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Cut approach to invariance groups of lattice-valued functions. (English) Zbl 1420.06022

Summary: This paper deals with lattice-valued \(n\)-variable functions on a \(k\)-element domain, considered as a generalization of lattice-valued Boolean functions. We investigate invariance groups of these functions, i.e., the group of such permutations that leaves the considered function invariant. We show that the invariance groups of lattice-valued functions depend only on the cuts of the function. Furthermore, we construct such lattice-valued Boolean function (and its generalization), the cuts of which represent all representable invariance groups.

MSC:

06E30 Boolean functions
06E75 Generalizations of Boolean algebras
03B50 Many-valued logic

Software:

JBool
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Full Text: DOI

References:

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