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Construction of monadic three-valued Łukasiewicz algebras

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Abstract

The notion of monadic three-valued Łukasiewicz algebras was introduced by L. Monteiro ([12], [14]) as a generalization of monadic Boolean algebras. A. Monteiro ([9], [10]) and later L. Monteiro and L. Gonzalez Coppola [17] obtained a method for the construction of a three-valued Łukasiewicz algebra from a monadic Boolea algebra. In this note we give the construction of a monadic three-valued Łukasiewicz algebra from a Boolean algebra B where we have defined two quantification operations ∃ and ∃* such that ∃∀*x=∀*∃x (where ∀*x=-∃*-x). In this case we shall say that ∃ and ∃* commutes. If B is finite and ∃ is an existential quantifier over B, we shall show how to obtain all the existential quantifiers ∃* which commute with ∃.

Taking into account R. Mayet [3] we also construct a monadic three-valued Łukasiewicz algebra from a monadic Boolean algebra B and a monadic ideal I of B.

The most essential results of the present paper will be submitted to the XXXIX Annual Meeting of the Unión Matemática Argentina (October 1989, Rosario, Argentina).

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Authors and Affiliations

  1. INMABB-CONICET and Departamento de Matemática, Universidad Nacional del Sur, 8.000, Bahía Blanca, Argentina

    Luiz Monteiro, Sonia Savini & Julio Sewald

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  1. Luiz Monteiro
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  2. Sonia Savini
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  3. Julio Sewald
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Monteiro, L., Savini, S. & Sewald, J. Construction of monadic three-valued Łukasiewicz algebras. Stud Logica 50, 473–483 (1991). https://doi.org/10.1007/BF00370683

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