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Strongly involutive uninorm algebras. (English) Zbl 1288.03044
Summary: We investigate uninorm algebras satisfying a strong version of involutiveness. More precisely, we require that negation is an order reversing monoid isomorphism between the positive cone and the negative cone. A rather surprising consequence of this property is that the negative cones of these algebras are BL-algebras which do not admit MV-components with more than two elements. Among other things, we prove standard completeness and co-NP completeness of the logic corresponding to these algebras.

MSC:
03G25 Other algebras related to logic
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
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