A discriminator variety of Gödel algebras with operators arising in quantum computation

GIUNTINI, ROBERTO;FREYTES, HECTOR CARLOS;LEDDA, ANTONIO;PAOLI, FRANCESCO

2009-01-01

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Abstract

In order to appropriately model the strong quantum computational logic of Cattaneo et al., we introduce an expansion of p′ quasi-MV al- gebras by lattice operations and a G¨odel-like implication. We call the resulting algebras G¨odel quantum computational algebras, and we show that every such algebra arises as a pair algebra over a Heyting-Wajsberg algebra. After proving a standard completeness theorem, we prove that G¨odel quantum computational algebras form a discriminator variety and we point out some consequence threoef