Geodesic
Quasi-implication algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 2, pp. 183-198

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A quasi-implication algebra is introduced as an algebraic counterpart of an implication reduct of propositional logic having non-involutory negation (e.g. intuitionistic logic). We show that every pseudocomplemented semilattice induces a quasi-implication algebra (but not conversely). On the other hand, a more general algebra, a so-called pseudocomplemented q-semilattice is introduced and a mutual correspondence between this algebra and a quasi-implication algebra is shown.
Keywords: implication, non-involutory negation, quasi-implication algebra, implitcation algebra, pseudocomplemented semilattice, q-semilattice 
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Chajda, Ivan; Dušek, Kamil. Quasi-implication algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 2, pp. 183-198. http://geodesic.mathdoc.fr/item/DMGAA_2002_22_2_a7/