Generalizations of Boolean algebras. An attribute exploration
Léonard Kwuida, Christian Pech, Heiko Reppe (2006)
Mathematica Slovaca
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Léonard Kwuida, Christian Pech, Heiko Reppe (2006)
Mathematica Slovaca
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R. A. Herrmann (1979)
Matematički Vesnik
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R. Kaufman (1968)
Colloquium Mathematicae
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William A. Lampe (1974)
Colloquium Mathematicae
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Enric Trillas, Eloy Renedo, Claudi Alsina (2006)
Mathware and Soft Computing
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This short note shows that the scheme of disjunctive reasoning, , not , does not hold neither in proper ortholattices nor in proper de Morgan algebras. In both cases the scheme, once translated into the inequality , forces the structure to be a boolean algebra.
Robert Lagrange (1967)
Colloquium Mathematicae
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Wojciech Dzik, Sándor Radeleczki (2016)
Bulletin of the Section of Logic
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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...
Maronna, Ricardo (1964)
Portugaliae mathematica
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G. Rousseau (1970)
Fundamenta Mathematicae
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Leonardo Cabrer, Sergio Celani (2006)
Open Mathematics
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In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space. ...
Žarko Mijajlović (1979)
Publications de l'Institut Mathématique
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