Discussiones
Mathematicae General Algebra and Applications 22(2) (2002)
183198
doi: 10.7151/dmgaa.1057
QUASIIMPLICATION ALGEBRAS
Ivan Chajda and Kamil Dusek
Department of Algebra and Geometry
Palacký University of Olomouc
Tomkova 40, CZ77900 Olomouc, Czech Republic
email: chajda@risc.upol.cz
Abstract
A quasiimplication algebra is introduced as an algebraic counterpart of an implication reduct of
propositional logic having noninvolutory negation (e.g. intuitionistic logic). We show that every
pseudocomplemented semilattice induces a quasiimplication algebra (but not conversely). On the other hand, a
more general algebra, a socalled pseudocomplemented qsemilattice is introduced and a mutual correspondence
between this algebra and a quasiimplication algebra is shown.
Keywords: implication, noninvolutory negation, quasiimplication algebra, implitcation algebra,
pseudocomplemented semilattice, qsemilattice.
2000 Mathematics Subject Classification: 03G25, 06A12, 06D15.
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Received 10 October 2002
Revised 23 January 2003