Search results for 'Duality' (try it on Scholar)

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  1. Yoshihiro Maruyama (2010). Fuzzy Topology and Łukasiewicz Logics From the Viewpoint of Duality Theory. Studia Logica 94 (2):245 - 269.score: 18.0
    This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Łukasiewicz n -valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n -valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the algebras of modal Łukasiewicz n -valued logic with truth constants, which generalizes Jónsson-Tarski (...) for modal algebras to the n -valued case via fuzzy topology. We emphasize that fuzzy topological spaces naturally arise as spectrums of algebras of many-valued logics. (shrink)
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  2. Jonathan Bentwich (2006). The Duality Principle: Irreducibility of Sub-Threshold Psychophysical Computation to Neuronal Brain Activation. Synthese 153 (3):451-455.score: 18.0
    A key working hypothesis in neuroscience is ‘materialistic reductionism’, i.e., the assumption whereby all physiological, behavioral or cognitive phenomena is produced by localized neurochemical brain activation (but not vice versa). However, analysis of sub-threshold Weber’s psychophysical stimulation indicates its computational irreducibility to the direct interaction between psychophysical stimulation and any neuron/s. This is because the materialistic-reductionistic working hypothesis assumes that the determination of the existence or non-existence of any psychophysical stimulation [s] may only be determined through its direct interaction [di1] (...)
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  3. Steven S. Gubser (2013). The Gauge-String Duality and Heavy Ion Collisions. Foundations of Physics 43 (1):140-155.score: 18.0
    I review at a non-technical level the use of the gauge-string duality to study aspects of heavy ion collisions, with special emphasis on the trailing string calculation of heavy quark energy loss. I include some brief speculations on how variants of the trailing string construction could provide a toy model of black hole formation and evaporation. This essay is an invited contribution to “Forty Years of String Theory” and is aimed at philosophers and historians of science as well as (...)
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  4. Guram Bezhanishvili & Ramon Jansana (2011). Priestley Style Duality for Distributive Meet-Semilattices. Studia Logica 98 (1-2):83-122.score: 18.0
    We generalize Priestley duality for distributive lattices to a duality for distributive meet-semilattices. On the one hand, our generalized Priestley spaces are easier to work with than Celani’s DS-spaces, and are similar to Hansoul’s Priestley structures. On the other hand, our generalized Priestley morphisms are similar to Celani’s meet-relations and are more general than Hansoul’s morphisms. As a result, our duality extends Hansoul’s duality and is an improvement of Celani’s duality.
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  5. A. Jung & U. Rivieccio (2012). Priestley Duality for Bilattices. Studia Logica 100 (1-2):223-252.score: 18.0
    We develop a Priestley-style duality theory for different classes of algebras having a bilattice reduct. A similar investigation has already been realized by B. Mobasher, D. Pigozzi, G. Slutzki and G. Voutsadakis, but only from an abstract category-theoretic point of view. In the present work we are instead interested in a concrete study of the topological spaces that correspond to bilattices and some related algebras that are obtained through expansions of the algebraic language.
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  6. Roland Puccetti (1981). The Case for Mental Duality: Evidence From Split-Brain Data and Other Considerations. Behavioral and Brain Sciences 4 (1):93-123.score: 18.0
    Contrary to received opinion among philosophers, psychologists, and neuroscientists, conscious duality as a principle of brain organization is neither incoherent nor demonstrably false. The present paper begins by reviewing the history of the theory and its anatomical basis and defending it against the claim that it rests upon an arbitrary decision as to what constitutes the biological substratum of mind or person.
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  7. Martin Land (2005). Duality in Off-Shell Electromagnetism. Foundations of Physics 35 (7):1245-1262.score: 18.0
    In this paper, we examine the Dirac monopole in the framework of Off-Shell Electromagnetism, the five-dimensional U(1) gauge theory associated with Stueckelberg–Schrodinger relativistic quantum theory. After reviewing the Dirac model in four dimensions, we show that the structure of the five-dimensional theory prevents a natural generaliza tion of the Dirac monopole, since the theory is not symmetric under duality transforma tions. It is shown that the duality symmetry can be restored by generalizing the electromagnetic field strength to an (...)
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  8. B. A. Davey, M. Haviar & H. A. Priestley (1995). The Syntax and Semantics of Entailment in Duality Theory. Journal of Symbolic Logic 60 (4):1087-1114.score: 18.0
    Both syntactic and semantic solutions are given for the entailment problem of duality theory. The test algebra theorem provides both a syntactic solution to the entailment problem in terms of primitive positive formulae and a new derivation of the corresponding result in clone theory, viz. the syntactic description of $\operatorname{Inv(Pol}(R))$ for a given set R of finitary relations on a finite set. The semantic solution to the entailment problem follows from the syntactic one, or can be given in the (...)
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  9. Sergei P. Odintsov (2010). Priestley Duality for Paraconsistent Nelson's Logic. Studia Logica 96 (1):65 - 93.score: 18.0
    The variety of N4┴ -lattices provides an algebraic semantics for the logic N4┴, a version of Nelson's logic combining paraconsistent strong negation and explosive intuitionistic negation. In this paper we construct the Priestley duality for the category of N4┴-lattices and their homomorphisms. The obtained duality naturally extends the Priestley duality for Nelson algebras constructed by R. Cignoli and A. Sendlewski.
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  10. Hans Smessaert (2012). The Classical Aristotelian Hexagon Versus the Modern Duality Hexagon. Logica Universalis 6 (1-2):171-199.score: 18.0
    Peters and Westerståhl (Quantifiers in Language and Logic, 2006), and Westerståhl (New Perspectives on the Square of Opposition, 2011) draw a crucial distinction between the “classical” Aristotelian squares of opposition and the “modern” Duality squares of opposition. The classical square involves four opposition relations, whereas the modern one only involves three of them: the two horizontal connections are fundamentally distinct in the Aristotelian case (contrariety, CR vs. subcontrariety, SCR) but express the same Duality relation of internal negation (SNEG). (...)
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  11. Stevan Harnad (1982). Metaphor and Mental Duality. In Language, Mind, And Brain. Hillsdale: Erlbaum.score: 15.0
    I am going to attempt to argue, given certain premises, there are reasons, not only empirical, but also logical, for expecting a certain division of labor in the processing of information by the human brain. This division of labor consists specifically of a functional bifurcation into what may be called, to a first approximation, "verbal" and "nonverbal" modes of information- processing. That this dichotomy is not quite satisfactory, however, will be one of the principal conclusions of this chapter, for I (...)
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  12. Shahriar S. Afshar, Eduardo Flores, Keith F. McDonald & Ernst Knoesel (2007). Paradox in Wave-Particle Duality. Foundations of Physics 37 (2):295-305.score: 15.0
    We report on the simultaneous determination of complementary wave and particle aspects of light in a double-slit type “welcher-weg” experiment beyond the limitations set by Bohr’s Principle of Complementarity. Applying classical logic, we verify the presence of sharp interference in the single photon regime, while reliably maintaining the information about the particular pinhole through which each individual photon had passed. This experiment poses interesting questions on the validity of Complementarity in cases where measurements techniques that avoid Heisenberg’s uncertainty principle and (...)
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  13. Katalin Bimbó (2007). Functorial Duality for Ortholattices and de Morgan Lattices. Logica Universalis 1 (2):311-333.score: 15.0
    . Relational semantics for nonclassical logics lead straightforwardly to topological representation theorems of their algebras. Ortholattices and De Morgan lattices are reducts of the algebras of various nonclassical logics. We define three new classes of topological spaces so that the lattice categories and the corresponding categories of topological spaces turn out to be dually isomorphic. A key feature of all these topological spaces is that they are ordered relational or ordered product topologies.
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  14. Michael Washburn (1987). Human Wholeness in Light of Five Types of Psychic Duality. Zygon 22 (1):67-85.score: 15.0
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  15. A. Harrington (1985). Nineteenth-Century Ideas on Hemisphere Differences and "Duality of Mind". Behavioral and Brain Sciences 8 (4):617-660.score: 15.0
    It is widely felt that the sorts of ideas current in modern laterality and split-brain research are largely without precedent in the behavioral and brain sciences. This paper not only challenges that view, but makes a first attempt to define the relevance of older concepts and data to present research programs.
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  16. Howard Barnum, Carl Philipp Gaebler & Alexander Wilce (2013). Ensemble Steering, Weak Self-Duality, and the Structure of Probabilistic Theories. Foundations of Physics 43 (12):1411-1427.score: 15.0
    In any probabilistic theory, we say that a bipartite state ω on a composite system AB steers its marginal state ω B if, for any decomposition of ω B as a mixture ω B =∑ i p i β i of states β i on B, there exists an observable {a i } on A such that the conditional states $\omega_{B|a_{i}}$ are exactly the states β i . This is always so for pure bipartite states in quantum mechanics, a fact (...)
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  17. Miguel Pina E. Cunha, Arménio Rego & Antonino Vaccaro (2014). Organizations as Human Communities and Internal Markets: Searching for Duality. Journal of Business Ethics 120 (4):441-455.score: 15.0
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  18. Stuart Macdonald (forthcoming). The Role of the Courts in Imposing Terrorism Prevention and Investigation Measures: Normative Duality and Legal Realism. [REVIEW] Criminal Law and Philosophy:1-19.score: 15.0
    This article argues that the courts, not the Home Secretary, should be empowered to issue Terrorism Prevention and Investigation Measures (TPIMs). It explains that at the heart of the debate are three questions: whether measures like TPIMs should be viewed primarily from the perspective of security or liberty; how we should conceive the executive and the courts; and the empirical question of how these two arms of government answer these questions. The non-mechanistic nature of legal reasoning means that legal reasons (...)
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  19. I. J. Good (1968). Creativity and Duality in Perception and Recall. In Proceedings of the Iee/Npl Conference on Pattern Recognition No. 42. Inst Elec Eng Npl.score: 15.0
     
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  20. Andrea Christofidou (2009). Self and Self-Consciousness: Aristotelian Ontology and Cartesian Duality. Philosophical Investigations 32 (2):134-162.score: 12.0
    The relationship between self-consciousness, Aristotelian ontology, and Cartesian duality is far closer than it has been thought to be. There is no valid inference either from considerations of Aristotle's hylomorphism or from the phenomenological distinction between body and living body, to the undermining of Cartesian dualism. Descartes' conception of the self as both a reasoning and willing being informs his conception of personhood; a person for Descartes is an unanalysable, integrated, self-conscious and autonomous human being. The claims that Descartes (...)
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  21. Jonathan C. Gold (2006). No Outside, No Inside: Duality, Reality and Vasubandhu's Illusory Elephant. Asian Philosophy 16 (1):1 – 38.score: 12.0
    Some of the basic terminology of Yogācāra philosophy needs reevaluation. Whereas commentaries almost universally gloss the term dvaya ('duality') with some version of the phrase grāhya grāhaka ca (lit. 'grasped and grasper', but usually translated as 'subject and object'), in fact this gloss is absent from the earliest strata. The term and its gloss are derived from separate streams of Yogācāra reasoning - one from discussions of linguistic conceptualization and the other from discussions of perception. Once we see that (...)
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  22. Jonathan Bain (2000). Against Particle/Field Duality: Asymptotic Particle States and Interpolating Fields in Interacting Qft (Or: Who's Afraid of Haag's Theorem?). [REVIEW] Erkenntnis 53 (3):375-406.score: 12.0
    This essay touches on a number of topics in philosophy of quantum field theory from the point of view of the LSZ asymptotic approach to scattering theory. First, particle/field duality is seen to be a property of free field theory and not of interacting QFT. Second, it is demonstrated how LSZ side-steps the implications of Haag's theorem. Finally, a recent argument due to Redhead (1995), Malament (1996) and Arageorgis (1995) against the concept of localized particle states is addressed. Briefly, (...)
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  23. J. L. Martin (1973). The Duality of the Present. Man and World 6 (September):293-301.score: 12.0
    A reflection upon the experience of time reveals two data : An infinitely rapid flow of nows through the present, and the unmoving everpresence of the now in which I live. This all-pervasive duality of the present is implicit in many analyses of time, including Husse'rl's, but it needs to, be made ex- plicit. Although our data are, by the nature of the case, perfectly available for our inspection, their explication is not easy (as Augustine's frustration indicates). Consequently, the (...)
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  24. Walter Wyss (1978). Duality. Foundations of Physics 8 (3-4):271-275.score: 12.0
    Starting from the study of the physical world, we develop the concept of a dual pair, Comparing dual pairs is known as duality. We show that duality is a basic mechanism for our intellectual curiosity.
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  25. Chrysafis Hartonas (1997). Duality for Lattice-Ordered Algebras and for Normal Algebraizable Logics. Studia Logica 58 (3):403-450.score: 12.0
    Part I of this paper is developed in the tradition of Stone-type dualities, where we present a new topological representation for general lattices (influenced by and abstracting over both Goldblatt's [17] and Urquhart's [46]), identifying them as the lattices of stable compact-opens of their dual Stone spaces (stability refering to a closure operator on subsets). The representation is functorial and is extended to a full duality.In part II, we consider lattice-ordered algebras (lattices with additional operators), extending the Jónsson and (...)
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  26. Guram Bezhanishvili (1999). Varieties of Monadic Heyting Algebras Part II: Duality Theory. Studia Logica 62 (1):21-48.score: 12.0
    In this paper we continue the investigation of monadic Heyting algebras which we started in [2]. Here we present the representation theorem for monadic Heyting algebras and develop the duality theory for them. As a result we obtain an adequate topological semantics for intuitionistic modal logics over MIPC along with a Kripke-type semantics for them. It is also shown the importance and the effectiveness of the duality theory for further investigation of monadic Heyting algebras and logics over MIPC.
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  27. Alasdair Urquhart (1996). Duality for Algebras of Relevant Logics. Studia Logica 56 (1-2):263 - 276.score: 12.0
    This paper defines a category of bounded distributive lattice-ordered grupoids with a left-residual operation that corresponds to a weak system in the family of relevant logics. Algebras corresponding to stronger systems are obtained by adding further postulates. A duality theoey piggy-backed on the Priestley duality theory for distributive lattices is developed for these algebras. The duality theory is then applied in providing characterizations of the dual spaces corresponding to stronger relevant logics.
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  28. Partha Ghose & Dipankar Home (1996). The Two-Prism Experiment and Wave-Particle Duality of Light. Foundations of Physics 26 (7):943-953.score: 12.0
    A number of papers on wave-particle duality has appeared since the two-prism experiment was performed by Mizobuchi and Ohtake, based on a suggestion by Ghose, Home, and Agarwal. Against this backdrop, the present paper provides further clarification of the key issues involved in the analysis of the two-prism experiment. In the process, we present an overview of wave-particle duality vis-a vis Bohr's complementarity principle.
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  29. Moshe S. Goldberg (1983). Topological Duality for Distributive Ockham Algebras. Studia Logica 42 (1):23 - 31.score: 12.0
    In this note, we give a representation of distributive Ockham algebras via natural hom-functors. In order to do this, we describe two different structures (one algebraic, and the other order-topological) on the set of subsets of the natural numbers. The topological duality previously obtained by A. Urquhart is used throughout.
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  30. Tom Grimwood (2012). The Concept of Reading: Kierkegaard, Irony, and Duality—A Response to Mark Cortes Favis. The European Legacy 17 (4):471 - 483.score: 12.0
    In a recent article in The European Legacy, Mark Cortes Favis argued that the figure of Kierkegaard expressed a tension between two aspects of writing?the Socratic and the Platonic. While Favis is correct to see a duality in Kierkegaard's writing, his article does not fully answer the problem of how we can account for our interpretation of this tension. Given that the duality within Kierkegaard's writing transgresses the boundaries of author and reader, we cannot easily circumscribe any claims (...)
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  31. Georges Hansoul (1996). Priestley Duality for Some Subalgebra Lattices. Studia Logica 56 (1-2):133 - 149.score: 12.0
    Priestley duality can be used to study subalgebras of Heyting algebras and related structures. The dual concept is that of congruence on the dual space and the congruence lattice of a Heyting space is dually isomorphic to the subalgebra lattice of the dual algebra. In this paper we continue our investigation of the congruence lattice of a Heyting space that was undertaken in [10], [8] and [12]. Our main result is a characterization of the modularity of this lattice (Theorem (...)
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  32. Viorica Sofronie-Stokkermans (2000). Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics II. Studia Logica 64 (2):151-172.score: 12.0
    The main goal of this paper is to explain the link between the algebraic models and the Kripke-style models for certain classes of propositional non-classical logics. We consider logics that are sound and complete with respect to varieties of distributive lattices with certain classes of well-behaved operators for which a Priestley-style duality holds, and present a way of constructing topological and non-topological Kripke-style models for these types of logics. Moreover, we show that, under certain additional assumptions on the variety (...)
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  33. C. Cormier-Delanoue (1995). Wave-Corpuscle Duality of Light Reconsidered. Foundations of Physics 25 (3):465-479.score: 12.0
    The old and yet unanswered question of the precise nature of light, although completely and deliberately neglected nowadays, is reexamined by several new methods, both theoretical and experimental. The wave-corpuscle duality of light then appears somewhat different, and a new hypothesis on the process of electromagnetic interaction may be proposed in an attempt to untangle the dilemma and reach a more realistic description.
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  34. N. G. Martínez (1990). The Priestley Duality for Wajsberg Algebras. Studia Logica 49 (1):31 - 46.score: 12.0
    The Priestley duality for Wajsberg algebras is developed. The Wajsberg space is a De Morgan space endowed with a family of functions that are obtained in rather natural way.As a first application of this duality, a theorem about unicity of the structure is given.
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  35. Kosta Došen (1989). Duality Between Modal Algebras and Neighbourhood Frames. Studia Logica 48 (2):219 - 234.score: 12.0
    This paper presents duality results between categories of neighbourhood frames for modal logic and categories of modal algebras (i.e. Boolean algebras with an additional unary operation). These results extend results of Goldblatt and Thomason about categories of relational frames for modal logic.
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  36. M. Gehrke & H. A. Priestley (2007). Duality for Double Quasioperator Algebras Via Their Canonical Extensions. Studia Logica 86 (1):31 - 68.score: 12.0
    This paper is a study of duality in the absence of canonicity. Specifically it concerns double quasioperator algebras, a class of distributive lattice expansions in which, coordinatewise, each operation either preserves both join and meet or reverses them. A variety of DQAs need not be canonical, but as has been shown in a companion paper, it is canonical in a generalized sense and an algebraic correspondence theorem is available. For very many varieties, canonicity (as traditionally defined) and correspondence lead (...)
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  37. Roberto Magari (1975). Representation and Duality Theory for Diagonalizable Algebras. Studia Logica 34 (4):305 - 313.score: 12.0
    The duality theory established by Halmos in [2] for boolean hemimorphism applies of course to the diagonalizable algebra, because ντν is an hemimorphism. For commodity in working on diagonalizable algebras we recall the basic facts and give the characteristic conditions on the dual of ντν.
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  38. Bruno Teheux (2007). A Duality for the Algebras of a Łukasiewicz N + 1-Valued Modal System. Studia Logica 87 (1):13 - 36.score: 12.0
    In this paper, we develop a duality for the varieties of a Łukasiewicz n + 1-valued modal System. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory...) are then derived and we propose some ideas for future research.
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  39. Silvio Ghilardi & Marek Zawadowski (1995). A Sheaf Representation and Duality for Finitely Presented Heyting Algebras. Journal of Symbolic Logic 60 (3):911-939.score: 12.0
    A. M. Pitts in [Pi] proved that HA op fp is a bi-Heyting category satisfying the Lawrence condition. We show that the embedding $\Phi: HA^\mathrm{op}_\mathrm{fp} \longrightarrow Sh(\mathbf{P_0,J_0})$ into the topos of sheaves, (P 0 is the category of finite rooted posets and open maps, J 0 the canonical topology on P 0 ) given by $H \longmapsto HA(H,\mathscr{D}(-)): \mathbf{P_0} \longrightarrow \text{Set}$ preserves the structure mentioned above, finite coproducts, and subobject classifier, it is also conservative. This whole structure on HA op (...)
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  40. Brian A. Davey & John C. Galati (2003). A Coalgebraic View of Heyting Duality. Studia Logica 75 (3):259 - 270.score: 12.0
    We give a coalgebraic view of the restricted Priestley duality between Heyting algebras and Heyting spaces. More precisely, we show that the category of Heyting spaces is isomorphic to a full subcategory of the category of all -coalgebras, based on Boolean spaces, where is the functor which maps a Boolean space to its hyperspace of nonempty closed subsets. As an appendix, we include a proof of the characterization of Heyting spaces and the morphisms between them.
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  41. Peter Ping Li (2009). The Duality of Crony Corruption in Economic Transition: Toward an Integrated Framework. [REVIEW] Journal of Business Ethics 85 (1):41 - 55.score: 12.0
    In order to shed light on the issue of crony corruption in the context of economic transition, I focus on the puzzle of China's unique experience of economic transition characterized by the duality forms and effects of crony corruption underlying local corporatism in a dual-track (i.e., market and political tracks) transition. I argue that the duality of local corporatism derives from the duality of crony corruption. First, the early form of local corporatism as state-business public alliance is (...)
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  42. Kh M. Rukhaia (1978). A Duality Theorem. Studia Logica 37 (2):157 - 159.score: 12.0
    For a sufficiently large class of formal systems a duality theorem is proved. We consider such formal set theories $\widetilde{\scr{T}}$ [2] which, at least, satisfy the following conditions: 1. The theory $\widetilde{\scr{T}}$ contains its own (either bounded or introduced by a definition) substantive constant U, for which $\vdash \forall x[x\in U]$ or $\vdash \forall x[x\subset U]$ . 2. The operation of "complement", denoted by C, is defined with respect to U. 3. For any formula (resp. a term), A ⊦ (...)
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  43. Dimiter Vakarelov (1995). A Duality Between Pawlak's Knowledge Representation Systems and Bi-Consequence Systems. Studia Logica 55 (1):205 - 228.score: 12.0
    A duality between Pawlak's knowledge representation systems and certain information systems of logical type, called bi-consequence systems is established. As an application a first-order characterization of some informational relations is given and a completeness theorem for the corresponding modal logic INF is proved. It is shown that INF possesses finite model property and hence is decidable.
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  44. Claudia B. Wegener (2002). Free Modal Lattices Via Priestley Duality. Studia Logica 70 (3):339 - 352.score: 12.0
    A Priestley duality is developed for the variety j of all modal lattices. This is achieved by restricting to j a known Priestley duality for the variety of all bounded distributive lattices with a meet-homomorphism. The variety j was first studied by R. Beazer in 1986.The dual spaces of free modal lattices are constructed, paralleling P.R. Halmos'' construction of the dual spaces of free monadic Boolean algebras and its generalization, by R. Cignoli, to distributive lattices with a quantifier.
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  45. Fabio Bellissima & Saverio Cittadini (1998). Duality and Completeness for US-Logics. Notre Dame Journal of Formal Logic 39 (2):231-242.score: 12.0
    The semantics of e-models for tense logics with binary operators for `until' and `since' (US-logics) was introduced by Bellissima and Bucalo in 1995. In this paper we show the adequacy of these semantics by proving a general Henkin-style completeness theorem. Moreover, we show that for these semantics there holds a Stone-like duality theorem with the algebraic structures that naturally arise from US-logics.
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  46. Partha Ghose & Dipankar Home (1992). Wave-Particle Duality of Single-Photon States. Foundations of Physics 22 (12):1435-1447.score: 12.0
    We review the present status of wave-particle duality of single-photon states in the context of some recent experiments. In particular, Bohr's complementarity principle is critically reexamined. It is explained in detail how this principle is confronted in these experiments and how a contradiction with the notion of “mutual exclusiveness” of classical wave and particle pictures emerges.
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  47. Brian A. Davey & Miroslav Haviar (2004). Applications of Priestley Duality in Transferring Optimal Dualities. Studia Logica 78 (1-2):213 - 236.score: 12.0
    This paper illustrates how Priestley duality can be used in the transfer of an optimal natural duality from a minimal generating algebra for a quasi-variety to other generating algebras. Detailed calculations are given for the quasi-variety of Kleene algebras and the quasi-varieties n of pseudocomplemented distributive lattices (n 1).
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  48. B. A. Davey & H. A. Priestley (2012). Canonical Extensions and Discrete Dualities for Finitely Generated Varieties of Lattice-Based Algebras. Studia Logica 100 (1-2):137-161.score: 12.0
    The paper investigates completions in the context of finitely generated lattice-based varieties of algebras. In particular the structure of canonical extensions in such a variety $${\mathcal {A}}$$ is explored, and the role of the natural extension in providing a realisation of the canonical extension is discussed. The completions considered are Boolean topological algebras with respect to the interval topology, and consequences of this feature for their structure are revealed. In addition, we call on recent results from duality theory to (...)
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  49. John Hendry (2006). The Development of Attitudes to the Wave-Particle Duality of Light and Quantum Theory, 1900–1920. Annals of Science 37 (1):59-79.score: 12.0
    (1980). The development of attitudes to the wave-particle duality of light and quantum theory, 1900–1920. Annals of Science: Vol. 37, No. 1, pp. 59-79.
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  50. Paul Koziey (2012). Beyond Duality and Polarization: Understanding Barack Obama and His Vital Act of Participation. University Press of America.score: 12.0
    Beyond Duality and Polarization explores an experience-based learning model, the Phenomenal Patterning approach for personal transformation.
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