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Quasi-implication algebras

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Chajda I., Dušek K.

Discussiones Mathematicae - General Algebra and Applications

2002

tom 22

nr 2

183-198

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.

Hilbert algebras as implicative partial semilattices

100%

Cīrulis J.

Open Mathematics

2007

tom 5

nr 2

264-279

The infimum of elements a and b of a Hilbert algebra are said to be the compatible meet of a and b, if the elements a and b are compatible in a certain strict sense. The subject of the paper will be Hilbert algebras equipped with the compatible meet operation, which normally is partial. A partial lower semilattice is shown to be a reduct of such an expanded Hilbert algebra i ?both algebras have the same ?lters.An expanded Hilbert algebra is actually an implicative partial semilattice (i.e., a relative subalgebra of an implicative semilattice),and conversely.The implication in an implicative partial semilattice is characterised in terms of ?lters of the underlying partial semilattice.

Ograniczanie wyników

1 Discussiones Mathematicae - General Algebra and Applications

1 Open Mathematics

1 Chajda I.

1 Cīrulis J.

1 Dušek K.

1 2007

1 2002

Wyniki wyszukiwania

Quasi-implication algebras

Hilbert algebras as implicative partial semilattices