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Wyszukujesz frazę "Heyting algebra" wg kryterium: Temat

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    Wyświetlanie 1-5 z 5
    Tytuł:
    Semi-Heyting Algebras and Identities of Associative Type
    Autorzy:
    Cornejo, Juan M.
    Sankappanavar, Hanamantagouda P.
    Powiązania:
    https://bibliotekanauki.pl/articles/749914.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    semi-Heyting algebra
    Heyting algebra
    identity of associative type
    subvariety of associative type
    Opis:
    An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ (x → y) ≈ x ∧ y, x ∧ (y → z) ≈ x ∧ [(x ∧ y) → (x ∧ z)], and x → x ≈ 1. ℋ denotes the variety of semi-Heyting algebras. Semi-Heyting algebras were introduced by the second author as an abstraction from Heyting algebras.  They share several important properties with Heyting algebras.  An identity of associative type of length 3 is a groupoid identity, both sides of which contain the same three (distinct) variables that occur in any order and that are grouped in one of the two (obvious) ways. A subvariety of ℋ is of associative type of length 3 if it is defined by a single identity of associative type of length 3. In this paper we describe all the distinct subvarieties of the variety ℋ of asociative type of length 3.  Our main result shows that there are 3 such subvarities of ℋ.
    Źródło:
    Bulletin of the Section of Logic; 2019, 48, 2
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On k-cyclic SHn-algebra
    Autorzy:
    Fernandez, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/200167.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    de Morgan algebra
    Łukasiewicz algebras
    Heyting algebra
    Lattices and duality
    Opis:
    In this work we consider a new class of algebra called k-cyclic SHn-algebra (A, T) where A is an SHn-algebra and T is a lattice endomorphism such that Tk(x) = x, for all x, k is a positive integer. The main goal of this paper is to show a Priestley duality theorem for k-cyclic SHn-algebra.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2011, 59, 3; 303-304
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Equimorphy in varieties of double Heyting algebras
    Autorzy:
    Koubek, V.
    Sichler, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/966055.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    categorical universality
    variety
    double Heyting algebra
    endomorphism monoid
    equimorphy
    Opis:
    We show that any finitely generated variety V of double Heyting algebras is finitely determined, meaning that for some finite cardinal n(V), any class $\Cal S$ ⊆ V consisting of algebras with pairwise isomorphic endomorphism monoids has fewer than n(V) pairwise non-isomorphic members. This result complements the earlier established fact of categorical universality of the variety of all double Heyting algebras, and contrasts with categorical results concerning finitely generated varieties of distributive double p-algebras.
    Źródło:
    Colloquium Mathematicum; 1998, 77, 1; 41-58
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Preserving Filtering Unification by Adding Compatible Operations to Some Heyting Algebras
    Autorzy:
    Dzik, Wojciech
    Radeleczki, Sándor
    Powiązania:
    https://bibliotekanauki.pl/articles/749994.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    filtering unification
    compatible operation
    intuitionistic logic
    Heyting algebra
    residuated lattice
    Opis:
    We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x ⋁ ¬¬x = 1, preserves filtering (or directed) unification, that is, the property that for every two unifiers there is a unifier more general then both of them. Contrary to that, often adding new operations to algebras results in changing the unification type. To prove the results we apply the theorems of [9] on direct products of l-algebras and filtering unification. We consider examples of frontal Heyting algebras, in particular Heyting algebras with the successor, γ and G operations as well as expansions of some commutative integral residuated lattices with successor operations.
    Źródło:
    Bulletin of the Section of Logic; 2016, 45, 3/4
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Quantum geometry, logic and probability
    Autorzy:
    Majid, Shahn
    Powiązania:
    https://bibliotekanauki.pl/articles/1047619.pdf
    Data publikacji:
    2020-12-29
    Wydawca:
    Copernicus Center Press
    Tematy:
    logic
    noncommutative geometry
    digital geometry
    quantum gravity
    duality
    power set
    Heyting algebra
    Opis:
    Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these ‘lattice spacing’ weights do not have to be independent of the direction of the arrow. We use this greater freedom to give a quantum geometric interpretation of discrete Markov processes with transition probabilities as arrow weights, namely taking the diffusion form ∂+f = (−Δθ + q − p)f for the graph Laplacian Δθ, potential functions q, p built from the probabilities, and finite difference ∂+ in the time direction. Motivated by this new point of view, we introduce a ‘discrete Schrödinger process’ as ∂+ψ = ı(−Δ + V )ψ for the Laplacian associated to a bimodule connection such that the discrete evolution is unitary. We solve this explicitly for the 2-state graph, finding a 1-parameter family of such connections and an induced ‘generalised Markov process’ for f = |ψ|2 in which there is an additional source current built from ψ. We also mention our recent work on the quantum geometry of logic in ‘digital’ form over the field F2 = {0, 1}, including de Morgan duality and its possible generalisations.
    Źródło:
    Zagadnienia Filozoficzne w Nauce; 2020, 69; 191-236
    0867-8286
    2451-0602
    Pojawia się w:
    Zagadnienia Filozoficzne w Nauce
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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