Search results for 'Algebra Congresses' (try it on Scholar)

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  1. John N. Crossley (ed.) (1975). Algebra and Logic: Papers From the 1974 Summer Research Institute of the Australian Mathematical Society, Monash University, Australia. Springer-Verlag.score: 90.0
     
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  2. Mirja Hartimo (2012). Husserl and the Algebra of Logic: Husserl's 1896 Lectures. [REVIEW] Axiomathes 22 (1):121-133.score: 24.0
    In his 1896 lecture course on logic–reportedly a blueprint for the Prolegomena to Pure Logic –Husserl develops an explicit account of logic as an independent and purely theoretical discipline. According to Husserl, such a theory is needed for the foundations of logic (in a more general sense) to avoid psychologism in logic. The present paper shows that Husserl’s conception of logic (in a strict sense) belongs to the algebra of logic tradition. Husserl’s conception is modeled after arithmetic, and respectively (...)
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  3. K. Muralidhar (2014). Complex Vector Formalism of Harmonic Oscillator in Geometric Algebra: Particle Mass, Spin and Dynamics in Complex Vector Space. Foundations of Physics 44 (3):266-295.score: 24.0
    Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been shown (...)
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  4. Pablo F. Castro & Piotr Kulicki (forthcoming). Deontic Logics Based on Boolean Algebra. In Robert Trypuz (ed.), Krister Segerberg on Logic of Actions. Springer.score: 24.0
    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 properties of (...)
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  5. Sho Tanaka (2009). Kinematical Reduction of Spatial Degrees of Freedom and Holographic Relation in Yang's Quantized Space-Time Algebra. Foundations of Physics 39 (5):510-518.score: 24.0
    We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang’s quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, λ and R, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of the latter fact, we find (...)
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  6. I. C. Baianu, R. Brown, G. Georgescu & J. F. Glazebrook (2006). Complex Non-Linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks. [REVIEW] Axiomathes 16 (1-2):65-122.score: 24.0
    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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  7. Yingxu Wang (2003). Using Process Algebra to Describe Human and Software Behaviors. Brain and Mind 4 (2):199-213.score: 24.0
    Although there are various ways to express actions and behaviors in natural languages, it is found in cognitive informatics that human and system behaviors may be classified into three basic categories: to be , to have , and to do . All mathematical means and forms, in general, are an abstract description of these three categories of system behaviors and their common rules. Taking this view, mathematical logic may be perceived as the abstract means for describing to be, set theory (...)
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  8. P. Watson & A. J. Bracken (2014). Quantum Phase Space From Schwinger's Measurement Algebra. Foundations of Physics 44 (7):762-780.score: 24.0
    Schwinger’s algebra of microscopic measurement, with the associated complex field of transformation functions, is shown to provide the foundation for a discrete quantum phase space of known type, equipped with a Wigner function and a star product. Discrete position and momentum variables label points in the phase space, each taking \(N\) distinct values, where \(N\) is any chosen prime number. Because of the direct physical interpretation of the measurement symbols, the phase space structure is thereby related to definite experimental (...)
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  9. Tamar Lando (2012). Completeness of S4 for the Lebesgue Measure Algebra. Journal of Philosophical Logic 41 (2):287-316.score: 24.0
    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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  10. Albrecht Heeffer (2008). The Emergence of Symbolic Algebra as a Shift in Predominant Models. Foundations of Science 13 (2):149--161.score: 24.0
    Historians of science find it difficult to pinpoint to an exact period in which symbolic algebra came into existence. This can be explained partly because the historical process leading to this breakthrough in mathematics has been a complex and diffuse one. On the other hand, it might also be the case that in the early twentieth century, historians of mathematics over emphasized the achievements in algebraic procedures and underestimated the conceptual changes leading to symbolic algebra. This paper attempts (...)
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  11. Dirk Leinders, Maarten Marx, Jerzy Tyszkiewicz & Jan Van den Bussche (2005). The Semijoin Algebra and the Guarded Fragment. Journal of Logic, Language and Information 14 (3):331-343.score: 24.0
    In the 1970s Codd introduced the relational algebra, with operators selection, projection, union, difference and product, and showed that it is equivalent to first-order logic. In this paper, we show that if we replace in Codd’s relational algebra the product operator by the “semijoin” operator, then the resulting “semijoin algebra” is equivalent to the guarded fragment of first-order logic. We also define a fixed point extension of the semijoin algebra that corresponds to μGF.
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  12. Jeffrey A. Oaks (2007). Medieval Arabic Algebra as an Artificial Language. Journal of Indian Philosophy 35 (5-6):543-575.score: 24.0
    Medieval Arabic algebra is a good example of an artificial language.Yet despite its abstract, formal structure, its utility was restricted to problem solving. Geometry was the branch of mathematics used for expressing theories. While algebra was an art concerned with finding specific unknown numbers, geometry dealtwith generalmagnitudes.Algebra did possess the generosity needed to raise it to a more theoretical level—in the ninth century Abū Kāmil reinterpreted the algebraic unknown “thing” to prove a general result. But mathematicians had (...)
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  13. David J. Foulis & Sylvia Pulmannová (2013). Type-Decomposition of a Synaptic Algebra. Foundations of Physics 43 (8):948-968.score: 24.0
    A synaptic algebra is a generalization of the self-adjoint part of a von Neumann algebra. In this article we extend to synaptic algebras the type-I/II/III decomposition of von Neumann algebras, AW∗-algebras, and JW-algebras.
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  14. Lei-Bo Wang (2010). Congruences on a Balanced Pseudocomplemented Ockham Algebra Whose Quotient Algebras Are Boolean. Studia Logica 96 (3):421-431.score: 24.0
    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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  15. Imants Barušs & Robert Woodrow (2013). A Reduction Theorem for the Kripke–Joyal Semantics: Forcing Over an Arbitrary Category Can Always Be Replaced by Forcing Over a Complete Heyting Algebra. [REVIEW] Logica Universalis 7 (3):323-334.score: 24.0
    It is assumed that a Kripke–Joyal semantics \({\mathcal{A} = \left\langle \mathbb{C},{\rm Cov}, {\it F},\Vdash \right\rangle}\) has been defined for a first-order language \({\mathcal{L}}\) . To transform \({\mathbb{C}}\) into a Heyting algebra \({\overline{\mathbb{C}}}\) on which the forcing relation is preserved, a standard construction is used to obtain a complete Heyting algebra made up of cribles of \({\mathbb{C}}\) . A pretopology \({\overline{{\rm Cov}}}\) is defined on \({\overline{\mathbb{C}}}\) using the pretopology on \({\mathbb{C}}\) . A sheaf \({\overline{{\it F}}}\) is made up of (...)
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  16. Alex Citkin (2012). Not Every Splitting Heyting or Interior Algebra is Finitely Presentable. Studia Logica 100 (1-2):115-135.score: 24.0
    We give an example of a variety of Heyting algebras and of a splitting algebra in this variety that is not finitely presentable. Moreover, we show that the corresponding splitting pair cannot be defined by any finitely presentable algebra. Also, using the Gödel-McKinsey-Tarski translation and the Blok-Esakia theorem, we construct a variety of Grzegorczyk algebras with similar properties.
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  17. Jie Fang, Lei-Bo Wang & Ting Yang (2014). The Lattice of Kernel Ideals of a Balanced Pseudocomplemented Ockham Algebra. Studia Logica 102 (1):29-39.score: 24.0
    In this note we shall show that if L is a balanced pseudocomplemented Ockham algebra then the set ${\fancyscript{I}_{k}(L)}$ of kernel ideals of L is a Heyting lattice that is isomorphic to the lattice of congruences on B(L) where ${B(L) = \{x^* | x \in L\}}$ . In particular, we show that ${\fancyscript{I}_{k}(L)}$ is boolean if and only if B(L) is finite, if and only if every kernel ideal of L is principal.
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  18. Todor D. Todorov & Hans Vernaeve (2008). Full Algebra of Generalized Functions and Non-Standard Asymptotic Analysis. Logic and Analysis 1 (3-4):205-234.score: 24.0
    We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions.We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution.We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring with zero divisors. We prove a Hahn–Banach extension principle which does not hold in Colombeau theory. We establish a (...)
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  19. Ivo D.[Uuml ]Ntsch, Gunther Schmidt & Michael Winter (2001). A Necessary Relation Algebra for Mereotopology. Studia Logica 69 (3):381-409.score: 24.0
    The standard model for mereotopological structures are Boolean subalgebras of the complete Boolean algebra of regular closed subsets of a nonempty connected regular T0 topological space with an additional "contact relation" C defined by xCy ? x n ? Ø.
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  20. Daniele Mundici (2006). A Characterization of the Free N-Generated MV-Algebra. Archive for Mathematical Logic 45 (2):239-247.score: 24.0
    An MV-algebra A=(A,0,¬,⊕) is an abelian monoid (A,0,⊕) equipped with a unary operation ¬ such that ¬¬x=x,x⊕¬0=¬0, and y⊕¬(y⊕¬x)=x⊕¬(x⊕¬y). Chang proved that the equational class of MV-algebras is generated by the real unit interval [0,1] equipped with the operations ¬x=1−x and x⊕y=min(1,x+y). Therefore, the free n-generated MV-algebra Free n is the algebra of [0,1]-valued functions over the n-cube [0,1] n generated by the coordinate functions ξ i ,i=1, . . . ,n, with pointwise operations. Any such function (...)
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  21. Camilo Argoty (2013). The Model Theory of Modules of a C*-Algebra. Archive for Mathematical Logic 52 (5-6):525-541.score: 24.0
    We study the theory of a Hilbert space H as a module for a unital C*-algebra ${\mathcal{A}}$ from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are elementary equivalent to it. Also, we show that this theory has quantifier elimination and we characterize the model companion of the incomplete theory of all non-degenerate representations of ${\mathcal{A}}$ . Finally, we show that there is an (...)
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  22. 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: 24.0
    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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  23. Ivo Düntsch & Sanjiang Li (2013). On the Homogeneous Countable Boolean Contact Algebra. Logic and Logical Philosophy 22 (2):213-251.score: 24.0
    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 the (...)
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  24. J. Donald Monk (2001). The Spectrum of Partitions of a Boolean Algebra. Archive for Mathematical Logic 40 (4):243-254.score: 24.0
    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 maximal (...)
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  25. Gido Scharfenberger-Fabian (2011). Souslin Algebra Embeddings. Archive for Mathematical Logic 50 (1-2):75-113.score: 24.0
    A Souslin algebra is a complete Boolean algebra whose main features are ruled by a tight combination of an antichain condition with an infinite distributive law. The present article divides into two parts. In the first part a representation theory for the complete and atomless subalgebras of Souslin algebras is established (building on ideas of Jech and Jensen). With this we obtain some basic results on the possible types of subalgebras and their interrelation. The second part begins with (...)
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  26. Matatyahu Rubin & Sabine Koppelberg (2001). A Superatomic Boolean Algebra with Few Automorphisms. Archive for Mathematical Logic 40 (2):125-129.score: 24.0
    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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  27. David J. Foulis & Sylvia Pulmannová (2010). Type-Decomposition of an Effect Algebra. Foundations of Physics 40 (9-10):1543-1565.score: 22.0
    Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets, orthomodular lattices, modular ortholattices, and boolean algebras.We study centrally orthocomplete effect algebras (COEAs), i.e., EAs satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. For COEAs, we introduce a general notion of decomposition into types; prove that a COEA factors uniquely as a (...)
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  28. Murdoch J. Gabbay (2012). Finite and Infinite Support in Nominal Algebra and Logic: Nominal Completeness Theorems for Free. Journal of Symbolic Logic 77 (3):828-852.score: 21.0
    By operations on models we show how to relate completeness with respect to permissivenominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal models, so the construction hinges on generating from an instance of the latter, some instance of the former in which sufficiently many inequalities are preserved between elements. We do this using an infinite generalisation of nominal atoms-abstraction. The results are of interest in their own right, (...)
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  29. A. F. Lavrik (ed.) (1979). Twelve Papers in Logic and Algebra. American Mathematical Society.score: 21.0
    (2) VoL ll3, l979 PROPERTIES OF SOME SUBSYSTEMS OF CLASSICAL AND INTUITIONISTIC PROPOSITIONAL CALCULI* MI SEMENENKO Preface In both classical and ...
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  30. Kenneth R. Koedinger, Martha W. Alibali & Mitchell J. Nathan (2008). Trade‐Offs Between Grounded and Abstract Representations: Evidence From Algebra Problem Solving. Cognitive Science 32 (2):366-397.score: 21.0
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  31. M. Alizadeh & M. Ardeshir (2004). On the Linear Lindenbaum Algebra of Basic Propositional Logic. Mathematical Logic Quarterly 50 (1):65.score: 21.0
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  32. Gurgen Asatryan (2008). On Models of Exponentiation. Identities in the HSI-Algebra of Posets. Mathematical Logic Quarterly 54 (3):280-287.score: 21.0
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  33. L. P. Belluce, Antonio Di Nola & Salvatore Sessa (1994). The Prime Spectrum of an MV‐Algebra. Mathematical Logic Quarterly 40 (3):331-346.score: 21.0
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  34. Cheryl C. Graesser & Norman H. Anderson (1974). Cognitive Algebra of the Equation: Gift Size = Generosity = Income. Journal of Experimental Psychology 103 (4):692.score: 21.0
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  35. Hirokazu Nishimura (1994). Boolean Valued and Stone Algebra Valued Measure Theories. Mathematical Logic Quarterly 40 (1):69-75.score: 21.0
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  36. Yunfu Shen (1999). Elimination of Algorithmic Quantifiers for Ordered Differential Algebra. Archive for Mathematical Logic 38 (3):139-144.score: 21.0
    In [2], Singer proved that the theory of ordered differential fields has a model completion, i.e, the theory of closed ordered differential fields, CODF. As a result, CODF admits elimination of quantifiers. In this paper we give an algorithm to eliminate the quantifiers of CODF-formulas.
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  37. Thomas Mormann, The Contact Algebra of the Euclidean Plane has Infinitely Many Elements.score: 20.0
    Abstract. Let REL(O*E) be the relation algebra of binary relations defined on the Boolean algebra O*E of regular open regions of the Euclidean plane E. The aim of this paper is to prove that the canonical contact relation C of O*E generates a subalgebra REL(O*E, C) of REL(O*E) that has infinitely many elements. More precisely, REL(O*,C) contains an infinite family {SPPn, n ≥ 1} of relations generated by the relation SPP (Separable Proper Part). This relation can be used (...)
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  38. Jean-Yves Béziau (2003). Logic May Be Simple. Logic, Congruence and Algebra. Logic and Logical Philosophy 5:129-147.score: 20.0
    This paper is an attempt to clear some philosophical questions about the nature of logic by setting up a mathematical framework. The notion of congruence in logic is defined. A logical structure in which there is no non-trivial congruence relation, like some paraconsistent logics, is called simple. The relations between simplicity, the replacement theorem and algebraization of logic are studied (including MacLane-Curry’s theorem and a discussion about Curry’s algebras). We also examine how these concepts are related to such notions as (...)
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  39. James Cummings & Saharon Shelah (1995). A Model in Which Every Boolean Algebra has Many Subalgebras. Journal of Symbolic Logic 60 (3):992-1004.score: 20.0
    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 is intended (...)
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  40. Ladislav Kvasz (2006). The History of Algebra and the Development of the Form of its Language. Philosophia Mathematica 14 (3):287-317.score: 18.0
    This paper offers an epistemological reconstruction of the historical development of algebra from al-Khwrizm, Cardano, and Descartes to <span class='Hi'>Euler</span>, Lagrange, and Galois. In the reconstruction it interprets the algebraic formulas as a symbolic language and analyzes the changes of this language in the course of history. It turns out that the most fundamental epistemological changes in the development of algebra can be interpreted as changes of the pictorial form (in the sense of Wittgenstein's Tractatus) of the symbolic (...)
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  41. Sergiy Melnyk, ALGEBRA OF FUNDAMENTAL MEASUREMENTS AS A BASIS OF DYNAMICS OF ECONOMIC SYSTEMS. arXiv.score: 18.0
    We propose an axiomatic approach to constructing the dynamics of systems, in which one the main elements 9e8 is the consciousness of a subject. The main axiom is the statements that the state of consciousness is completely determined by the results of measurements performed on it. In case of economic systems we propose to consider an offer of transaction as a fundamental measurement. Transactions with delayed choice, discussed in this paper, represent a logical generalization of incomplete transactions and allow for (...)
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  42. K. Britz (1999). A Power Algebra for Theory Change. Journal of Logic, Language and Information 8 (4):429-443.score: 18.0
    Various representation results have been established for logics of belief revision, in terms of remainder sets, epistemic entrenchment, systems of spheres and so on. In this paper I present another representation for logics of belief revision, as an algebra of theories. I show that an algebra of theories, enriched with a set of rejection operations, provides a suitable algebraic framework to characterize the theory change operations of systems of belief revision. The theory change operations arise as power operations (...)
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  43. Mark Sharlow, Generalizing the Algebra of Physical Quantities.score: 18.0
    In this paper, I define and study an abstract algebraic structure, the dimensive algebra, which embodies the most general features of the algebra of dimensional physical quantities. I prove some elementary results about dimensive algebras and suggest some directions for future work.
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  44. Matej Pavšič (2001). Clifford-Algebra Based Polydimensional Relativity and Relativistic Dynamics. Foundations of Physics 31 (8):1185-1209.score: 18.0
    Starting from the geometric calculus based on Clifford algebra, the idea that physical quantities are Clifford aggregates (“polyvectors”) is explored. A generalized point particle action (“polyvector action”) is proposed. It is shown that the polyvector action, because of the presence of a scalar (more precisely a pseudoscalar) variable, can be reduced to the well known, unconstrained, Stueckelberg action which involves an invariant evolution parameter. It is pointed out that, starting from a different direction, DeWitt and Rovelli postulated the existence (...)
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  45. B. Tom King (1995). An Einstein Addition Law for Nonparallel Boosts Using the Geometric Algebra of Space-Time. Foundations of Physics 25 (12):1741-1755.score: 18.0
    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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  46. F. Sommen & N. Van Acker (1993). SO(M)-Invariant Differential Operators on Clifford Algebra-Valued Functions. Foundations of Physics 23 (11):1491-1519.score: 18.0
    In this paper we consider the algebra of differential operators with polynomial coefficients acting on Clifford algebra-valued functions from both sides. We characterize the subalgebra of SO(m)-invariant differential operators, which itself contains the subalgebra of GL(m)-invariant differential operators.
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  47. Amr M. Shaarawi (2000). Clifford Algebra Formulation of an Electromagnetic Charge-Current Wave Theory. Foundations of Physics 30 (11):1911-1941.score: 18.0
    In this work, a Clifford algebra approach is used to introduce a charge-current wave structure governed by a Maxwell-like set of equations. A known spinor representation of the electromagnetic field intensities is utilized to recast the equations governing the charge-current densities in a Dirac-like spinor form. Energy-momentum considerations lead to a generalization of the Maxwell electromagnetic symmetric energy-momentum tensor. The generalized tensor includes new terms that represent contributions from the charge-current densities. Stationary spherical modal solutions representing the charge-current densities (...)
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  48. Harvey Friedman, A Consistency Proof for Elementary Algebra and Geometry.score: 18.0
    We give a consistency proof within a weak fragment of arithmetic of elementary algebra and geometry. For this purpose, we use EFA (exponential function arithmetic), and various first order theories of algebraically closed fields and real closed fields.
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  49. Janet Folina (2012). Newton and Hamilton: In Defense of Truth in Algebra. Southern Journal of Philosophy 50 (3):504-527.score: 18.0
    Although it is clear that Sir William Rowan Hamilton supported a Kantian account of algebra, I argue that there is an important sense in which Hamilton's philosophy of mathematics can be situated in the Newtonian tradition. Drawing from both Niccolo Guicciardini's (2009) and Stephen Gaukroger's (2010) readings of the Newton–Leibniz controversy over the calculus, I aim to show that the very epistemic ideals that underpin Newton's argument for the superiority of geometry over algebra also motivate Hamilton's philosophy of (...)
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