Results for 'Algebra'

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  1. Models, Algebras, and Proofs Selected Papers of the X Latin American Symposium on Mathematical Logic Held in Bogotá.Xavier Caicedo & Carlos Montenegro - 1998 - Crc Press.
    "Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts worldwide.".
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  2.  60
    Algebraic Methods in Philosophical Logic.J. Michael Dunn - 2001 - Oxford, England: Oxford University Press.
    This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects.
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  3.  36
    Algebraic and Topological Semantics for Inquisitive Logic Via Choice-Free Duality.Nick Bezhanishvili, Gianluca Grilletti & Wesley H. Holliday - 2019 - In Rosalie Iemhoff, Michael Moortgat & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation. WoLLIC 2019. Lecture Notes in Computer Science, Vol. 11541. Springer. pp. 35-52.
    We introduce new algebraic and topological semantics for inquisitive logic. The algebraic semantics is based on special Heyting algebras, which we call inquisitive algebras, with propositional valuations ranging over only the ¬¬-fixpoints of the algebra. We show how inquisitive algebras arise from Boolean algebras: for a given Boolean algebra B, we define its inquisitive extension H(B) and prove that H(B) is the unique inquisitive algebra having B as its algebra of ¬¬-fixpoints. We also show that inquisitive (...)
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  4. Algebraic Quantum Field Theory.Hans Halvorson & Michael Mueger - 2006 - In J. Butterfield & J. Earman (eds.), Handbook of the philosophy of physics. Kluwer Academic Publishers.
    Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, (...)
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  5.  8
    Algebraic Logic.H. Andréka, James Donald Monk & I. Németi - 1991 - North Holland.
    This volume is not restricted to papers presented at the 1988 Colloquium, but instead aims to provide the reader with a coherent reading on Algebraic Logic, with an emphasis on current research. To help the non-specialist reader, the book contains an introduction to cylindric and relation algebras by Roger D. Maddux and an introduction to Boolean Algebras by Bjarni Joacute;nsson.
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  6.  30
    Pseudomonadic Algebras as Algebraic Models of Doxastic Modal Logic.Nick Bezhanishvili - 2002 - Mathematical Logic Quarterly 48 (4):624-636.
    We generalize the notion of a monadic algebra to that of a pseudomonadic algebra. In the same way as monadic algebras serve as algebraic models of epistemic modal system S5, pseudomonadic algebras serve as algebraic models of doxastic modal system KD45. The main results of the paper are: Characterization of subdirectly irreducible and simple pseudomonadic algebras, as well as Tokarz's proper filter algebras; Ordertopological representation of pseudomonadic algebras; Complete description of the lattice of subvarieties of the variety of (...)
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  7.  5
    Algebraic Foundations of Many-Valued Reasoning.Roberto Cignoli - 1999 - Kluwer Academic Publishers.
    This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such (...)
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  8.  44
    The Algebra of Revolution: The Dialectic and the Classical Marxist Tradition.John Rees - 1998 - Routledge.
    The Algebra of Revolution is the first book to study Marxist method as it has been developed by the main representatives of the classical Marxist tradition, namely Marx and Engels, Luxembourg, Lenin, Lukacs, Gramsci, and Trotsky. This book provides the only single volume study of major Marxist thinkers' views on the crucial question of the dialectic, connecting them with pressing contemporary, political and theoretical questions. This title available in eBook format. Click here for more information . Visit our eBookstore (...)
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  9.  38
    Orthoimplication Algebras.J. C. Abbott - 1976 - Studia Logica 35 (2):173 - 177.
    Orthologic is defined by weakening the axioms and rules of inference of the classical propositional calculus. The resulting Lindenbaum-Tarski quotient algebra is an orthoimplication algebra which generalizes the author's implication algebra. The associated order structure is a semi-orthomodular lattice. The theory of orthomodular lattices is obtained by adjoining a falsity symbol to the underlying orthologic or a least element to the orthoimplication algebra.
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  10. The Algebra of Revolution: The Dialectic and the Classical Marxist Tradition.John Rees - 1998 - Routledge.
    _The Algebra of Revolution_ is the first book to study Marxist method as it has been developed by the main representatives of the classical Marxist tradition, namely Marx and Engels, Luxembourg, Lenin, Lukacs, Gramsci and Trotsky. This book provides the only single volume study of major Marxist thinkers' views on the crucial question of the dialectic, connecting them with pressing contemporary, political and theoretical questions. John Rees's _The Algebra of Revolution_ is vital reading for anyone interested in gaining (...)
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  11.  1
    An Algebraic Introduction to Mathematical Logic.D. W. Barnes - 1975 - New York, NY, USA: Springer Verlag.
    This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a sub stantial course on abstract algebra. Consequently, our treatment ofthe sub ject is algebraic. Although we assurne a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of . the exercises. (...)
  12.  49
    Algebraic Proofs of Cut Elimination.Jeremy Avigad - manuscript
    Algebraic proofs of the cut-elimination theorems for classical and intuitionistic logic are presented, and are used to show how one can sometimes extract a constructive proof and an algorithm from a proof that is nonconstructive. A variation of the double-negation translation is also discussed: if ϕ is provable classically, then ¬(¬ϕ)nf is provable in minimal logic, where θnf denotes the negation-normal form of θ. The translation is used to show that cut-elimination theorems for classical logic can be viewed as special (...)
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  13.  9
    Algebraic Methods in Philosophical Logic.J. Michael Dunn & Gary Hardegree - 2001 - Oxford, England: Oxford University Press UK.
    This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects.
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  14.  5
    Algebraic Semantics in Language and Philosophy.Godehard Link - 1998 - CSLI Publications.
    An analysis of the structural properties of collections or pluralities, homogeneous objects like water, and the semantics and philosophy of events.
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  15. The Algebra of Logic.Louis Couturat - 1914 - Open Court.
  16.  96
    Improving Algebraic Thinking Skill, Beliefs And Attitude For Mathematics Throught Learning Cycle Based On Beliefs.Widodo Winarso & Toheri - 2017 - Munich University Library.
    In the recent years, problem-solving become a central topic that discussed by educators or researchers in mathematics education. it’s not only as the ability or as a method of teaching. but also, it is a little in reviewing about the components of the support to succeed in problem-solving, such as student's belief and attitude towards mathematics, algebraic thinking skills, resources and teaching materials. In this paper, examines the algebraic thinking skills as a foundation for problem-solving, and learning cycle as a (...)
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  17. Algebraic Aggregation Theory.Perm C. Fishburn - unknown
    An aggregation procedure merges a list of objects into a representative object. This paper considers the problem of aggregating n rows in an n-by-m matrix into a summary row, where every entry is an element in an algebraic field. It focuses on consistent aggregators, which require each entry in the summary row to depend only on its column entries in the matrix and to be the same as the column entry if the column is constant. Consistent aggregators are related to (...)
     
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  18.  18
    Algebraic Analysis of Demodalised Analytic Implication.Antonio Ledda, Francesco Paoli & Michele Pra Baldi - 2019 - Journal of Philosophical Logic 48 (6):957-979.
    The logic DAI of demodalised analytic implication has been introduced by J.M. Dunn as a variation on a time-honoured logical system by C.I. Lewis’ student W.T. Parry. The main tenet underlying this logic is that no implication can be valid unless its consequent is “analytically contained” in its antecedent. DAI has been investigated both proof-theoretically and model-theoretically, but no study so far has focussed on DAI from the viewpoint of abstract algebraic logic. We provide several different algebraic semantics for DAI, (...)
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  19. Algebraic Foundations for the Semantic Treatment of Inquisitive Content.Floris Roelofsen - 2013 - Synthese 190:79-102.
    In classical logic, the proposition expressed by a sentence is construed as a set of possible worlds, capturing the informative content of the sentence. However, sentences in natural language are not only used to provide information, but also to request information. Thus, natural language semantics requires a logical framework whose notion of meaning does not only embody informative content, but also inquisitive content. This paper develops the algebraic foundations for such a framework. We argue that propositions, in order to embody (...)
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  20.  8
    The Algebraic Mind: Integrating Connectionism and Cognitive Science.Gary F. Marcus - 2001 - MIT Press.
    1 Cognitive Architectures 2 Multilayer Perceptrons 3 Relations between Variables 4 Structured Representations 5 Individuals 6 Where does the Machinery of Symbol Manipulation Come From? 7 Conclusions.
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  21. Algebraic Aspects of Deduction Theorems.Janusz Czelakowski - 1983 - Bulletin of the Section of Logic 12 (3):111-114.
    By a sentential logic we understand a pair, where S is a sentential language, i.e. an absolutely free algebra freely generated by an infinite set p, q, r,... of sentential variables and endowed with countably many finitary connectives §1, §2,... and C is a consequence operation on S, the underlying set of S, satisfying the condition of structurality: eC ⊆ C, for every endomorphism e of S and for every X ⊆ S. If no confusion is likely we shall (...)
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  22. Algebraic Methods of Mathematical Logic.Ladislav Rieger - 1967 - New York: Academic Press.
  23. Algebraic Methods in Philosophical Logic.J. Michael Dunn & Gary M. Hardegree - 2005 - Studia Logica 79 (2):305-306.
     
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  24.  74
    MV-Algebras and Quantum Computation.Antonio Ledda, Martinvaldo Konig, Francesco Paoli & Roberto Giuntini - 2006 - Studia Logica 82 (2):245-270.
    We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers.
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  25. Algebraic Methods in Philosophical Logic.J. Michael Dunn & Gary M. Hardegree - 2003 - Bulletin of Symbolic Logic 9 (2):231-234.
     
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  26. Toposes, Algebraic Geometry and Logic.Ionel Bucur & F. W. Lawvere - 1972
     
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  27. The Algebra of Negativity. Hegel, Heidegger and Their Legacy in the Contemporary Scenario.Francesca Brencio - 2021 - In Jan Knobloch Antonio Lucci (ed.), Gegen das Leben, gegen die Welt, gegen mich selbst. Figuren der Negativität. Heidelberg, Germania: pp. 117-132.
  28. An Algebraic Approach to Intuitionistic Connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.
    It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...)
     
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  29. Algebraic Semantics and Mixed Validities: A Reply to Cotnoir.Andrea Strollo - 2018 - Logique Et Analyse 61.
    Alethic pluralism holds that there are many ways of being true. Such a view has been challenged to make sense of the standard account of logical validity as necessary truth preservation. In this paper, the recent solution elaborated by Aaron Cotnoir, based on an algebraic approach, is shown to be untenable. Some reflections about the relation of many-valued logics with truth pluralism are also discussed.
     
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  30.  20
    An Algebraic and Kripke-Style Approach to a Certain Extension of Intuitionistic Logic.Cecylia Rauszer - 1980 - [Available From Ars Polona].
  31. The Algebra of Intensional Logics.Jon Michael Dunn - 1966 - Dissertation, University of Pittsburgh
     
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  32.  52
    Cylindric Algebras.Leon Henkin - 1971 - Amsterdam: North-Holland Pub. Co..
    Volume I provides a detailed analysis of cylindric algebras, starting with a formulation of their axioms and a development of their elementary properties, and proceeding to a deeper study of their interrelationships by means of general algebraic notions such as subalgebras, homomorphisms, direct products, free algebras, reducts and relativized algebras.
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  33. Algebraic Analysis of Entailment I.Robert K. Meyer & Richard Routley - 1972 - Logique Et Analyse 15 (59/60):407-428.
     
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  34.  61
    Álgebras booleanas, órdenes parciales y axioma de elección.Franklin Galindo - 2017 - Divulgaciones Matematicas 18 ( 1):34-54.
    El objetivo de este artículo es presentar una demostración de un teorema clásico sobre álgebras booleanas y ordenes parciales de relevancia actual en teoría de conjuntos, como por ejemplo, para aplicaciones del método de construcción de modelos llamado “forcing” (con álgebras booleanas completas o con órdenes parciales). El teorema que se prueba es el siguiente: “Todo orden parcial se puede extender a una única álgebra booleana completa (salvo isomorfismo)”. Donde extender significa “sumergir densamente”. Tal demostración se realiza utilizando cortaduras de (...)
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  35. Agglomerative Algebras.Jeremy Goodman - 2018 - Journal of Philosophical Logic 48 (4):631-648.
    This paper investigates a generalization of Boolean algebras which I call agglomerative algebras. It also outlines two conceptions of propositions according to which they form an agglomerative algebra but not a Boolean algebra with respect to conjunction and negation.
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  36.  82
    Algebraic Semantics for Modal Logics I.E. J. Lemmon - 1966 - Journal of Symbolic Logic 31 (1):46-65.
  37. Algebraic Logic and Predicate Functors.W. V. Quine - 1971 - [Indianapolis, Bobbs-Merrill.
  38.  16
    Algebraic Perspectives on Substructural Logics.Davide Fazio, Antonio Ledda & Francesco Paoli (eds.) - 2020 - Springer International Publishing.
    This volume presents the state of the art in the algebraic investigation into substructural logics. It features papers from the workshop AsubL (Algebra & Substructural Logics - Take 6). Held at the University of Cagliari, Italy, this event is part of the framework of the Horizon 2020 Project SYSMICS: SYntax meets Semantics: Methods, Interactions, and Connections in Substructural logics. -/- Substructural logics are usually formulated as Gentzen systems that lack one or more structural rules. They have been intensively studied (...)
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  39. Algebraic Substantivalism and the Hole Argument.Jonathan Bain - manuscript
    Algebraic substantivalism, as an interpretation of general relativity formulated in the Einstein algebra formalism, avoids the hole argument against manifold substantivalism. In this essay, I argue that this claim is well-founded. I first identify the hole argument as an argument against a specific form of semantic realism with respect to spacetime. I then consider algebraic substantivalism as an alternative form of semantic realism. In between, I justify this alternative form by reviewing the Einstein algebra formalism and indicating the (...)
     
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  40. Boolean Algebra as the Basis of Mathematical Logic.John-Michael Kuczynski - 2016 - Madison, WI, USA: Philosophypedia.
    The theorems of the propositional calculus and the predicate calculus are stated, and the analogous principles of Boolean Algebra are identified. Also, the primary principles of modal logic are stated, and a procedure is described for identifying their Boolean analogues.
     
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  41. ALGEBRA OF FUNDAMENTAL MEASUREMENTS AS A BASIS OF DYNAMICS OF ECONOMIC SYSTEMS.Sergiy Melnyk - 2012 - arXiv.
    We propose an axiomatic approach to constructing the dynamics of systems, in which one the main elements 9e8 is the consciousness of a subject. The main axiom is the statements that the state of consciousness is completely determined by the results of measurements performed on it. In case of economic systems we propose to consider an offer of transaction as a fundamental measurement. Transactions with delayed choice, discussed in this paper, represent a logical generalization of incomplete transactions and allow for (...)
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  42.  61
    Algebraic Kripke-Style Semantics for Relevance Logics.Eunsuk Yang - 2014 - Journal of Philosophical Logic 43 (4):803-826.
    This paper deals with one kind of Kripke-style semantics, which we shall call algebraic Kripke-style semantics, for relevance logics. We first recall the logic R of relevant implication and some closely related systems, their corresponding algebraic structures, and algebraic completeness results. We provide simpler algebraic completeness proofs. We then introduce various types of algebraic Kripke-style semantics for these systems and connect them with algebraic semantics.
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  43.  24
    An Algebraic Characterization of the Notion of Structural Completeness.Tadeusz Prucnal & Andrzej Wronski - 1974 - Bulletin of the Section of Logic 3 (1):30-33.
  44.  46
    Algebraic Semantics for Modal Logics II.E. J. Lemmon - 1966 - Journal of Symbolic Logic 31 (2):191-218.
  45.  23
    Mutually Algebraic Structures and Expansions by Predicates.Michael C. Laskowski - 2013 - Journal of Symbolic Logic 78 (1):185-194.
    We introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory $T$ is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model $M$ of $T$ has an expansion $(M,A)$ by a unary predicate with the finite cover property. We show that every structure has a maximal mutually algebraic reduct, and give a strong structure theorem for the class of elementary extensions of a fixed mutually algebraic (...)
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  46.  9
    Equality Algebras.Sándor Jenei - 2012 - Studia Logica 100 (6):1201-1209.
    A new structure, called equality algebras, will be introduced. It has two connectives, a meet operation and an equivalence, and a constant. A closure operator will be defined in the class of equality algebras, and we call the closed algebras equivalential. We show that equivalential equality algebras are term equivalent with BCK-algebras with meet. As a by-product, we obtain a quite general result, which is analogous to a result of Kabziński and Wroński: we provide an equational characterization for the equivalential (...)
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  47.  3
    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 that (...)
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  48. McKinsey Algebras and Topological Models of S4.1.Thomas Mormann - manuscript
    The aim of this paper is to show that every topological space gives rise to a wealth of topological models of the modal logic S4.1. The construction of these models is based on the fact that every space defines a Boolean closure algebra (to be called a McKinsey algebra) that neatly reflects the structure of the modal system S4.1. It is shown that the class of topological models based on McKinsey algebras contains a canonical model that can be (...)
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  49. Hyperboolean Algebras and Hyperboolean Modal Logic.Valentin Goranko & Dimiter Vakarelov - 1999 - Journal of Applied Non-Classical Logics 9 (2):345-368.
    Hyperboolean algebras are Boolean algebras with operators, constructed as algebras of complexes (or, power structures) of Boolean algebras. They provide an algebraic semantics for a modal logic (called here a {\em hyperboolean modal logic}) with a Kripke semantics accordingly based on frames in which the worlds are elements of Boolean algebras and the relations correspond to the Boolean operations. We introduce the hyperboolean modal logic, give a complete axiomatization of it, and show that it lacks the finite model property. The (...)
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  50.  22
    Predicative Algebraic Set Theory.Steve Awodey & Michael A. Warren - unknown
    In this paper the machinery and results developed in [Awodey et al, 2004] are extended to the study of constructive set theories. Specifically, we introduce two constructive set theories BCST and CST and prove that they are sound and complete with respect to models in categories with certain structure. Specifically, basic categories of classes and categories of classes are axiomatized and shown to provide models of the aforementioned set theories. Finally, models of these theories are constructed in the category of (...)
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