Results for 'ordered algebraic structures: Historical'

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  1.  42
    Free ordered algebraic structures towards proof theory.Andreja Prijatelj - 2001 - Journal of Symbolic Logic 66 (2):597-608.
    In this paper, constructions of free ordered algebras on one generator are given that correspond to some one-variable fragments of affine propositional classical logic and their extensions with n-contraction (n ≥ 2). Moreover, embeddings of the already known infinite free structures into the algebras introduced below are furnished with; thus, solving along the respective cardinality problems.
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  2. Free Ordered Algebraic Structures towards Proof Theory.Andreja Prijatelj - 2001 - Journal of Symbolic Logic 66 (2):597-608.
    In this paper, constructions of free ordered algebras on one generator are given that correspond to some one-variable fragments of affine propositional classical logic and their extensions with n-contraction. Moreover, embeddings of the already known infinite free structures into the algebras introduced below are furnished with; thus, solving along the respective cardinality problems.
     
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  3.  12
    The Shaping of Dedekind’s Rigorous Mathematics: What Do Dedekind’s Drafts Tell Us about His Ideal of Rigor?Emmylou Haffner - 2021 - Notre Dame Journal of Formal Logic 62 (1).
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  4. The role of epistemological models in Veronese's and Bettazzi's theory of magnitudes.Paola Cantù - 2010 - In Marcello D'Agostino, Federico Laudisa, Giulio Giorello, Telmo Pievani & Corrado Sinigaglia (eds.), New Essays in Logic and Philosophy of Science. College Publications.
    The philosophy of mathematics has been accused of paying insufficient attention to mathematical practice: one way to cope with the problem, the one we will follow in this paper on extensive magnitudes, is to combine the `history of ideas' and the `philosophy of models' in a logical and epistemological perspective. The history of ideas allows the reconstruction of the theory of extensive magnitudes as a theory of ordered algebraic structures; the philosophy of models allows an investigation into (...)
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  5.  6
    From Problems to Structures: the Cousin Problems and the Emergence of the Sheaf Concept.Renaud Chorlay - 2009 - Archive for History of Exact Sciences 64 (1):1-73.
    Historical work on the emergence of sheaf theory has mainly concentrated on the topological origins of sheaf cohomology in the period from 1945 to 1950 and on subsequent developments. However, a shift of emphasis both in time-scale and disciplinary context can help gain new insight into the emergence of the sheaf concept. This paper concentrates on Henri Cartan’s work in the theory of analytic functions of several complex variables and the strikingly different roles it played at two stages of (...)
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  6.  45
    Reconfiguring the centre: The structure of scientific exchanges between colonial India and Europe.Dhruv Raina - 1996 - Minerva 34 (2):161-176.
    The “centre-periphery” relationship historically structured scientific exchanges between metropolis and province, between the fount of empire and its outposts. But the exchange, if regarded merely as a one-way flow of scientific information, ignores both the politics of knowledge and the nature of its appropriation. Arguably, imperial structures do not entirely determine scientific practices and the exchange of knowledge. Several factors neutralise the over-determining influence of politics—and possibly also the normative values of science—on scientific practice.In examining these four examples of (...)
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  7. Mathematics embodied: Merleau-Ponty on geometry and algebra as fields of motor enaction.Jan Halák - 2022 - Synthese 200 (1):1-28.
    This paper aims to clarify Merleau-Ponty’s contribution to an embodied-enactive account of mathematical cognition. I first identify the main points of interest in the current discussions of embodied higher cognition and explain how they relate to Merleau-Ponty and his sources, in particular Husserl’s late works. Subsequently, I explain these convergences in greater detail by more specifically discussing the domains of geometry and algebra and by clarifying the role of gestalt psychology in Merleau-Ponty’s account. Beyond that, I explain how, for Merleau-Ponty, (...)
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  8.  34
    Algebraic Structures Arising in Axiomatic Unsharp Quantum Physics.Gianpiero Cattaneo & Stanley Gudder - 1999 - Foundations of Physics 29 (10):1607-1637.
    This article presents and compares various algebraic structures that arise in axiomatic unsharp quantum physics. We begin by stating some basic principles that such an algebraic structure should encompass. Following G. Mackey and G. Ludwig, we first consider a minimal state-effect-probability (minimal SEFP) structure. In order to include partial operations of sum and difference, an additional axiom is postulated and a SEFP structure is obtained. It is then shown that a SEFP structure is equivalent to an effect (...)
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  9.  4
    Encoding true second‐order arithmetic in the real‐algebraic structure of models of intuitionistic elementary analysis.Miklós Erdélyi-Szabó - 2021 - Mathematical Logic Quarterly 67 (3):329-341.
    Based on the paper [4] we show that true second‐order arithmetic is interpretable over the real‐algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras.
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  10.  17
    Undecidability of the Real-Algebraic Structure of Scott's Model.Miklós Erdélyi-Szabó - 1998 - Mathematical Logic Quarterly 44 (3):344-348.
    We show that true first-order arithmetic of the positive integers is interpretable over the real-algebraic structure of Scott's topological model for intuitionistic analysis. From this the undecidability of the structure follows.
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  11.  52
    The algebraic structure of the isomorphic types of tally, polynomial time computable sets.Yongge Wang - 2002 - Archive for Mathematical Logic 41 (3):215-244.
    We investigate the polynomial time isomorphic type structure of (the class of tally, polynomial time computable sets). We partition P T into six parts: D −, D^ − , C, S, F, F^, and study their p-isomorphic properties separately. The structures of , , and are obvious, where F, F^, and C are the class of tally finite sets, the class of tally co-finite sets, and the class of tally bi-dense sets respectively. The following results for the structures (...)
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  12. A neglected aspect of the puzzle of chemical structure: how history helps.Joseph E. Earley - 2012 - Foundations of Chemistry 14 (3):235-243.
    Intra-molecular connectivity (that is, chemical structure) does not emerge from computations based on fundamental quantum-mechanical principles. In order to compute molecular electronic energies (of C 3 H 4 hydrocarbons, for instance) quantum chemists must insert intra-molecular connectivity “by hand.” Some take this as an indication that chemistry cannot be reduced to physics: others consider it as evidence that quantum chemistry needs new logical foundations. Such discussions are generally synchronic rather than diachronic —that is, they neglect ‘historical’ aspects. However, systems (...)
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  13.  15
    Algebraic structure of the truth-values for Lω.Alexander S. Karpenko - 1988 - Bulletin of the Section of Logic 17 (3/4):127-133.
    This paper is an abstract of the report which was presented on the Polish-Soviet meeting on logic . It is shown that one can consider a lineary-ordered Heyting’s and Brouwer’s algebras as truth-values for Lukasiewicz’s infinite-valued logic’s Lω.
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  14.  19
    Join-completions of partially ordered algebras.José Gil-Férez, Luca Spada, Constantine Tsinakis & Hongjun Zhou - 2020 - Annals of Pure and Applied Logic 171 (10):102842.
    We present a systematic study of join-extensions and join-completions of partially ordered algebras, which naturally leads to a refined and simplified treatment of fundamental results and constructions in the theory of ordered structures ranging from properties of the Dedekind–MacNeille completion to the proof of the finite embeddability property for a number of varieties of lattice-ordered algebras.
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  15.  9
    Algebraic Structures Formalizing the Logic of Quantum Mechanics Incorporating Time Dimension.Ivan Chajda & Helmut Länger - forthcoming - Studia Logica:1-19.
    As Classical Propositional Logic finds its algebraic counterpart in Boolean algebras, the logic of Quantum Mechanics, as outlined within G. Birkhoff and J. von Neumann’s approach to Quantum Theory (Birkhoff and von Neumann in Ann Math 37:823–843, 1936) [see also (Husimi in I Proc Phys-Math Soc Japan 19:766–789, 1937)] finds its algebraic alter ego in orthomodular lattices. However, this logic does not incorporate time dimension although it is apparent that the propositions occurring in the logic of Quantum Mechanics (...)
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  16.  8
    Learning families of algebraic structures from informant.Luca San Mauro, Nikolay Bazhenov & Ekaterina Fokina - 2020 - Information And Computation 1 (275):104590.
    We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a model-theoretic characterization of the learning type InfEx_\iso, consisting of the structures whose isomorphism types can be learned in the limit. We show that a family of structures is InfEx_\iso-learnable if and only if the structures can be distinguished in terms of their \Sigma^2_inf-theories. We apply this characterization to familiar cases and we show the (...)
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  17.  22
    Undecidability of the Real-Algebraic Structure of Models of Intuitionistic Elementary Analysis.Miklós Erdélyi-Szabó - 2000 - Journal of Symbolic Logic 65 (3):1014-1030.
    We show that true first-order arithmetic is interpretable over the real-algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras. From this the undecidability of the structures follows. We also show that Scott's model is equivalent to true second-order arithmetic. In the appendix we argue that undecidability on the language of ordered rings follows from intuitionistically plausible properties of the real numbers.
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  18.  73
    Introduction to the Symbolic Plithogenic Algebraic Structures (revisited).Florentin Smarandache - 2023 - Neutrosophic Sets and Systems 53.
    In this paper, we recall and study the new type of algebraic structures called Symbolic Plithogenic Algebraic Structures. Their operations are given under the Absorbance Law and the Prevalence Order.
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  19.  34
    Degree spectra and computable dimensions in algebraic structures.Denis R. Hirschfeldt, Bakhadyr Khoussainov, Richard A. Shore & Arkadii M. Slinko - 2002 - Annals of Pure and Applied Logic 115 (1-3):71-113.
    Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting. However, this can be an unnecessary duplication of effort, and lacks generality. Another method is to code the original structure into a structure in (...)
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  20.  8
    A Category of Ordered Algebras Equivalent to the Category of Multialgebras.Marcelo Esteban Coniglio & Guilherme V. Toledo - 2023 - Bulletin of the Section of Logic 52 (4):517-550.
    It is well known that there is a correspondence between sets and complete, atomic Boolean algebras (\(\textit{CABA}\)s) taking a set to its power-set and, conversely, a complete, atomic Boolean algebra to its set of atomic elements. Of course, such a correspondence induces an equivalence between the opposite category of \(\textbf{Set}\) and the category of \(\textit{CABA}\)s. We modify this result by taking multialgebras over a signature \(\Sigma\), specifically those whose non-deterministic operations cannot return the empty-set, to \(\textit{CABA}\)s with their zero element (...)
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  21.  17
    On Boolean Algebraic Structure of Proofs: Towards an Algebraic Semantics for the Logic of Proofs.Amir Farahmand Parsa & Meghdad Ghari - 2023 - Studia Logica 111 (4):573-613.
    We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on proof terms and equality predicate on terms. Moreover, the completeness theorem and certain generalizations of Stone’s representation theorem are obtained for all proposed algebras.
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  22.  14
    The notion of independence in categories of algebraic structures, part I: Basic properties.Gabriel Srour - 1988 - Annals of Pure and Applied Logic 38 (2):185-213.
    We define a formula φ in a first-order language L , to be an equation in a category of L -structures K if for any H in K , and set p = {φ;i ϵI, a i ϵ H} there is a finite set I 0 ⊂ I such that for any f : H → F in K , ▪. We say that an elementary first-order theory T which has the amalgamation property over substructures is equational if every (...)
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  23.  43
    Angus Macintyre, Kenneth McKenna, and Lou van den Dries. Elimination of quantifiers in algebraic structures. Advances in mathematics, vol. 47 , pp. 74–87. - L. P. D. van den Dries. A linearly ordered ring whose theory admits elimination of quantifiers is a real closed field. Proceedings of the American Mathematical Society, vol. 79 , pp. 97–100. - Bruce I. Rose. Rings which admit elimination of quantifiers. The journal of symbolic logic, vol. 43 , pp. 92–112; Corrigendum, vol. 44 , pp. 109–110. - Chantal Berline. Rings which admit elimination of quantifiers. The journal of symbolic logic, vol. 43 , vol. 46 , pp. 56–58. - M. Boffa, A. Macintyre, and F. Point. The quantifier elimination problem for rings without nilpotent elements and for semi-simple rings. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture. [REVIEW]Gregory L. Cherlin - 1985 - Journal of Symbolic Logic 50 (4):1079-1080.
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  24.  10
    On P Versus NP for Parameter‐Free Programs Over Algebraic Structures.Armin Hemmerling - 2001 - Mathematical Logic Quarterly 47 (1):67-92.
    Based on the computation mode introduced in [13], we deal with the time complexity of computations over arbitrary first-order structures.The main emphasis is on parameter-free computations. Some transfer results for solutions of P versus NP problems as well as relationships to quantifier elimination are discussed. By computation tree analysis using first-order formulas, it follows that P versus NP solutions and other results of structural complexity theory are invariant under elementary equivalence of structures.
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  25.  27
    On the structure of linearly ordered pseudo-BCK-algebras.Anatolij Dvurečenskij & Jan Kühr - 2009 - Archive for Mathematical Logic 48 (8):771-791.
    Pseudo-BCK-algebras are a non-commutative generalization of well-known BCK-algebras. The paper describes a situation when a linearly ordered pseudo-BCK-algebra is an ordinal sum of linearly ordered cone algebras. In addition, we present two identities giving such a possibility of the decomposition and axiomatize the residuation subreducts of representable pseudo-hoops and pseudo-BL-algebras.
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  26.  50
    The algebraization of quantum mechanics and the implicate order.F. A. M. Frescura & B. J. Hiley - 1980 - Foundations of Physics 10 (9-10):705-722.
    It has been proposed that the implicate order can be given mathematical expression in terms of an algebra and that this algebra is similar to that used in quantum theory. In this paper we bring out in a simple way those aspects of the algebraic formulation of quantum theory that are most relevant to the implicate order. By using the properties of the standard ket introduced by Dirac we describe in detail how the Heisenberg algebra can be generalized to (...)
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  27.  18
    A construction of Boolean algebras from first-order structures.Sabine Koppelberg - 1993 - Annals of Pure and Applied Logic 59 (3):239-256.
    We give a construction assigning classes of Boolean algebras to first-order theories; several classes of Boolean algebras considered previously in the literature can be thus obtained. In particular it turns out that the class of semigroup algebras can be defined in this way, in fact by a Horn theory, and it is the largest class of Boolean algebras defined by a Horn theory.
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  28.  23
    On the algebraization of Henkin‐type second‐order logic.Miklós Ferenczi - 2022 - Mathematical Logic Quarterly 68 (2):149-158.
    There is an extensive literature related to the algebraization of first‐order logic. But the algebraization of full second‐order logic, or Henkin‐type second‐order logic, has hardly been researched. The question arises: what kind of set algebra is the algebraic version of a Henkin‐type model of second‐order logic? The question is investigated within the framework of the theory of cylindric algebras. The answer is: a kind of cylindric‐relativized diagonal restricted set algebra. And the class of the subdirect products of these set (...)
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  29.  13
    Ramsey Algebras and Formal Orderly Terms.Wen Chean Teh - 2017 - Notre Dame Journal of Formal Logic 58 (1):115-125.
    Hindman’s theorem says that every finite coloring of the natural numbers has a monochromatic set of finite sums. A Ramsey algebra is a structure that satisfies an analogue of Hindman’s theorem. In this paper, we present the basic notions of Ramsey algebras by using terminology from mathematical logic. We also present some results regarding classification of Ramsey algebras.
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  30.  21
    First-Order Axiomatisations of Representable Relation Algebras Need Formulas of Unbounded Quantifier Depth.Rob Egrot & Robin Hirsch - 2022 - Journal of Symbolic Logic 87 (3):1283-1300.
    Using a variation of the rainbow construction and various pebble and colouring games, we prove that RRA, the class of all representable relation algebras, cannot be axiomatised by any first-order relation algebra theory of bounded quantifier depth. We also prove that the class At(RRA) of atom structures of representable, atomic relation algebras cannot be defined by any set of sentences in the language of RA atom structures that uses only a finite number of variables.
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  31.  15
    Lattice Ordered O -Minimal Structures.Carlo Toffalori - 1998 - Notre Dame Journal of Formal Logic 39 (4):447-463.
    We propose a notion of -minimality for partially ordered structures. Then we study -minimal partially ordered structures such that is a Boolean algebra. We prove that they admit prime models over arbitrary subsets and we characterize -categoricity in their setting. Finally, we classify -minimal Boolean algebras as well as -minimal measure spaces.
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  32.  81
    Partial structures and Jeffrey-Keynes algebras.Marcelo Tsuji - 2000 - Synthese 125 (1-2):283-299.
    In Tsuji 1997 the concept of Jeffrey-Keynes algebras was introduced in order to construct a paraconsistent theory of decision under uncertainty. In the present paper we show that these algebras can be used to develop a theory of decision under uncertainty that measures the degree of belief on the quasi (or partial) truth of the propositions. As applications of this new theory of decision, we use it to analyze Popper's paradox of ideal evidence and to indicate a possible way of (...)
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  33.  6
    Pluralism, Structural Injustice, and Reparations for Historical Injustice: A Reply to Daniel Butt.Felix Lambrecht - 2024 - Ethical Theory and Moral Practice 27 (2):269-275.
    This paper discusses the pluralist theory of reparations for historical injustice offered by Daniel Butt (Ethical Theory and Moral Practice 24(5):1161–75, 2021). Butt attempts to vindicate purely past-regarding corrective duties in response to Alasia Nuti’s historical-structural model of reparations. I agree with Butt that reparative justice requires both past-regarding and future-looking structural duties. And I agree with him that Nuti’s model leaves out purely past-regarding duties. I argue, however, that Butt does not offer a genuinely pluralist account. I (...)
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  34. Being and Order: The Metaphysics of Thomas Aquinas in Historical Perspective by Andrew N. Woznicki.Robert E. Lauder - 1992 - The Thomist 56 (1):151-154.
    In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 151 highly conscientious translator, and a sign of this are the Latin-English and English-Latin glossaries that are appended at the end of the work. The glossaries show how he has tried to remain consistent in his choice of terms and how he decided to render difficult terms like ratio and esse, which cause every translator of Aquinas problems. One could complain, however, that these nine pages of (...)
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  35.  20
    Δ20-categoricity in Boolean algebras and linear orderings.Charles F. D. McCoy - 2003 - Annals of Pure and Applied Logic 119 (1-3):85-120.
    We characterize Δ20-categoricity in Boolean algebras and linear orderings under some extra effectiveness conditions. We begin with a study of the relativized notion in these structures.
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  36.  48
    Symmetrical Heyting algebras with a finite order type of operators.Luisa Iturrioz - 1995 - Studia Logica 55 (1):89 - 98.
    The main purpose of this paper is to introduce a class of algebraic structures related to many-valued ukasiewicz algebras. They are symmetrical Heyting algebras with a set of modal operators indexed by a finite completely symmetric poset. A representation theorem is given for these (not functionally complete) algebras.
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  37.  46
    Informational branching universe.Pierre Uzan - 2010 - Foundations of Science 15 (1):1-28.
    This paper suggests an epistemic interpretation of Belnap’s branching space-times theory based on Everett’s relative state formulation of the measurement operation in quantum mechanics. The informational branching models of the universe are evolving structures defined from a partial ordering relation on the set of memory states of the impersonal observer. The totally ordered set of their information contents defines a linear “time” scale to which the decoherent alternative histories of the informational universe can be referred—which is quite necessary (...)
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  38.  22
    The First-Order Theories of Dedekind Algebras.George Weaver - 2003 - Studia Logica 73 (3):337-365.
    A Dedekind Algebra is an ordered pair (B,h) where B is a non-empty set and h is an injective unary function on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called configurations of the Dedekind algebra. There are N0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on omega called its configuration signature. The configuration signature of a Dedekind algebra counts the number of configurations in the decomposition of (...)
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  39.  13
    Graph structure and monadic second-order logic: a language-theoretic approach.B. Courcelle - 2012 - New York: Cambridge University Press. Edited by Joost Engelfriet.
    The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The author not only provides a thorough (...)
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  40.  36
    Second-order wave equation for spin-1/2 fields: 8-Spinors and canonical formulation.Nicola Cufaro-Petroni, Philippe Gueret & Jean-Pierre Vigier - 1988 - Foundations of Physics 18 (11):1057-1075.
    The algebraic structure of the 8-spinor formalism is discussed, and the general form of the 8-component wave equation, equivalent to the second-order 4-component one, is presented. This allows a canonical formulation that will be the first stage of the future Clebsch parametrization, i.e., a relativistic generalization of the Bohm-Schiller-Tiomno pioneering work on the Pauli equation.
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  41.  14
    Conceptual Distance and Algebras of Concepts.Mohamed Khaled & Gergely Székely - forthcoming - Review of Symbolic Logic:1-16.
    We show that the conceptual distance between any two theories of first-order logic is the same as the generator distance between their Lindenbaum–Tarski algebras of concepts. As a consequence of this, we show that, for any two arbitrary mathematical structures, the generator distance between their meaning algebras (also known as cylindric set algebras) is the same as the conceptual distance between their first-order logic theories. As applications, we give a complete description for the distances between meaning algebras corresponding to (...)
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  42.  20
    An Algebraic Analysis of Normative Systems.Lars Lindahl & Jan Odelstad - 2000 - Ratio Juris 13 (3):261-278.
    In the present paper we study how subsystems of a normative system can be combined, and the role of such combinations for the understanding of hypothetical legal consequences. A combination of two subsystems is often accomplished by a normative correlation or an intermediate concept. To obtain a detailed analysis of such phenomena we use an algebraic framework. Normative systems are represented as algebraic structures over sets of conditions. This representation makes it possible to study normative systems using (...)
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  43.  30
    Algebraic Models of Mental Number Axes: Part II.Wojciech Krysztofiak - 2016 - Axiomathes 26 (2):123-155.
    The paper presents a formal model of the system of number representations as a multiplicity of mental number axes with a hierarchical structure. The hierarchy is determined by the mind as it acquires successive types of mental number axes generated by virtue of some algebraic mechanisms. Three types of algebraic structures, responsible for functioning these mechanisms, are distinguished: BASAN-structures, CASAN-structures and CAPPAN-structures. A foundational order holds between these structures. CAPPAN-structures are derivative from (...)
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  44.  16
    Undecidable Varieties of Semilattice—ordered Semigroups, of Boolean Algebras with Operators, and logics extending Lambek Calculus.A. Kurucz, I. Nemeti, I. Sain & A. Simon - 1993 - Logic Journal of the IGPL 1 (1):91-98.
    We prove that the equational theory of a semigroups becomes undecidable if we add a semilattice structure with a ‘touch of symmetric difference’. As a corollary we obtain that the variety of all Boolean algebras with an associative binary operator has a ‘hereditarily’ undecidable equational theory. Our results have implications in logic, e.g. they imply undecidability of modal logics extending the Lambek Calculus and undecidability of Arrow Logics with an associative arrow modality.
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  45. Definable sets in Boolean ordered o-minimal structures. II.Roman Wencel - 2003 - Journal of Symbolic Logic 68 (1):35-51.
    Let (M, ≤,...) denote a Boolean ordered o-minimal structure. We prove that a Boolean subalgebra of M determined by an algebraically closed subset contains no dense atoms. We show that Boolean algebras with finitely many atoms do not admit proper expansions with o-minimal theory. The proof involves decomposition of any definable set into finitely many pairwise disjoint cells, i.e., definable sets of an especially simple nature. This leads to the conclusion that Boolean ordered structures with o-minimal theories (...)
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  46.  29
    On the maximality of logics with approximations.José Iovino - 2001 - Journal of Symbolic Logic 66 (4):1909-1918.
    In this paper we analyze some aspects of the question of using methods from model theory to study structures of functional analysis.By a well known result of P. Lindström, one cannot extend the expressive power of first order logic and yet preserve its most outstanding model theoretic characteristics (e.g., compactness and the Löwenheim-Skolem theorem). However, one may consider extending the scope of first order in a different sense, specifically, by expanding the class of structures that are regarded as (...)
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  47.  44
    Definable sets in Boolean-ordered o-minimal structures. I.Ludomir Newelski & Roman Wencel - 2001 - Journal of Symbolic Logic 66 (4):1821-1836.
    We prove weak elimination of imaginary elements for Boolean orderings with finitely many atoms. As a consequence we obtain equivalence of the two notions of o-minimality for Boolean ordered structures, introduced by C. Toffalori. We investigate atoms in Boolean algebras induced by algebraically closed subsets of Boolean ordered structures. We prove uniqueness of prime models in strongly o-minimal theories of Boolean ordered structures.
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  48.  20
    Nondefinability results with entire functions of finite order in polynomially bounded o-minimal structures.Hassan Sfouli - 2024 - Archive for Mathematical Logic 63 (3):491-498.
    Let \({\mathcal {R}}\) be a polynomially bounded o-minimal expansion of the real field. Let _f_(_z_) be a transcendental entire function of finite order \(\rho \) and type \(\sigma \in [0,\infty ]\). The main purpose of this paper is to show that if ( \(\rho ) or ( \(\rho =1\) and \(\sigma =0\) ), the restriction of _f_(_z_) to the real axis is not definable in \({\mathcal {R}}\). Furthermore, we give a generalization of this result for any \(\rho \in [0,\infty )\).
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  49.  20
    Truth and Falsehood: An Inquiry Into Generalized Logical Values.Yaroslav Shramko & Heinrich Wansing - 2011 - Dordrecht, Netherland: Springer.
    The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...)
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  50. D-algebras.Stanley Gudder - 1996 - Foundations of Physics 26 (6):813-822.
    A D-algebra is a generalization of a D-poset in which a partial order is not assumed. However, if a D-algebra is equipped with a natural partial order, then it becomes a D-poset. It is shown that D-algebras and effect algebras are equivalent algebraic structures. This places the partial operation ⊝ for a D-algebra on an equal footing with the partial operation ⊕ for an effect algebra. An axiomatic structure called an effect stale-space is introduced. Such spaces provide an (...)
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