A Discriminator Variety Of Goedel Algebras With Operators Arising In Quantum Computation

摘要

In order to appropriately model the strong quantum computational logic of Cattaneo et al., we introduce an expansion of '~(1/2) quasi-MV algebras by lattice operations and a Goedel-like implication. We call the resulting algebras Goedel 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 Goedel quantum computational algebras form a discriminator variety and we point out some consequences thereof.