On the orthogonalization of arbitrary Boolean formulae.
Bruni, Renato (2005)
Journal of Applied Mathematics and Decision Sciences
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Bruni, Renato (2005)
Journal of Applied Mathematics and Decision Sciences
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Abad Manuel, Cimadamore Cecilia, Díaz Varela José (2009)
Open Mathematics
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In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.
Paul R. Halmos (1954-1956)
Compositio Mathematica
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Denecke, K. (1991)
Acta Mathematica Universitatis Comenianae. New Series
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Slobodan Vujošević (1989)
Publications de l'Institut Mathématique
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Janusz Czelakowski (1981)
Colloquium Mathematicae
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Sergiu Rudeanu (1998)
Mathware and Soft Computing
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An abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].
Enric Trillas, Susana Cubillo (1996)
Mathware and Soft Computing
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In a Boolean Algebra B, an inequality f(x,x --> y)) ≤ y satisfying the condition f(1,1)=1, is considered for defining operations a --> b among the elements of B. These operations are called Conditionals'' for f. In this paper, we obtain all the boolean Conditionals and Internal Conditionals, and some of their properties as, for example, monotonicity are briefly discussed.