Gödel numbers: a new approach to structured programming

The category of Gödel spaces GS (with strongly isotone maps as morphisms), which are dually equivalent to the category of Gödel algebras, is transferred by a contravariant functor H into the category M V ( C ) G of MV-algebras generated by perfect MV-...

It is introduced a new algebra $(A,\otimes ,\oplus ,\ast ,\rightharpoonup ,0,1)$ called $L_{P}G$-algebra if $(A,\otimes ,\oplus ,\ast ,0,1)$ is $L_P$-algebra (i.e. an algebra from the variety generated by perfect MV-algebras) and $(A,\rightharpoonup ,0,1)$ is a Gödel algebra (i.e. Heyting algebra satisfying the identity $(x\rightharpoonup \mathrm{...}\mathrm{}$${}_{}$$\mathrm{}\mathrm{}$$\mathrm{}\mathrm{}$${\mathbf{}}_{\mathbf{}}\mathbf{}$${}_{}$$\mathrm{}\mathrm{}$$\mathrm{}\mathrm{}$${}_{}$${}_{}$${}_{}$

In order to appropriately model the strong quantum computational logic of Cattaneo et al., we introduce an expansion of ^' quasi-MV algebras by lattice operations and a Godel-like implication. We call the resulting algebras Godel quantum computational ...