Results for 'AL*‐algebra'

910 found
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  1.  80
    A Generalization of the Łukasiewicz Algebras.Teresa Almada & JÚlia Vaz de Carvalho - 2001 - Studia Logica 69 (3):329 - 338.
    We introduce the variety $\scr{L}_{n}^{m}$ , m ≥ 1 and n ≥ 2, of m-generalized Łukasiewicz algebras of order n and characterize its subdirectly irreducible algebras. The variety $\scr{L}_{n}^{m}$ is semisimple, locally finite and has equationally definable principal congruences. Furthermore, the variety $\scr{L}_{n}^{m}$ contains the variety of Łukasiewicz algebras of order n.
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  2.  8
    Computational Thinking and The Algebra Project.Alan Shaw, Brian R. Lawler, William Crombie, Tom McKlin & Tamika Richards - 2023 - Prometeica - Revista De Filosofía Y Ciencias 27:565-574.
    Through our work to examine mathematical and computational learning in authentic and convivial contexts that requires creativity, imagination, reasoning, and discourse, we have theorized an experiential learning cycle that attends to the development of voice, agency, and identity needed in young people for an earned insurgency—the right to demand change. Our work underscores how the current situation that many students face in classrooms amounts to a type of cognitive segregation that denies these students access to authentic and empowering intellectual agency. (...)
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  3.  37
    Subprevarieties Versus Extensions. Application to the Logic of Paradox.Alexej P. Pynko - 2000 - Journal of Symbolic Logic 65 (2):756-766.
    In the present paper we prove that the poset of all extensions of the logic defined by a class of matrices whose sets of distinguished values are equationally definable by their algebra reducts is the retract, under a Galois connection, of the poset of all subprevarieties of the prevariety generated by the class of the algebra reducts of the matrices involved. We apply this general result to the problem of finding and studying all extensions of the logic of paradox. In (...)
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  4.  29
    The Embedding Theorem: Its Further Developments and Consequences. Part 1.Alexei Y. Muravitsky - 2006 - Notre Dame Journal of Formal Logic 47 (4):525-540.
    We outline the Gödel-McKinsey-Tarski Theorem on embedding of Intuitionistic Propositional Logic Int into modal logic S4 and further developments which led to the Generalized Embedding Theorem. The latter in turn opened a full-scale comparative exploration of lattices of the (normal) extensions of modal propositional logic S4, provability logic GL, proof-intuitionistic logic KM, and others, including Int. The present paper is a contribution to this part of the research originated from the Gödel-McKinsey-Tarski Theorem. In particular, we show that the lattice ExtInt (...)
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  5. Relation Algebras by Games.I. Hodkinson & Robin Hirsch - 2004 - Studia Logica 77 (1):139-141.
  6.  25
    Perfect MV-Algebras Are Categorically Equivalent to Abelian l-Groups.Antonio Di Nola & Ada Lettieri - 1994 - Studia Logica 53 (3):417-432.
    In this paper we prove that the category of abelian l-groups is equivalent to the category of perfect MV-algebras. Furthermore, we give a finite equational axiomatization of the variety generated by perfect MV-algebras.
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  7.  31
    Babylonian algebra: Form VS. content.O. Neugebauer - 1971 - Studies in History and Philosophy of Science Part A 1 (4):369-380.
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  8.  54
    Frames and MV-Algebras.Lawrence P. Belluce & Antonio Di Nola - 2005 - Studia Logica 81 (3):357 - 385.
    We describe a class of MV-algebras which is a natural generalization of the class of "algebras of continuous functions". More specifically, we're interested in the algebra of frame maps $Hom_{\scr{F}}(\Omega (A),\text{K})$ in the category $\scr{F}$ of frames, where A is a topological MV-algebra, Ω(A) the lattice of open sets of A, and K an arbitrary frame. Given a topological space X and a topological MV-algebra A, we have the algebra C(X, A) of continuous functions from X to A. We can (...)
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  9.  24
    Exponentiations over the universal enveloping algebra of s l 2.Sonia L’Innocente, Angus Macintyre & Françoise Point - 2010 - Annals of Pure and Applied Logic 161 (12):1565-1580.
    We construct, by model-theoretic methods, several exponentiations on the universal enveloping algebra U of the Lie algebra.
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  10.  4
    L'algebra By Rafael Bombelli; Federigo Enriques. [REVIEW]A. Pogo - 1930 - Isis 14:425-426.
  11.  12
    Logic in Algebraic Form. Three Languages and Theories.Stephen D. Comer - 1977 - Journal of Symbolic Logic 42 (1):108-109.
  12.  36
    Functions definable in Sugihara algebras and their fragments. II.Marek Tokarz - 1976 - Studia Logica 35:279.
  13.  21
    Reconstructing Bohr’s Reply to EPR in Algebraic Quantum Theory.Ozawa Masanao & Yuichiro Kitajima - 2012 - Foundations of Physics 42 (4):475-487.
    Halvorson and Clifton have given a mathematical reconstruction of Bohr’s reply to Einstein, Podolsky and Rosen, and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr’s reply. In the present paper, we generalize the above consistency theorem, with a rather elementary proof, (...)
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  14.  11
    Independent Families in Complete Boolean Algebras.B. Balcar, F. Franek, Bohuslav Balcar, Jan Pelant, Petr Simon & Boban Velickovic - 2002 - Bulletin of Symbolic Logic 8 (4):554-554.
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  15. Properties of forking in {$ømega$}-free pseudo-algebraically closed fields.Zoé Chatzidakis - 2002 - Journal of Symbolic Logic 67 (3):957-996.
  16.  79
    Continuum Cardinals Generalized to Boolean Algebras.J. Donald Monk - 2001 - Journal of Symbolic Logic 66 (4):1928-1958.
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  17.  21
    Decidable Regularly Closed Fields of Algebraic Numbers.Lou van den Dries & Rick L. Smith - 1985 - Journal of Symbolic Logic 50 (2):468 - 475.
  18.  17
    Victor J. Katz and Karen Hunger Parshall, Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century. Princeton: Princeton University Press, 2014. Pp. xiii + 485. ISBN 978-0-691-14905-9. £34.95. [REVIEW]Christopher Hollings - 2015 - British Journal for the History of Science 48 (4):687-689.
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  19.  37
    Logical reduction of relations: From relational databases to Peirce’s reduction thesis.Sergiy Koshkin - 2023 - Logic Journal of the IGPL 31.
    We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of predicate calculus. Our algebraic framework unifies natural joins and data dependencies of database theory and relational algebra of clone theory with the bond algebra of C.S. Peirce. We also offer new constructions of reductions, systematically study irreducible relations and reductions to them and introduce a new characteristic of (...)
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  20.  12
    An Algebraic Proof of Completeness for Monadic Fuzzy Predicate Logic.Jun Tao Wang & Hongwei Wu - forthcoming - Review of Symbolic Logic:1-27.
    Monoidal t-norm based logic $\mathbf {MTL}$ is the weakest t-norm based residuated fuzzy logic, which is a $[0,1]$ -valued propositional logical system having a t-norm and its residuum as truth function for conjunction and implication. Monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ that consists of the formulas with unary predicates and just one object variable, is the monadic fragment of fuzzy predicate logic $\mathbf {MTL\forall }$, which is indeed the predicate version of monoidal t-norm based logic $\mathbf {MTL}$. The main (...)
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  21. Intuitionistic Modal Algebras.Sergio A. Celani & Umberto Rivieccio - 2024 - Studia Logica 112 (3):611-660.
    Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations (...)
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  22.  10
    Operator algebras and quantum logic.Miklós Rédei - 2004 - In Paul Weingartner (ed.), Alternative Logics: Do Sciences Need Them? Dordrecht: Springer. pp. 349-360.
    Let K = (p, q...; &, ∨, ~) be a zeroth-order formal language with sentence variables p, q..., two place connectives & (and), ∨ (or) and negation sign ~, and let F be the formula algebra (set of well-formed formulas in K defined in the standard way by induction from the sentence variables). If v is an assignment of truth values 1(true), 0(f alse) to the sentence variables p, q..., then classical propositional logic is characterized by extending v by induction (...)
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  23. Table Des matieres editorial preface 3.Jair Minoro Abe, Curry Algebras Pt, Paraconsistent Logic, Newton Ca da Costa, Otavio Bueno, Jacek Pasniczek, Beyond Consistent, Complete Possible Worlds, Vm Popov & Inverse Negation - 1998 - Logique Et Analyse 41:1.
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  24.  6
    Algebra and logic: papers from the 1974 summer research institute of the Australian Mathematical Society, Monash University, Australia.John N. Crossley (ed.) - 1975 - New York: Springer Verlag.
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  25.  22
    An Algebraic Proof of Completeness for Monadic Fuzzy Predicate Logic Mmtl∀ – Erratum.Juntao Wang, W. U. Hongwei, H. E. Pengfei & S. H. E. Yanhong - forthcoming - Review of Symbolic Logic:1-1.
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  26. Using process algebra to describe human and software behaviors.Yingxu Wang - 2003 - Brain and Mind 4 (2):199-213.
    Although there are various ways to express actions and behaviors in natural languages, it is found in cognitive informatics that human and system behaviors may be classified into three basic categories: to be , to have , and to do . All mathematical means and forms, in general, are an abstract description of these three categories of system behaviors and their common rules. Taking this view, mathematical logic may be perceived as the abstract means for describing to be, set theory (...)
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  27.  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 of and (...)
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  28.  17
    Congruences and Kernel Ideals on a Subclass of Ockham Algebras.Xue-Ping Wang & Lei-Bo Wang - 2015 - Studia Logica 103 (4):713-731.
    In this note, it is shown that the set of kernel ideals of a K n, 0-algebra L is a complete Heyting algebra, and the largest congruence on L such that the given kernel ideal as its congruence class is derived and finally, the necessary and sufficient conditions that such a congruence is pro-boolean are given.
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  29.  28
    Closure extended double stone algebras.Lei-Bo Wang - 2013 - Bulletin of the Section of Logic 42 (1/2):69-81.
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  30.  14
    Gödel algebras free over finite distributive lattices.Stefano Aguzzoli, Brunella Gerla & Vincenzo Marra - 2008 - Annals of Pure and Applied Logic 155 (3):183-193.
    Gödel algebras form the locally finite variety of Heyting algebras satisfying the prelinearity axiom =. In 1969, Horn proved that a Heyting algebra is a Gödel algebra if and only if its set of prime filters partially ordered by reverse inclusion–i.e. its prime spectrum–is a forest. Our main result characterizes Gödel algebras that are free over some finite distributive lattice by an intrisic property of their spectral forest.
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  31.  17
    Two comments on the vacuum in algebraic quantum field theory.Miklós Rédei - 2002 - In Meinard Kuhlmann, Holger Lyre & Andrew Wayne (eds.), Ontological Aspects of Quantum Field Theory. Singapore: World Scientific.
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  32.  50
    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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  33.  59
    Grundzüge der theoretischen Logik.David Hilbert & Wilhelm Ackermann - 1972 - Berlin,: Springer. Edited by W. Ackermann.
    Die theoretische Logik, auch mathematische oder symbolische Logik genannt, ist eine Ausdehnung der fonnalen Methode der Mathematik auf das Gebiet der Logik. Sie wendet fUr die Logik eine ahnliche Fonnel­ sprache an, wie sie zum Ausdruck mathematischer Beziehungen schon seit langem gebrauchlich ist. In der Mathematik wurde es heute als eine Utopie gelten, wollte man beim Aufbau einer mathematischen Disziplin sich nur der gewohnlichen Sprache bedienen. Die groBen Fortschritte, die in der Mathematik seit der Antike gemacht worden sind, sind zum (...)
  34. Multiversism and Concepts of Set: How Much Relativism Is Acceptable?Neil Barton - 2016 - In Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics. Cham, Switzerland: Springer International Publishing. pp. 189-209.
    Multiverse Views in set theory advocate the claim that there are many universes of sets, no-one of which is canonical, and have risen to prominence over the last few years. One motivating factor is that such positions are often argued to account very elegantly for technical practice. While there is much discussion of the technical aspects of these views, in this paper I analyse a radical form of Multiversism on largely philosophical grounds. Of particular importance will be an account of (...)
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  35. Ghost world: A context for Frege's context principle.Mark Wilson - 2005 - In Michael Beaney & Erich H. Reck (eds.), Gottlob Frege: Frege's philosophy of mathematics. London: Routledge. pp. 157-175.
    There is considerable likelihood that Gottlob Frege began writing his Foundations of Arithmetic with the expectation that he could introduce his numbers, not with sets, but through some algebraic techniques borrowed from earlier writers of the Gottingen school. These rewriting techniques, had they worked, would have required strong philosophical justification provided by Frege's celebrated "context principle," which otherwise serves little evident purpose in the published Foundations.
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  36.  22
    Glivenko sequent classes and constructive cut elimination in geometric logics.Giulio Fellin, Sara Negri & Eugenio Orlandelli - 2023 - Archive for Mathematical Logic 62 (5):657-688.
    A constructivisation of the cut-elimination proof for sequent calculi for classical, intuitionistic and minimal infinitary logics with geometric rules—given in earlier work by the second author—is presented. This is achieved through a procedure where the non-constructive transfinite induction on the commutative sum of ordinals is replaced by two instances of Brouwer’s Bar Induction. The proof of admissibility of the structural rules is made ordinal-free by introducing a new well-founded relation based on a notion of embeddability of derivations. Additionally, conservativity for (...)
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  37. Review: V. I. Sestakov, An Algebraic Method for the Synthesis of Switching Circuits. [REVIEW]Andrzej Wakulicz - 1957 - Journal of Symbolic Logic 22 (2):221-221.
  38. The Non-categoricity of Logic (I). The Problem of a Full Formalization (in Romanian).Constantin C. Brîncuș - 2022 - Probleme de Logică (Problems of Logic) (1):137-156.
    A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires in addition the preservation of the standard (...)
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  39.  78
    Neutrosophic quadruple algebraic hyperstructures.A. A. A. Agboola, B. Davvaz & Florentin Smarandache - 2017 - Annals of Fuzzy Mathematics and Informatics 14.
    The objective of this paper is to develop neutrosophic quadruple algebraic hyperstructures. Specifically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them.
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  40.  29
    Almutairi's C ritical C ultural C ompetence model for a multicultural healthcare environment.Adel F. Almutairi, V. Susan Dahinten & Patricia Rodney - 2015 - Nursing Inquiry 22 (4):317-325.
    The increasing demographic changes of populations in many countries require an approach for managing the complexity of sociocultural differences. Such an approach could help healthcare organizations to address healthcare disparities and inequities, and promote cultural safety for healthcare providers and patients alike. Almutairi's critical cultural competence (CCC) is a comprehensive approach that holds great promise for managing difficulties arising from sociocultural and linguistic issues during cross‐cultural interactions.CCChas addressed the limitations of many other cultural competence approaches that have been discussed in (...)
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  41.  37
    Varieties of BL-Algebras III: Splitting Algebras.Paolo Aglianó - 2019 - Studia Logica 107 (6):1235-1259.
    In this paper we investigate splitting algebras in varieties of logics, with special consideration for varieties of BL-algebras and similar structures. In the case of the variety of all BL-algebras a complete characterization of the splitting algebras is obtained.
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  42.  9
    Algebra of Approximate Computation.Karl Aberer - 1995 - In Erwin Engeler (ed.), The combinatory programme. Boston: Birkhäuser. pp. 77--96.
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  43. Curry algebras Pτ.J. M. Abe - 1998 - Logique Et Analyse 161:5-15.
     
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  44.  31
    Algebras of sentences.Tarek Sayed Ahmed - 2006 - Bulletin of the Section of Logic 35 (1):1-10.
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  45.  7
    Algebraic independence in an infinite Steiner triple system.Abraham Goetz - 1967 - Notre Dame Journal of Formal Logic 8 (1-2):51-55.
  46.  23
    Tarski Alfred. Axiomatic and algebraic aspects of two theorems on sums of cardinals. Ebd., S. 79–104.W. Ackermann - 1950 - Journal of Symbolic Logic 14 (4):257-258.
  47.  17
    Cut elimination for coherent theories in negation normal form.Paolo Maffezioli - 2024 - Archive for Mathematical Logic 63 (3):427-445.
    We present a cut-free sequent calculus for a class of first-order theories in negation normal form which include coherent and co-coherent theories alike. All structural rules, including cut, are admissible.
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  48.  28
    Free Double Ockham Algebras.Manuel Abad & J. Patricio Díaz Varela - 1999 - Journal of Applied Non-Classical Logics 9 (1):173-183.
    The variety O2 of double Ockham algebras consists of the algebras (A ∨, ∧, f,g 0,1) of type (2,2,1,1,0,0) where (A; ∨, ∧,f, 0,1) and (A; ∨, ∧,g 0,1) are Ockham algebras. In [16], M. Sequeira introduced several subvarieties of O2. In this paper we give a construction of free double Ockham algebras on a partially ordered set. We also describe free objects for the subvarieties of O2 considered in [16].
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  49.  50
    A note on the enumeration degrees of 1-generic sets.Liliana Badillo, Caterina Bianchini, Hristo Ganchev, Thomas F. Kent & Andrea Sorbi - 2016 - Archive for Mathematical Logic 55 (3):405-414.
    We show that every nonzero $${\Delta^{0}_{2}}$$ enumeration degree bounds the enumeration degree of a 1-generic set. We also point out that the enumeration degrees of 1-generic sets, below the first jump, are not downwards closed, thus answering a question of Cooper.
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  50.  38
    Free‐decomposability in varieties of semi‐Heyting algebras.Manuel Abad, Juan Manuel Cornejo & Patricio Díaz Varela - 2012 - Mathematical Logic Quarterly 58 (3):168-176.
    In this paper we prove that the free algebras in a subvariety equation image of the variety equation image of semi-Heyting algebras are directly decomposable if and only if equation image satisfies the Stone identity.
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