Results for 'Duality'

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  1. Duality and Ontology.Baptiste Le Bihan & James Read - 2018 - Philosophy Compass 13 (12):e12555.
    A ‘duality’ is a formal mapping between the spaces of solutions of two empirically equivalent theories. In recent times, dualities have been found to be pervasive in string theory and quantum field theory. Naïvely interpreted, duality-related theories appear to make very different ontological claims about the world—differing in e.g. space-time structure, fundamental ontology, and mereological structure. In light of this, duality-related theories raise questions familiar from discussions of underdetermination in the philosophy of science: in the presence of (...)
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  2. Metainferential Duality.Bruno Da Ré, Federico Pailos, Damian Szmuc & Paula Teijeiro - 2020 - Journal of Applied Non-Classical Logics 30 (4):312-334.
    The aim of this article is to discuss the extent to which certain substructural logics are related through the phenomenon of duality. Roughly speaking, metainferences are inferences between collect...
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  3.  20
    Motivating Dualities.James Read & Thomas Møller-Nielsen - 2020 - Synthese 197 (1):263-291.
    There exists a common view that for theories related by a ‘duality’, dual models typically may be taken ab initio to represent the same physical state of affairs, i.e. to correspond to the same possible world. We question this view, by drawing a parallel with the distinction between ‘interpretational’ and ‘motivational’ approaches to symmetries.
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  4.  42
    On Dualities and Equivalences Between Physical Theories.Jeremy Butterfield - forthcoming - In Christian Wüthrich, Baptiste Le Bihan & Nick Huggett (eds.), Philosophy Beyond Spacetime. Oxford: Oxford University Press.
    The main aim of this paper is to make a remark about the relation between dualities between theories, as `duality' is understood in physics and equivalence of theories, as `equivalence' is understood in logic and philosophy. The remark is that in physics, two theories can be dual, and accordingly get called `the same theory', though we interpret them as disagreeing---so that they are certainly not equivalent, as `equivalent' is normally understood. So the remark is simple: but, I shall argue, (...)
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  5.  58
    Dualities and Emergent Gravity: Gauge/Gravity Duality.Sebastian de Haro - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 59:109-125.
    In this paper I develop a framework for relating dualities and emergence: two notions that are close to each other but also exclude one another. I adopt the conception of duality as 'isomorphism', from the physics literature, cashing it out in terms of three conditions. These three conditions prompt two conceptually different ways in which a duality can be modified to make room for emergence; and I argue that this exhausts the possibilities for combining dualities and emergence. I (...)
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  6.  82
    Comparing Dualities and Gauge Symmetries.Sebastian De Haro, Nicholas Teh & Jeremy N. Butterfield - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 59:68-80.
    We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have the ‘flavour’ that two dual theories are ‘closer in content’ than you might think. For both points, we adopt a simple conception of a duality as an ‘isomorphism’ between theories: more precisely, as appropriate bijections between the two theories’ sets of (...)
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  7.  13
    A Duality for Involutive Bisemilattices.Stefano Bonzio, Andrea Loi & Luisa Peruzzi - 2019 - Studia Logica 107 (2):423-444.
    We establish a duality between the category of involutive bisemilattices and the category of semilattice inverse systems of Stone spaces, using Stone duality from one side and the representation of involutive bisemilattices as Płonka sum of Boolean algebras, from the other. Furthermore, we show that the dual space of an involutive bisemilattice can be viewed as a GR space with involution, a generalization of the spaces introduced by Gierz and Romanowska equipped with an involution as additional operation.
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  8. Out of Nowhere: Duality.Nick Huggett & Christian Wüthrich - manuscript
    This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www<dot>beyondspacetime<dot>net.) This chapter investigates the meaning and significance of string theoretic dualities, arguing they reveal a surprising physical indeterminateness to spacetime.
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  9.  21
    Dualities of Fields and Strings.Joseph Polchinski - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 59:6-20.
  10.  83
    Duality and ‘Particle’ Democracy.Elena Castellani - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 59:100-108.
    Weak/strong duality is usually accompanied by what seems a puzzling ontological feature: the fact that under this kind of duality what is viewed as 'elementary' in one description gets mapped to what is viewed as 'composite' in the dual description. This paper investigates the meaning of this apparent 'particle democracy', as it has been called, by adopting an historical approach. The aim is to clarify the nature of the correspondence between 'dual particles' in the light of an historical (...)
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  11. Code-Duality and the Semiotics of Nature.Claus Emmeche - manuscript
    The final version of the paper is published pp. 117-166 in: Myrdene Anderson and Floyd Merrell (eds.): On Semiotic Modeling . Mouton de Gruyter, Berlin and New York, 1991.
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  12.  37
    String Dualities and Empirical Equivalence.Richard Dawid - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 59:21-29.
    String dualities establish empirical equivalence between theories that often look entirely different with respect to their basic ontology and physical structure. Therefore, they represent a particularly interesting example of empirical equivalence in physics. However, the status of duality relations in string physics differs substantially from the traditional understanding of the role played by empirical equivalence. The paper specifies three important differences and argues that they are related to a substantially altered view on the underdetermination of theory building.
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  13. The Duality of Mind: An Historical Perspective.Keith Frankish & Jsbt Evans - 2009 - In Keith Frankish & Jonathan St B. T. Evans (eds.), In Two Minds: Dual Processes and Beyond. Oxford University Press.
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  14.  71
    Priestley Duality for Bilattices.A. Jung & U. Rivieccio - 2012 - Studia Logica 100 (1-2):223-252.
    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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  15. The Case for Mental Duality: Evidence From Split-Brain Data and Other Considerations.Roland Puccetti - 1981 - Behavioral and Brain Sciences 4 (1):93-123.
    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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  16. Duality of the Mind.Ron Sun - manuscript
    Synthesizing situated cognition, reinforcement learning, and hybrid connectionist modeling, a generic cognitive architecture focused on situated involvement and interaction with the world is developed in this book. The architecture notably incorporates the distinction of implicit and explicit processes.
     
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  17.  80
    Dualities and Intertheoretic Relations.Elena Castellani - 2009 - In Mauricio Suarez, Mauro Dorato & Miklos Redei (eds.), EPSA Philosophical Issues in the Sciences · Launch of the European Philosophy of Science Association. Springer. pp. 9--19.
    This is the first of two papers concerned with the philosophical significance of dualities as applied in recent fundamental physics. The general idea is that, for its peculiarity, this ‘new’ ingredient in theory construction can open unexpected perspectives in the current philosophical reflection on contemporary physics. In particular, today’s physical dualities represent an unusual type of intertheory relation, the meaning of which deserves to be investigated. The aim is to show how discussing this point brings into play, at the same (...)
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  18.  15
    Dualities for Płonka Sums.Stefano Bonzio - 2018 - Logica Universalis 12 (3-4):327-339.
    Płonka sums consist of an algebraic construction similar, in some sense, to direct limits, which allows to represent classes of algebras defined by means of regular identities. Recently, Płonka sums have been connected to logic, as they provide algebraic semantics to logics obtained by imposing a syntactic filter to given logics. In this paper, I present a very general topological duality for classes of algebras admitting a Płonka sum representation in terms of dualisable algebras.
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  19.  25
    Duality, Fundamentality, and Emergence.Elena Castellani & Sebastian De Haro - unknown
    We argue that dualities offer new possibilities for relating fundamentality, levels, and emergence. Namely, dualities often relate two theories whose hierarchies of levels are inverted relative to each other, and so allow for new fundamentality relations, as well as for epistemic emergence. We find that the direction of emergence typically found in these cases is opposite to the direction of emergence followed in the standard accounts. Namely, the standard emergence direction is that of decreasing fundamentality: there is emergence of less (...)
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  20.  38
    Hilbert, Duality, and the Geometrical Roots of Model Theory.Günther Eder & Georg Schiemer - 2018 - Review of Symbolic Logic 11 (1):48-86.
    The article investigates one of the key contributions to modern structural mathematics, namely Hilbert’sFoundations of Geometry and its mathematical roots in nineteenth-century projective geometry. A central innovation of Hilbert’s book was to provide semantically minded independence proofs for various fragments of Euclidean geometry, thereby contributing to the development of the model-theoretic point of view in logical theory. Though it is generally acknowledged that the development of model theory is intimately bound up with innovations in 19th century geometry, so far, little (...)
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  21.  11
    Duality in Logic and Language.Lorenz Demey, and & Hans Smessaert - 2016 - Internet Encyclopedia of Philosophy.
    Duality in Logic and Language [draft--do not cite this article] Duality phenomena occur in nearly all mathematically formalized disciplines, such as algebra, geometry, logic and natural language semantics. However, many of these disciplines use the term ‘duality’ in vastly different senses, and while some of these senses are intimately connected to each other, others seem to be entirely … Continue reading Duality in Logic and Language →.
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  22.  35
    Duality Between Modal Algebras and Neighbourhood Frames.Kosta Došen - 1989 - Studia Logica 48 (2):219 - 234.
    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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  23.  91
    Science, Dualities and the Phenomenological Map.H. G. Solari & Mario Natiello - forthcoming - Foundations of Science:1-28.
    We present an epistemological schema of natural sciences inspired by Peirce's pragmaticist view, stressing the role of the \emph{phenomenological map}, that connects reality and our ideas about it. The schema has a recognisable mathematical/logical structure which allows to explore some of its consequences. We show that seemingly independent principles as the requirement of reproducibility of experiments and the Principle of Sufficient Reason are both implied by the schema, as well as Popper's concept of falsifiability. We show that the schema has (...)
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  24.  2
    Heyting Algebras: Duality Theory.Leo Esakia - 2019 - Cham, Switzerland: Springer Verlag.
    This book presents an English translation of a classic Russian text on duality theory for Heyting algebras. Written by Georgian mathematician Leo Esakia, the text proved popular among Russian-speaking logicians. This translation helps make the ideas accessible to a wider audience and pays tribute to an influential mind in mathematical logic. The book discusses the theory of Heyting algebras and closure algebras, as well as the corresponding intuitionistic and modal logics. The author introduces the key notion of a hybrid (...)
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  25.  54
    Duality for Lattice-Ordered Algebras and for Normal Algebraizable Logics.Chrysafis Hartonas - 1997 - Studia Logica 58 (3):403-450.
    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.  76
    Duality, Projectivity, and Unification in Łukasiewicz Logic and MV-Algebras.Vincenzo Marra & Luca Spada - 2013 - Annals of Pure and Applied Logic 164 (3):192-210.
    We prove that the unification type of Łukasiewicz logic and of its equivalent algebraic semantics, the variety of MV-algebras, is nullary. The proof rests upon Ghilardiʼs algebraic characterisation of unification types in terms of projective objects, recent progress by Cabrer and Mundici in the investigation of projective MV-algebras, the categorical duality between finitely presented MV-algebras and rational polyhedra, and, finally, a homotopy-theoretic argument that exploits lifts of continuous maps to the universal covering space of the circle. We discuss the (...)
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  27. Teaching & Learning Guide For: Duality and Ontology.Baptiste Le Bihan & James Read - 2018 - Philosophy Compass 13 (12):e12555.
    Dualities are a pervasive phenomenon in contemporary physics, in which two physical theories are empirically equivalent, yet prima facie make different ontological claims about the world (potentially very different claims—differing in e.g. the number and radius of dimensions of the universe). Dualities thus present a particular instantiation of the well-known notion of underdetermination of theory by evidence. Many different philosophical proposals have been made for how such putative underdetermination might be resolved—this continues to be a programme of active research.
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  28.  68
    Duality as a Category-Theoretic Concept.David Corfield - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 59:55-61.
    In a paper published in 1939, Ernest Nagel described the role that projective duality had played in the reformulation of mathematical understanding through the turn of the nineteenth century, claiming that the discovery of the principle of duality had freed mathematicians from the belief that their task was to describe intuitive elements. While instances of duality in mathematics have increased enormously through the twentieth century, philosophers since Nagel have paid little attention to the phenomenon. In this paper (...)
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  29.  89
    The Duality of Mind: An Historical Perspective.Keith Frankish & Jonathan St B. T. Evans - unknown
    [About the book] This book explores the idea that we have two minds - automatic, unconscious, and fast, the other controlled, conscious, and slow. In recent years there has been great interest in so-called dual-process theories of reasoning and rationality. According to such theories, there are two distinct systems underlying human reasoning - an evolutionarily old system that is associative, automatic, unconscious, parallel, and fast, and a more recent, distinctively human system that is rule-based, controlled, conscious, serial, and slow. Within (...)
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  30.  98
    AdS/CFT Duality and the Emergence of Spacetime.Dean Rickles - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (3):312-320.
    The AdS/CFT duality has been a source of several strong conceptual claims in the physics literature that have yet to be explored by philosophers. In this paper I focus on one of these: the extent to which spacetime geometry and locality can be said to emerge from this duality, so that neither is fundamental. I argue: that the kind of emergence in question is relatively weak, involving one kind of spacetime emerging from another kind of spacetime; inasmuch as (...)
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  31.  24
    Stone Duality for Lattice Expansions.Chrysafis Hartonas - 2018 - Logic Journal of the IGPL 26 (5):475-504.
  32.  33
    Duality for Algebras of Relevant Logics.Alasdair Urquhart - 1996 - Studia Logica 56 (1-2):263 - 276.
    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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  33.  72
    Duality and Nonduality in Meditation Research☆.Zoran Josipovic - 2010 - Consciousness and Cognition 19 (4):1119-1121.
    The great variety of meditation techniques found in different contemplative traditions presents a challenge when attempting to create taxonomies based on the constructs of contemporary cognitive sciences. In the current issue of Consciousness and Cognition, Travis and Shear add ‘automatic self-transcending’ to the previously proposed categories of ‘focused attention’ and ‘open monitoring’, and suggest characteristic EEG bands as the defining criteria for each of the three categories. Accuracy of current taxonomies and potential limitations of EEG measurements as classifying criteria are (...)
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  34.  73
    Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics I.Viorica Sofronie-Stokkermans - 2000 - Studia Logica 64 (1):93-132.
    The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class of well-behaved operators. We then show that finitely-generated varieties of distributive lattices with operators are closed under canonical embedding algebras. The results are used in the second part of the paper to construct topological and non-topological Kripke-style models for logics that (...)
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  35.  19
    Natural Dualities Through Product Representations: Bilattices and Beyond.L. M. Cabrer & H. A. Priestley - 2016 - Studia Logica 104 (3):567-592.
    This paper focuses on natural dualities for varieties of bilattice-based algebras. Such varieties have been widely studied as semantic models in situations where information is incomplete or inconsistent. The most popular tool for studying bilattices-based algebras is product representation. The authors recently set up a widely applicable algebraic framework which enabled product representations over a base variety to be derived in a uniform and categorical manner. By combining this methodology with that of natural duality theory, we demonstrate how to (...)
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  36.  7
    Equivalence and Duality in Electromagnetism.James Owen Weatherall - 2020 - Philosophy of Science 87 (5):1172-1183.
    In this article I bring the recent philosophical literature on theoretical equivalence to bear on dualities in physics. Focusing on electromagnetic duality, which is a simple example of S-duality i...
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  37.  10
    Duality Results for (Co)Residuated Lattices.Chrysafis Hartonas - 2019 - Logica Universalis 13 (1):77-99.
    We present dualities for implicative and residuated lattices. In combination with our recent article on a discrete duality for lattices with unary modal operators, the present article contributes in filling in a gap in the development of Orłowska and Rewitzky’s research program of discrete dualities, which seemed to have stumbled on the case of non-distributive lattices with operators. We discuss dualities via truth, which are essential in relating the non-distributive logic of two-sorted frames with their sorted, residuated modal logic, (...)
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  38.  28
    Priestley Duality for Paraconsistent Nelson’s Logic.Sergei P. Odintsov - 2010 - Studia Logica 96 (1):65-93.
    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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  39. The Duality of Content.Jesse J. Prinz - 2000 - Philosophical Studies 100 (1):1-34.
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  40.  26
    "Duality of Structure" and "Intentionality" in an Ecological Psychology.John Shotter - 1983 - Journal for the Theory of Social Behaviour 13 (1):19–44.
  41.  15
    Duality, Epistemic Efficiency and Consistency.Michael Detlefsen - 2014 - In G. Link (ed.), Formalism & Beyond. De Gruyter. pp. 1-24.
    Duality has often been described as a means of extending our knowledge with a minimal additional outlay of investigative resources. I consider possible arguments for this view. Major elements of this argument are out of keeping with certain widely held views concerning the nature of axiomatic theories (both in projective geometry and elsewhere). They also require a special form of consistency requirement.
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  42. Univocity, Duality, and Ideal Genesis: Deleuze and Plato.John Bova & Paul M. Livingston - 2017 - In Abraham Jacob Greenstine & Ryan J. Johnson (eds.), Contemporary Encounters with Ancient Metaphysics. Edinburgh University Press. pp. 65-85.
    In this essay, we consider the formal and ontological implications of one specific and intensely contested dialectical context from which Deleuze’s thinking about structural ideal genesis visibly arises. This is the formal/ontological dualism between the principles, ἀρχαί, of the One (ἕν) and the Indefinite/Unlimited Dyad (ἀόριστος δυάς), which is arguably the culminating achievement of the later Plato’s development of a mathematical dialectic.3 Following commentators including Lautman, Oskar Becker, and Kenneth M. Sayre, we argue that the duality of the One (...)
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  43.  33
    Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics II.Viorica Sofronie-Stokkermans - 2000 - Studia Logica 64 (2):151-172.
    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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  44.  36
    Duality for the Logic of Quantum Actions.Jort M. Bergfeld, Kohei Kishida, Joshua Sack & Shengyang Zhong - 2015 - Studia Logica 103 (4):781-805.
    In this paper we show a duality between two approaches to represent quantum structures abstractly and to model the logic and dynamics therein. One approach puts forward a “quantum dynamic frame” :2267–2282, 2005), a labelled transition system whose transition relations are intended to represent projections and unitaries on a Hilbert space. The other approach considers a “Piron lattice”, which characterizes the algebra of closed linear subspaces of a Hilbert space. We define categories of these two sorts of structures and (...)
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  45.  40
    Duality in Off-Shell Electromagnetism.Martin Land - 2005 - Foundations of Physics 35 (7):1245-1262.
    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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  46.  88
    A Duality for the Algebras of a Łukasiewicz N + 1-Valued Modal System.Bruno Teheux - 2007 - Studia Logica 87 (1):13-36.
    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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  47.  27
    Supersymmetric Duality in Deformed Superloop Space.Mir Faizal & Tsou Sheung Tsun - 2015 - Foundations of Physics 45 (11):1421-1432.
    In this paper, we will analyse the superloop space formalism for a four dimensional supersymmetric Yang–Mills theory in deformed superspace. We will deform the \ superspace by imposing imposing non-anticommutativity. This non-anticommutative deformation of the superspace will break half the supersymmetry of the original theory. So, this theory will have \ supersymmetry. We will analyse the superloop space duality for this deformed supersymmetric Yang–Mills theory using the \ superspace formalism. We will demonstrate that the sources in the original theory (...)
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  48.  20
    Duality Via Truth: Semantic Frameworks for Lattice-Based Logics.Ewa Orlowska & Ingrid Rewitzky - 2005 - Logic Journal of the IGPL 13 (4):467-490.
    A method of defining semantics of logics based on not necessarily distributive lattices is presented. The key elements of the method are representation theorems for lattices and duality between classes of lattices and classes of some relational systems . We suggest a type of duality referred to as a duality via truth which leads to Kripke-style semantics and three-valued semantics in the style of Allwein-Dunn. We develop two new representation theorems for lattices which, together with the existing (...)
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  49.  20
    Indexical Duality: A Fregean Theory.Tomis Kapitan - 2016 - Rivista Internazionale di Filosofia e Psicologia 7 (3):303-320.
    : Frege’s remarks about the first-person pronoun in Der Gedanke have elicited numerous commentaries, but his insight has not been fully appreciated or developed. Commentators have overlooked Frege’s reasons for claiming that there are two distinct first-person senses, and failed to realize that his remarks easily generalize to all indexicals. I present a perspectival theory of indexicals inspired by Frege’s claim that all indexical types have a dual meaning which, in turn, leads to a duality of senses expressed by (...)
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  50.  50
    A Schema for Duality, Illustrated by Bosonization.Sebastian De Haro & Jeremy Butterfield - unknown
    In this paper we present a schema for describing dualities between physical theories, and illustrate it in detail with the example of bosonization: a boson-fermion duality in two-dimensional quantum field theory. The schema develops proposals in De Haro : these proposals include construals of notions related to duality, like representation, model, symmetry and interpretation. The aim of the schema is to give a more precise criterion for duality than has so far been considered. The bosonization example, or (...)
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