Results for 'Clifford spaces'

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  1. Lectures and Essays by the Late William Kingdon Clifford, F.R.S.William Kingdon Clifford, Leslie Stephen & Frederick Pollock - 1918 - Watts & Co.
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  2.  60
    The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification.Carlos Castro - 2005 - Foundations of Physics 35 (6):971-1041.
    We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upperR and lower length λ scales. The invariance symmetry leads naturally to the real Clifford algebra Cl and complexified Clifford ClC algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document}. Previous work led (...)
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  3.  44
    On Clifford Space Relativity, Black Hole Entropy, Rainbow Metrics, Generalized Dispersion and Uncertainty Relations.Carlos Castro - 2014 - Foundations of Physics 44 (9):990-1008.
    An analysis of some of the applications of Clifford space relativity to the physics behind the modified black hole entropy-area relations, rainbow metrics, generalized dispersion and minimal length stringy uncertainty relations is presented.
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  4.  24
    On Superluminal Particles and the Extended Relativity Theories.Carlos Castro - 2012 - Foundations of Physics 42 (9):1135-1152.
    Superluminal particles are studied within the framework of the Extended Relativity theory in Clifford spaces (C-spaces). In the simplest scenario, it is found that it is the contribution of the Clifford scalar component π of the poly-vector-valued momentum which is responsible for the superluminal behavior in ordinary spacetime due to the fact that the effective mass $\mathcal{M} = \sqrt{ M^{2} - \pi^{2} }$ is imaginary (tachyonic). However, from the point of view of C-space, there is no (...)
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  5.  93
    The Emergence of a Kaluza-Klein Microgenometry From the Invariants of Optimally Euclidean Lorentzian Spaces.José G. Vargas & Douglas G. Torr - 1997 - Foundations of Physics 27 (4):533-558.
    It is shown that relativistic spacetimes can be viewed as Finslerian spaces endowed with a positive definite distance rather than as pariah, pseudo-Riemannian spaces. Since the pursuit of better implementations of “Euclidicity in the small” advocates absolute parallelism, teleparallel nonlinear Euclidean connections are scrutinized.The fact that is the set of horizontal fundamental 1-forms in the Finslerian fibration implies that it can be used in principle for obtainingcompatible new structures. If the connection is teleparallel, a Kaluza-Klein space indeed emerges (...)
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  6.  6
    Russell, Clifford, Whitehead and Differential Geometry.Sylvia Nickerson & Nicholas Griffin - 2008 - Russell: The Journal of Bertrand Russell Studies 28 (1).
    When Russell was fifteen, he was given a copy of W.K. Clifford’s The Common Sense of the Exact Sciences . Russell later recalled reading it immediately “with passionate interest and with an intoxicating delight in intellectual clarification”. Why then, when Russell wrote An Essay on the Foundations of Geometry , did he choose to defend spaces of homogeneous curvature as a priori? Why was he almost completely silent thereafter on the subject of Clifford, and his writings on (...)
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  7.  1
    Conceptual Spaces, Generalisation Probabilities and Perceptual Categorisation.Nina Poth - 2019 - In Peter Gärdenfors, Antti Hautamäki, Frank Zenker & Mauri Kaipainen (eds.), Conceptual Spaces: Elaborations and Applications. Springer Verlag.
    Shepard’s (1987) universal law of generalisation (ULG) illustrates that an invariant gradient of generalisation across species and across stimuli conditions can be obtained by mapping the probability of a generalisation response onto the representations of similarity between individual stimuli. Tenenbaum and Griffiths (2001) Bayesian account of generalisation expands ULG towards generalisation from multiple examples. Though the Bayesian model starts from Shepard’s account it refrains from any commitment to the notion of psychological similarity to explain categorisation. This chapter presents the conceptual (...)
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  8. Vagueness: A Conceptual Spaces Approach.Igor Douven, Lieven Decock, Richard Dietz & Paul Égré - 2013 - Journal of Philosophical Logic 42 (1):137-160.
    The conceptual spaces approach has recently emerged as a novel account of concepts. Its guiding idea is that concepts can be represented geometrically, by means of metrical spaces. While it is generally recognized that many of our concepts are vague, the question of how to model vagueness in the conceptual spaces approach has not been addressed so far, even though the answer is far from straightforward. The present paper aims to fill this lacuna.
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  9. Clifford, William Kingdom.Luis R. G. Oliveira - forthcoming - In Stewart Goetz & Charles Taliaferro (eds.), Encyclopedia of the Philosophy of Religion. Wiley-Blackwell.
    W.K. Clifford’s famous 1876 essay The Ethics of Belief contains one of the most memorable lines in the history of philosophy: "it is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence." The challenge to religious belief stemming from this moralized version of evidentialism is still widely discussed today.
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  10. Theory Change as Dimensional Change: Conceptual Spaces Applied to the Dynamics of Empirical Theories.Peter Gärdenfors & Frank Zenker - 2013 - Synthese 190 (6):1039-1058.
    This paper offers a novel way of reconstructing conceptual change in empirical theories. Changes occur in terms of the structure of the dimensions—that is to say, the conceptual spaces—underlying the conceptual framework within which a given theory is formulated. Five types of changes are identified: (1) addition or deletion of special laws, (2) change in scale or metric, (3) change in the importance of dimensions, (4) change in the separability of dimensions, and (5) addition or deletion of dimensions. Given (...)
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  11. Conceptual Spaces for Cognitive Architectures: A Lingua Franca for Different Levels of Representation.Antonio Lieto, Antonio Chella & Marcello Frixione - 2017 - Biologically Inspired Cognitive Architectures 19:1-9.
    During the last decades, many cognitive architectures (CAs) have been realized adopting different assumptions about the organization and the representation of their knowledge level. Some of them (e.g. SOAR [35]) adopt a classical symbolic approach, some (e.g. LEABRA[ 48]) are based on a purely connectionist model, while others (e.g. CLARION [59]) adopt a hybrid approach combining connectionist and symbolic representational levels. Additionally, some attempts (e.g. biSOAR) trying to extend the representational capacities of CAs by integrating diagrammatical representations and reasoning are (...)
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  12. Meaning Vs. Power: Are Thick Description and Power Analysis Intrinsically at Odds? Response to Interpretation, Explanation, and Clifford Geertz.Jason A. Springs - 2012 - Religion Compass 6 (12):534-542.
    This essay clarifies and defends the methodological multidimensionality and improvisational character of Clifford Geertz’s account of interpretation and explanation. In contrast to accounts of power analysis offered by Michel Foucault and Talal Asad, I argue that Geertz’s work can simultaneously attend to meaning, power, identity, and experience in understanding and assessing religious practices and cultural formations.
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  13.  29
    A Case Against Convexity in Conceptual Spaces.José V. Hernández-Conde - 2017 - Synthese 194 (10):4011-4037.
    The notion of conceptual space, proposed by Gärdenfors as a framework for the representation of concepts and knowledge, has been highly influential over the last decade or so. One of the main theses involved in this approach is that the conceptual regions associated with properties, concepts, verbs, etc. are convex. The aim of this paper is to show that such a constraint—that of the convexity of the geometry of conceptual regions—is problematic; both from a theoretical perspective and with regard to (...)
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  14.  93
    Semantics, Conceptual Spaces, and the Meeting of Minds.Massimo Warglien & Peter Gärdenfors - 2013 - Synthese 190 (12):2165-2193.
    We present an account of semantics that is not construed as a mapping of language to the world but rather as a mapping between individual meaning spaces. The meanings of linguistic entities are established via a “meeting of minds.” The concepts in the minds of communicating individuals are modeled as convex regions in conceptual spaces. We outline a mathematical framework, based on fixpoints in continuous mappings between conceptual spaces, that can be used to model such a semantics. (...)
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  15.  8
    Kant, the Practical Postulates, and Clifford.Samuel J. M. Kahn - forthcoming - Contemporary Pragmatism 17 (1).
    In this paper I argue that Kant would have endorsed Clifford’s principle. The paper is divided into four sections. In the first, I review Kant’s argument for the practical postulates. In the second, I discuss a traditional objection to the style of argument Kant employs. In the third, I explain how Kant would respond to this objection and how this renders the practical postulates consistent with Clifford’s principle. In the fourth, I introduce positive grounds for thinking that Kant (...)
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  16.  93
    Prototypes, Poles, and Topological Tessellations of Conceptual Spaces.Thomas Mormann - manuscript
    The aim of this paper is to present a general method for constructing natural tessellations of conceptual spaces that is based on their topological structure. This method works for a class of spaces that was defined some 80 years ago by the Russian mathematician Pavel Alexandroff. Alexandroff spaces, as they are called today, are distinguished from other topological spaces by the fact that they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, (...)
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  17. Squares of Oppositions, Commutative Diagrams, and Galois Connections for Topological Spaces and Similarity Structures.Thomas Mormann - manuscript
    The aim of this paper is to elucidate the relationship between Aristotelian conceptual oppositions, commutative diagrams of relational structures, and Galois connections.This is done by investigating in detail some examples of Aristotelian conceptual oppositions arising from topological spaces and similarity structures. The main technical device for this endeavor is the notion of Galois connections of order structures.
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  18.  23
    Understanding Predication in Conceptual Spaces.Daniele Porello & Claudio Masolo - 2016 - In Roberta Ferrario & Werner Kuhn (eds.), Formal Ontology in Information Systems. Proceedings of the Ninth International Conference (FOIS 2016). pp. 139--152.
    We argue that a cognitive semantics has to take into account the possibly partial information that a cognitive agent has of the world. After discussing Gärdenfors's view of objects in conceptual spaces, we offer a number of viable treatments of partiality of information and we formalize them by means of alternative predicative logics. Our analysis shows that understanding the nature of simple predicative sentences is crucial for a cognitive semantics.
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  19.  28
    Locative and Directional Prepositions in Conceptual Spaces: The Role of Polar Convexity.Joost Zwarts & Peter Gärdenfors - 2016 - Journal of Logic, Language and Information 25 (1):109-138.
    We approach the semantics of prepositions from the perspective of conceptual spaces. Focusing on purely spatial locative and directional prepositions, we analyze both types of prepositions in terms of polar coordinates instead of Cartesian coordinates. This makes it possible to demonstrate that the property of convexity holds quite generally in the domain of prepositions of location and direction, supporting the important role that this property plays in conceptual spaces.
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  20.  11
    Changing Types: Information Dynamics for Qualitative Type Spaces.Dominik Klein & Eric Pacuit - 2014 - Studia Logica 102 (2):297-319.
    Many different approaches to describing the players’ knowledge and beliefs can be found in the literature on the epistemic foundations of game theory. We focus here on non-probabilistic approaches. The two most prominent are the so-called Kripkeor Aumann- structures and knowledge structures (non-probabilistic variants of Harsanyi type spaces). Much of the recent work on Kripke structures has focused on dynamic extensions and simple ways of incorporating these. We argue that many of these ideas can be applied to knowledge structures (...)
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  21.  38
    Topometric Spaces and Perturbations of Metric Structures.Itaï Ben Yaacov - 2008 - Logic and Analysis 1 (3-4):235-272.
    We develop the general theory of topometric spaces, i.e., topological spaces equipped with a well-behaved lower semi-continuous metric. Spaces of global and local types in continuous logic are the motivating examples for the study of such spaces. In particular, we develop Cantor-Bendixson analysis of topometric spaces, which can serve as a basis for the study of local stability (extending the ad hoc development in Ben Yaacov I and Usvyatsov A, Continuous first order logic and local (...)
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  22.  61
    Clifford Space as the Arena for Physics.Matej Pavšsič - 2003 - Foundations of Physics 33 (9):1277-1306.
    A new theory is considered according to which extended objects in n-dimensional space are described in terms of multivector coordinates which are interpreted as generalizing the concept of center of mass coordinates. While the usual center of mass is a point, by generalizing the latter concept, we associate with every extended object a set of r-loops, r=0,1,...,n−1, enclosing oriented (r+1)-dimensional surfaces represented by Clifford numbers called (r+1)-vectors or multivectors. Superpositions of multivectors are called polyvectors or Clifford aggregates and (...)
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  23.  67
    Axiomatization of Local-Global Principles for Pp-Formulas in Spaces of Orderings.Vincent Astier & Marcus Tressl - 2004 - Archive for Mathematical Logic 44 (1):77-95.
    .We use a model theoretic approach to investigate properties of local-global principles for positive primitive formulas in spaces of orderings, such as the existence of bounds and the axiomatizability of local-global principles. As a consequence we obtain various classes of special groups satisfying local-global principles for all positive primitive formulas, and we show that local-global principles are preserved by some natural constructions in special groups.
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  24.  25
    Setting Up Spaces for Collaboration in Industry Between Researchers From the Natural and Social Sciences.Steven M. Flipse, Maarten C. A. van der Sanden & Patricia Osseweijer - 2014 - Science and Engineering Ethics 20 (1):7-22.
    Policy makers call upon researchers from the natural and social sciences to collaborate for the responsible development and deployment of innovations. Collaborations are projected to enhance both the technical quality of innovations, and the extent to which relevant social and ethical considerations are integrated into their development. This could make these innovations more socially robust and responsible, particularly in new and emerging scientific and technological fields, such as synthetic biology and nanotechnology. Some researchers from both fields have embarked on collaborative (...)
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  25.  60
    Clifford Algebras and the Dirac-Bohm Quantum Hamilton-Jacobi Equation.B. J. Hiley & R. E. Callaghan - 2012 - Foundations of Physics 42 (1):192-208.
    In this paper we show how the dynamics of the Schrödinger, Pauli and Dirac particles can be described in a hierarchy of Clifford algebras, ${\mathcal{C}}_{1,3}, {\mathcal{C}}_{3,0}$ , and ${\mathcal{C}}_{0,1}$ . Information normally carried by the wave function is encoded in elements of a minimal left ideal, so that all the physical information appears within the algebra itself. The state of the quantum process can be completely characterised by algebraic invariants of the first and second kind. The latter enables us (...)
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  26. Born’s Reciprocal Gravity in Curved Phase-Spaces and the Cosmological Constant.Carlos Castro - 2012 - Foundations of Physics 42 (8):1031-1055.
    The main features of how to build a Born’s Reciprocal Gravitational theory in curved phase-spaces are developed. By recurring to the nonlinear connection formalism of Finsler geometry a generalized gravitational action in the 8D cotangent space (curved phase space) can be constructed involving sums of 5 distinct types of torsion squared terms and 2 distinct curvature scalars ${\mathcal{R}}, {\mathcal{S}}$ which are associated with the curvature in the horizontal and vertical spaces, respectively. A Kaluza-Klein-like approach to the construction of (...)
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  27.  42
    Exotic Smoothness and Noncommutative Spaces. The Model-Theoretical Approach.Jerzy Król - 2004 - Foundations of Physics 34 (5):843-869.
    We give an almost explicit presentation of exotic functions corresponding to some exotic smooth structure on topologically trivial R4. The construction relies on the model-theoretic tools from the previous paper. We can formulate unexpected, yet direct connection between ‘‘localized’’ exotic small R4’s and some noncommutative spaces. The formalism of QM can be interpreted in terms of exotic smooth R4’s localized in spacetime. A new way of looking at the problem of decoherence is suggested. The 4-dimensional spacetime itself has built-in (...)
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  28.  21
    Coalgebras, Chu Spaces, and Representations of Physical Systems.Samson Abramsky - 2013 - Journal of Philosophical Logic 42 (3):551-574.
    We investigate the use of coalgebra to represent quantum systems, thus providing a basis for the use of coalgebraic methods in quantum information and computation. Coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimulation and coalgebraic logic. However, the standard coalgebraic framework does not accommodate contravariance, and is too rigid to allow physical symmetries to be represented. We introduce a fibrational structure on coalgebras in which contravariance is represented by indexing. (...)
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  29.  43
    Compact and Loeb Hausdorff Spaces in Equation Image and the Axiom of Choice for Families of Finite Sets.Kyriakos Keremedis - 2012 - Mathematical Logic Quarterly 58 (3):130-138.
    Given a set X, equation image denotes the statement: “equation image has a choice set” and equation image denotes the family of all closed subsets of the topological space equation image whose definition depends on a finite subset of X. We study the interrelations between the statements equation image equation image equation image equation image and “equation imagehas a choice set”. We show: equation image iff equation image iff equation image has a choice set iff equation image. equation image iff (...)
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  30.  56
    Big Toy Models: Representing Physical Systems as Chu Spaces.Samson Abramsky - 2012 - Synthese 186 (3):697 - 718.
    We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, we aim for a 'big toy model', in which both quantum and classical systems can be faithfully represented—as well as, possibly, more exotic kinds of systems. To this end, we show how Chu spaces (...)
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  31.  76
    Gδ‐Pieces of Canonical Partitions of G‐Spaces.Barbara Majcher-Iwanow - 2005 - Mathematical Logic Quarterly 51 (5):450-461.
    Generalizing model companions from model theory we define companions of pieces of canonical partitions of Polish G-spaces. This unifies several constructions from logic. The central problem of the paper is the existence of companions which form a G-orbit which is a Gδ-set. We describe companions of some typical G-spaces.
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  32.  15
    On Countable Choice and Sequential Spaces.Gonçalo Gutierres - 2008 - Mathematical Logic Quarterly 54 (2):145-152.
    Under the axiom of choice, every first countable space is a Fréchet-Urysohn space. Although, in its absence even ℝ may fail to be a sequential space.Our goal in this paper is to discuss under which set-theoretic conditions some topological classes, such as the first countable spaces, the metric spaces, or the subspaces of ℝ, are classes of Fréchet-Urysohn or sequential spaces.In this context, it is seen that there are metric spaces which are not sequential spaces. (...)
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  33.  16
    Reduced Coproducts of Compact Hausdorff Spaces.Paul Bankston - 1987 - Journal of Symbolic Logic 52 (2):404-424.
    By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems (...)
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  34. A Re-Evaluation of Clifford and His Critics.Brian Zamulinski - 2002 - Southern Journal of Philosophy 40 (3):437-457.
    This paper re-evaluates W.K. Clifford on the ethics of belief in light of criticism due to William James and replies to James from David A. Hollinger.
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  35.  33
    The (Un)Bearable Educational Lightness of Common Practices: On the Use of Urban Spaces by Schoolchildren.Elisabete Xavier Gomes - 2012 - Studies in Philosophy and Education 31 (3):289-302.
    The present paper is about the author’s current research on children’s education in urban contexts. It departs from the rising offer of programmes for school children in out-of-school contexts (e.g. museums, libraries, science centres). It asks what makes these practices educational (and not just interesting, entertaining and/or audience building). Based on Biesta ( 2006a , 2010 ) theory of education, the author frames and analyses the educational characteristics of, and possibilities of articulating, in and out-of-school educational practices. This paper aims (...)
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  36.  25
    Imaginaries in Hilbert Spaces.Itay Ben-Yaacov & Alexander Berenstein - 2003 - Archive for Mathematical Logic 43 (4):459-466.
    We characterise imaginaries (up to interdefinability) in Hilbert spaces using a Galois theory for compact unitary groups.
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  37.  20
    The (Un) Bearable Educational Lightness of Common Practices: On the Use of Urban Spaces by Schoolchildren.Elisabete Xavier Gomes - 2012 - Studies in Philosophy and Education 31 (3):289-302.
    The present paper is about the author’s current research on children’s education in urban contexts. It departs from the rising offer of programmes for school children in out-of-school contexts (e.g. museums, libraries, science centres). It asks what makes these practices educational (and not just interesting, entertaining and/or audience building). Based on Biesta (2006a, 2010) theory of education, the author frames and analyses the educational characteristics of, and possibilities of articulating, in and out-of-school educational practices. This paper aims at understanding if (...)
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  38.  47
    Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings. [REVIEW]Matej Pavšič - 2005 - Foundations of Physics 35 (9):1617-1642.
    The idea that spacetime has to be replaced by Clifford space (C-space) is explored. Quantum field theory (QFT) and string theory are generalized to C-space. It is shown how one can solve the cosmological constant problem and formulate string theory without central terms in the Virasoro algebra by exploiting the peculiar pseudo-Euclidean signature of C-space and the Jackiw definition of the vacuum state. As an introduction into the subject, a toy model of the harmonic oscillator in pseudo-Euclidean space is (...)
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  39.  58
    Teleparallel Kähler Calculus for Spacetime.Jose G. Vargas & Douglas G. Torr - 1998 - Foundations of Physics 28 (6):931-958.
    In a recent paper [J. G. Vargas and D. G. Torr, Found. Phys. 27, 599 (1997)], we have shown that a subset of the differential invariants that define teleparallel connections in spacetime generates a teleparallel Kaluza-Klein space (KKS) endowed with a very rich Clifford structure. A canonical Dirac equation hidden in this structure might be uncovered with the help of a teleparallel Kähler calculus in KKS. To bridge the gap to such a calculus from the existing Riemannian Kähler calculus (...)
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  40.  18
    From the Geometry of Pure Spinors with Their Division Algebras to Fermion Physics.Paolo Budinich - 2002 - Foundations of Physics 32 (9):1347-1398.
    The Cartan equations defining simple spinors (renamed “pure” by C. Chevalley) are interpreted as equations of motion in compact momentum spaces, in a constructive approach in which at each step the dimensions of spinor space are doubled while those of momentum space increased by two. The construction is possible only in the frame of the geometry of simple or pure spinors, which imposes contraint equations on spinors with more than four components, and then momentum spaces result compact, isomorphic (...)
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  41.  41
    Products of Compact Spaces and the Axiom of Choice II.Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin - 2003 - Mathematical Logic Quarterly 49 (1):57-71.
    This is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces . We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products.
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  42.  13
    Model-Theory of Vector-Spaces Over Unspecified Fields.David Pierce - 2009 - Archive for Mathematical Logic 48 (5):421-436.
    Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector spaces over algebraically closed (...)
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  43.  70
    Clifford Algebras in Symplectic Geometry and Quantum Mechanics.Ernst Binz, Maurice A. de Gosson & Basil J. Hiley - 2013 - Foundations of Physics 43 (4):424-439.
    The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C 0,2 . This algebra is essentially the geometric algebra describing the rotational properties of space. Hidden within this algebra are symplectic structures with Heisenberg algebras at their core. This algebra also enables us to define a Poisson algebra of all homogeneous quadratic polynomials on a two-dimensional sub-space, $\mathbb{F}^{a}$ of the Euclidean three-space. (...)
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  44.  19
    Computing the Complexity of the Relation of Isometry Between Separable Banach Spaces.Julien Melleray - 2007 - Mathematical Logic Quarterly 53 (2):128-131.
    We compute here the Borel complexity of the relation of isometry between separable Banach spaces, using results of Gao, Kechris [2], Mayer-Wolf [5], and Weaver [8]. We show that this relation is Borel bireducible to the universal relation for Borel actions of Polish groups. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim).
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  45.  5
    Shared Spaces, Shared Mind: Connecting Past and Present Viewpoints in American Sign Language Narratives.Terry Janzen - 2019 - Cognitive Linguistics 30 (2):253-279.
    In American Sign Language narratives, signers map conceptualized spaces onto actual spaces around them that can reflect physical, conceptual, and metaphorical relations among entities. Because verb tenses are not attested in ASL, a question arises: How does a signer distinguish utterances about past events from utterances within a present conversational context? In narratives, the story-teller’s past-event utterances move the story along; accompanying these will often be subjective comments on the story, evaluative statements, and the like, that are geared, (...)
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  46.  59
    Direct Product and Decomposition of Certain Physically Important Algebras.Robert W. Johnson - 1996 - Foundations of Physics 26 (2):197-222.
    I consider the direct product algebra formed from two isomorphic Clifford algebras. More specifically, for an element x in each of the two component algebras I consider elements in the direct product space with the form x ⊗ x. I show how this construction can be used to model the algebraic structure of particular vector spaces with metric, to describe the relationship between wavefunction and observable in examples from quantum mechanics, and to express the relationship between the electromagnetic (...)
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  47.  22
    The Charge–Mass–Spin Relation of Clifford Polyparticles, Kerr–Newman Black Holes and the Fine Structure Constant.Carlos Castro - 2004 - Foundations of Physics 34 (7):1091-1113.
    A Clifford-algebraic interpretation is proposed of the charge, mass, spin relationship found recently by Cooperstock and Faraoini, which was based on the Kerr–Newman metric solutions of the Einstein–Maxwell equations. The components of the polymomentum associated with a Clifford polyparticle in four dimensions provide for such a charge, mass, spin relationship without the problems encountered in Kaluza–Klein compactifications which furnish an unphysically large value for the electron charge. A physical reasoning behind such charge, mass, spin relationship is provided, followed (...)
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  48.  58
    Killing Symmetries of Generalized Minkowski Spaces. Part 2: Finite Structure of Space—Time Rotation Groups in Four Dimensions.Fabio Cardone, Alessio Marrani & Roberto Mignani - 2004 - Foundations of Physics 34 (8):1155-1201.
    In this paper, we continue the study of the Killing symmetries of an N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the finite structure of the space–time rotations in such spaces, by confining ourselves to the four-dimensional case. In particular, the results obtained are specialized to the case of a “deformed” Minkowski space M_4, for which we derive the explicit general form of (...)
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  49.  60
    Extended Scale Relativity, P-Loop Harmonic Oscillator, and Logarithmic Corrections to the Black Hole Entropy.Carlos Castro & Alex Granik - 2003 - Foundations of Physics 33 (3):445-466.
    An extended scale relativity theory, actively developed by one of the authors, incorporates Nottale's scale relativity principle where the Planck scale is the minimum impassible invariant scale in Nature, and the use of polyvector-valued coordinates in C-spaces (Clifford manifolds) where all lengths, areas, volumes⋅ are treated on equal footing. We study the generalization of the ordinary point-particle quantum mechanical oscillator to the p-loop (a closed p-brane) case in C-spaces. Its solution exhibits some novel features: an emergence of (...)
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  50.  34
    Dutch Books and Nonclassical Probability Spaces.Leszek Wroński & Michał Tomasz Godziszewski - 2017 - European Journal for Philosophy of Science 7 (2):267-284.
    We investigate how Dutch Book considerations can be conducted in the context of two classes of nonclassical probability spaces used in philosophy of physics. In particular we show that a recent proposal by B. Feintzeig to find so called “generalized probability spaces” which would not be susceptible to a Dutch Book and would not possess a classical extension is doomed to fail. Noting that the particular notion of a nonclassical probability space used by Feintzeig is not the most (...)
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