Discussiones Mathematicae General Algebra and Applications 22(2) (2002) 183-198
doi: 10.7151/dmgaa.1057

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Ivan Chajda and Kamil Dusek

Department of Algebra and Geometry
Palacký University of Olomouc
Tomkova 40, CZ-77900 Olomouc, Czech Republic
e-mail: chajda@risc.upol.cz


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.

2000 Mathematics Subject Classification: 03G25, 06A12, 06D15.


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Received 10 October 2002
Revised 23 January 2003