013 - In Robert Trypuz (ed.), Krister Segerberg on Logic of Actions. Dordrecht, Netherland: Springer Verlag.
    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 properties of (...)
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