Results for ' Esakia duality'

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  1.  16
    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 (...)
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  2.  10
    Leo Esakia on Duality in Modal and Intuitionistic Logics.Guram Bezhanishvili (ed.) - 2014 - Dordrecht, Netherland: Springer.
    This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia (...) for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Gödel-Löb provability logic GL. One chapter scrutinizes Esakia’s work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues. (shrink)
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  3.  13
    Leo Esakia, Heyting Algebras: Duality Theory, Guram Bezhanishvili and Wesley A. Holliday, (eds.), Springer International Publishing, Series: Trends in Logic, Vol. 50, 2019, pp. 95+xv: ISBN 978-3-030-12095-5 (Hardcover) 80,24 e, ISBN 978-3-030-12096-2 (eBook) 46 €. [REVIEW]Hilary A. Priestley - 2021 - Studia Logica 109 (5):1171-1173.
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  4.  15
    On modal and intuitionistic logics: Guram Bezhanishvili : Leo Esakia on duality in modal and intuitionistic logics. Dordrecht: Springer, 2014, 334pp, €107.09 HB.Costas Dimitracopoulos - 2014 - Metascience 24 (2):337-340.
    The volume under review contains work dedicated to the memory of Leo Esakia, who died in 2010, after having worked for over 40 years towards developing duality theory for modal and intuitionistic logics. The collection comprises ten technical contributions that follow the first chapter, in which the reader can find information on Esakia’s studies and career, as well as a complete list of his research publications. In the sequel, we will refer briefly to each of these ten (...)
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  5.  10
    Dualities for Bounded Prelinear Hilbert Algebras.Hernán J. San Martín & Valeria A. Sígal - 2022 - Logic Journal of the IGPL 30 (3):409-421.
    This paper deals about dualities for bounded prelinear Hilbert algebras. In particular, we give an Esakia-style duality between the algebraic category of bounded prelinear Hilbert algebras and a category of H-spaces whose morphisms are certain continuous p-morphisms.
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  6.  18
    Hereditarily Structurally Complete Intermediate Logics: Citkin’s Theorem Via Duality.Nick Bezhanishvili & Tommaso Moraschini - 2023 - Studia Logica 111 (2):147-186.
    A deductive system is said to be structurally complete if its admissible rules are derivable. In addition, it is called hereditarily structurally complete if all its extensions are structurally complete. Citkin (1978) proved that an intermediate logic is hereditarily structurally complete if and only if the variety of Heyting algebras associated with it omits five finite algebras. Despite its importance in the theory of admissible rules, a direct proof of Citkin’s theorem is not widely accessible. In this paper we offer (...)
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  7.  21
    A negative solution of Kuznetsov’s problem for varieties of bi-Heyting algebras.Guram Bezhanishvili, David Gabelaia & Mamuka Jibladze - 2022 - Journal of Mathematical Logic 22 (3).
    Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. In this paper, we show that there exist (continuum many) varieties of bi-Heyting algebras that are not generated by their complete members. It follows that there exist (continuum many) extensions of the Heyting–Brouwer logic [math] that are topologically incomplete. This result provides further insight into the long-standing open problem of Kuznetsov by yielding a negative solution of the reformulation of the problem from extensions of [math] to extensions of [math].
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  8.  15
    An Algebraic Approach to Canonical Formulas: Intuitionistic Case.Guram Bezhanishvili - 2009 - Review of Symbolic Logic 2 (3):517.
    We introduce partial Esakia morphisms, well partial Esakia morphisms, and strong partial Esakia morphisms between Esakia spaces and show that they provide the dual description of (∧, →) homomorphisms, (∧, →, 0) homomorphisms, and (∧, →, ∨) homomorphisms between Heyting algebras, thus establishing a generalization of Esakia duality. This yields an algebraic characterization of Zakharyaschev’s subreductions, cofinal subreductions, dense subreductions, and the closed domain condition. As a consequence, we obtain a new simplified proof (which (...)
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  9.  9
    Intuitionistic Sahlqvist Theory for Deductive Systems.Damiano Fornasiere & Tommaso Moraschini - forthcoming - Journal of Symbolic Logic:1-59.
    Sahlqvist theory is extended to the fragments of the intuitionistic propositional calculus that include the conjunction connective. This allows us to introduce a Sahlqvist theory of intuitionistic character amenable to arbitrary protoalgebraic deductive systems. As an application, we obtain a Sahlqvist theorem for the fragments of the intuitionistic propositional calculus that include the implication connective and for the extensions of the intuitionistic linear logic.
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  10.  23
    Categories of models of R-mingle.Wesley Fussner & Nick Galatos - 2019 - Annals of Pure and Applied Logic 170 (10):1188-1242.
    We give a new Esakia-style duality for the category of Sugihara monoids based on the Davey-Werner natural duality for lattices with involution, and use this duality to greatly simplify a construction due to Galatos-Raftery of Sugihara monoids from certain enrichments of their negative cones. Our method of obtaining this simplification is to transport the functors of the Galatos-Raftery construction across our duality, obtaining a vastly more transparent presentation on duals. Because our duality extends Dunn's (...)
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  11. On a Generalization of Heyting Algebras I.Amirhossein Akbar Tabatabai, Majid Alizadeh & Masoud Memarzadeh - forthcoming - Studia Logica:1-45.
    \(\nabla \) -algebra is a natural generalization of Heyting algebra, unifying many algebraic structures including bounded lattices, Heyting algebras, temporal Heyting algebras and the algebraic presentation of the dynamic topological systems. In a series of two papers, we will systematically study the algebro-topological properties of different varieties of \(\nabla \) -algebras. In the present paper, we start with investigating the structure of these varieties by characterizing their subdirectly irreducible and simple elements. Then, we prove the closure of these varieties under (...)
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  12.  10
    Monadic $$k\times j$$ k × j -rough Heyting algebras.Federico Almiñana & Gustavo Pelaitay - 2022 - Archive for Mathematical Logic 61 (5):611-625.
    In this paper, we introduce the variety of algebras, which we call monadic \-rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in \ case they coincide with monadic 3-valued Łukasiewicz–Moisil algebras. Our main interest is the characterization of simple and subdirectly irreducible monadic \-rough Heyting algebras. In order to this, an Esakia-style duality for these algebras is developed.
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  13.  60
    Frontal Operators in Weak Heyting Algebras.Sergio A. Celani & Hernán J. San Martín - 2012 - Studia Logica 100 (1-2):91-114.
    In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [ 10 ]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation $${\tau(a) \leq b \vee (b \rightarrow a)}$$, for all $${a, b \in A}$$. These operators were studied from an algebraic, logical and topological point of view by Leo (...)
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  14.  7
    Monadic k×j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\times j$$\end{document}-rough Heyting algebras. [REVIEW]Gustavo Pelaitay & Federico Almiñana - 2021 - Archive for Mathematical Logic 61 (5-6):611-625.
    In this paper, we introduce the variety of algebras, which we call monadic k×j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\times j$$\end{document}-rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in 3×2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\times 2$$\end{document} case they coincide with monadic 3-valued Łukasiewicz–Moisil algebras. Our main interest is the characterization of simple and subdirectly irreducible monadic k×j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\times j$$\end{document}-rough Heyting algebras. (...)
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  15.  45
    Intuitionistic logic and modality via topology.Leo Esakia - 2004 - Annals of Pure and Applied Logic 127 (1-3):155-170.
    In the pioneering article and two papers, written jointly with McKinsey, Tarski developed the so-called algebraic and topological frameworks for the Intuitionistic Logic and the Lewis modal system. In this paper, we present an outline of modern systems with a topological tinge. We consider topological interpretation of basic systems GL and G of the provability logic in terms of the Cantor derivative and the Hausdorff residue.
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  16.  28
    The modalized Heyting calculus: a conservative modal extension of the Intuitionistic Logic ★.Leo Esakia - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):349-366.
    In this paper we define an augmentation mHC of the Heyting propositional calculus HC by a modal operator ?. This modalized Heyting calculus mHC is a weakening of the Proof-Intuitionistic Logic KM of Kuznetsov and Muravitsky. In Section 2 we present a short selection of attractive (algebraic, relational, topological and categorical) features of mHC. In Section 3 we establish some close connections between mHC and certain normal extension K4.Grz of the modal system K4. We define a translation of mHC into (...)
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  17.  46
    Five critical modal systems.L. Esakia & V. Meskhi - 1977 - Theoria 43 (1):52-60.
  18.  33
    Around provability logic.Leo Esakia - 2010 - Annals of Pure and Applied Logic 161 (2):174-184.
    We present some results on algebraic and modal analysis of polynomial distortions of the standard provability predicate in Peano Arithmetic PA, and investigate three provability-like modal systems related to the Gödel–Löb modal system GL. We also present a short review of relational and topological semantics for these systems, and describe the dual category of algebraic models of our main modal system.
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  19.  17
    Scattered toposes.Leo Esakia, Mamuka Jibladze & Dito Pataraia - 2000 - Annals of Pure and Applied Logic 103 (1-3):97-107.
    A class of toposes is introduced and studied, suitable for semantical analysis of an extension of the Heyting predicate calculus admitting Gödel's provability interpretation.
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  20.  16
    Formulas of one propositional variable in intuitionistic logic with the Solovay modality.Leo Esakia & Revaz Grigolia - 2008 - Logic and Logical Philosophy 17 (1-2):111-127.
    A description of the free cyclic algebra over the variety of Solovay algebras, as well as over its pyramid locally finite subvarieties is given.
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  21.  67
    Fatal Heyting Algebras and Forcing Persistent Sentences.Leo Esakia & Benedikt Löwe - 2012 - Studia Logica 100 (1-2):163-173.
    Hamkins and Löwe proved that the modal logic of forcing is S4.2 . In this paper, we consider its modal companion, the intermediate logic KC and relate it to the fatal Heyting algebra H ZFC of forcing persistent sentences. This Heyting algebra is equationally generic for the class of fatal Heyting algebras. Motivated by these results, we further analyse the class of fatal Heyting algebras.
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  22.  49
    Some Results on Modal Axiomatization and Definability for Topological Spaces.Guram Bezhanishvili, Leo Esakia & David Gabelaia - 2005 - Studia Logica 81 (3):325-355.
    We consider two topological interpretations of the modal diamond—as the closure operator (C-semantics) and as the derived set operator (d-semantics). We call the logics arising from these interpretations C-logics and d-logics, respectively. We axiomatize a number of subclasses of the class of nodec spaces with respect to both semantics, and characterize exactly which of these classes are modally definable. It is demonstrated that the d-semantics is more expressive than the C-semantics. In particular, we show that the d-logics of the six (...)
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  23. Particles and Ideas.Gabriel Moked, Peter J. Steinberger & Leo Esakia - 1990 - Studia Logica 49 (1):159-160.
  24. 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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  25.  41
    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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  26.  36
    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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  27. 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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  28.  52
    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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  29.  57
    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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  30. 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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  31.  22
    Embracing dualities: Principles of education for a VUCA world.Ariel Sarid & Maya Levanon - 2023 - Educational Philosophy and Theory 55 (12):1375-1386.
    In the wake of profound social changes, which have been accelerated due to a global pandemic, educators reconsider the role and goals of education, and subsequently, how its pragmatic expression should look like in a VUCA-world. We address this challenge by offering basic tenets of education and principles that are tailored to the current reality. We concentrate primarily on the merits of embracing dualities, dilemmas and tensions, for engaging in deep learning and personal development. Jon Wergin’s theory of ‘deep learning’ (...)
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  32. 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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  33.  36
    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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  34.  46
    Dualities and intertheoretic relations.Elena Castellani - 2009 - In Mauricio Suárez, Mauro Dorato & Miklós Rédei (eds.), EPSA Philosophical Issues in the Sciences · Launch of the European Philosophy of Science Association. Dordrecht, Netherland: 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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  35.  56
    Agentive Duality reconsidered.Annina Loets & Julia Zakkou - 2022 - Philosophical Studies 179 (12):3771-3789.
    A growing consensus in the literature on agentive modals has it that ability modals like ‘can’ or ‘able to’ have a _dual_, i.e. interpretations of ‘must’ or ‘cannot but’ which stand to _necessity_ as ability stands to _possibility_. We argue that this thesis (which we call ‘Agentive Duality’) is much more controversial than meets the eye. While Agentive Duality follows from the orthodox possibility analysis of ability given natural assumptions, it sits uneasily with a wide range of alternative (...)
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  36.  22
    Duality, Epistemic Efficiency and Consistency.Michael Detlefsen - 2014 - In G. Link (ed.), Formalism & Beyond. 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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  37.  43
    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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  38.  56
    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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  39.  35
    A duality between Pawlak's knowledge representation systems and bi-consequence systems.Dimiter Vakarelov - 1995 - Studia Logica 55 (1):205 - 228.
    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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  40.  13
    Duality, Epistemic Efficiency & Consistency.Michael Detlefsen - 2014 - In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. Boston: 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 attempt to construct a serious argument for this view. Certain major elements of this argument are then considered at length. They’re found to be out of keeping with certain widely held views concerning the nature of axiomatic theories (both in projective geometry and elsewhere). They’re also found to require a special form of consistency requirement.
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  41.  29
    Sentience and the Origins of Consciousness: From Cartesian Duality to Markovian Monism.Karl Friston, Wanja Wiese & J. Allan Hobson - 2020 - Entropy 22 (5):516.
    This essay addresses Cartesian duality and how its implicit dialectic might be repaired using physics and information theory. Our agenda is to describe a key distinction in the physical sciences that may provide a foundation for the distinction between mind and matter, and between sentient and intentional systems. From this perspective, it becomes tenable to talk about the physics of sentience and ‘forces’ that underwrite our beliefs (in the sense of probability distributions represented by our internal states), which may (...)
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  42.  47
    Natural dualities for varieties ofn-valued łukasiewicz algebras.H. A. Priestley - 1995 - Studia Logica 54 (3):333 - 370.
    Natural dualities are developed for varieties ofn-valued ukasiewicz algebras with and without negation. These dualities are based on hom-functors, and parallel Stone duality for Boolean algebras. A translation is described which relates the natural dualities to the corresponding restricted Priestley dualities. This enables a unified approach to free algebras to be presented, whence R. Cignoli's characterisations of the finitely generated free algebras are elucidated and new descriptions of arbitrary free algebras obtained. Finally it is shown how dualities for subvarieties (...)
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  43.  5
    Non-duality questions, non-duality answers: exploring spirituality and existence in the modern world.Richard Sylvester - 2016 - Oakland, CA: New Harbinger Publications.
    Non-Duality Questions, Non-Duality Answers is an organic, interactive exploration of non-duality--the understanding that in life there is no separation, only seamless Oneness. Designed to answer questions as they arise, this book invites readers to participate in the argument for non-separation, inquire about the nature of the self and the experience of liberation, and understand how non-dual awareness can impact our lives. With a unique blend of patience, compassion, respect, provocation, and humor, author Richard Sylvester helps frustrated spiritual (...)
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  44.  42
    Discrete Dualities for Double Stone Algebras.Ivo Düntsch & Ewa Orłowska - 2011 - Studia Logica 99 (1-3):127-142.
    We present two discrete dualities for double Stone algebras. Each of these dualities involves a different class of frames and a different definition of a complex algebra. We discuss relationships between these classes of frames and show that one of them is a weakening of the other. We propose a logic based on double Stone algebras.
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  45. 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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  46.  74
    On Dualities and Equivalences Between Physical Theories.Jeremy Butterfield - 2021 - In Christian Wüthrich, Baptiste Le Bihan & Nick Huggett (eds.), Philosophy Beyond Spacetime: Implications From Quantum Gravity. 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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  47.  27
    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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  48.  13
    Duality for Coalgebras for Vietoris and Monadicity.Marco Abbadini & Ivan di Liberti - forthcoming - Journal of Symbolic Logic:1-34.
    We prove that the opposite of the category of coalgebras for the Vietoris endofunctor on the category of compact Hausdorff spaces is monadic over $\mathsf {Set}$. We deliver an analogous result for the upper, lower, and convex Vietoris endofunctors acting on the category of stably compact spaces. We provide axiomatizations of the associated (infinitary) varieties. This can be seen as a version of Jónsson–Tarski duality for modal algebras beyond the zero-dimensional setting.
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    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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  50. 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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