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

Authors:
Roberto Giuntini;Hector Freytes;Antonio Ledda;Francesco Paoli
Affiliations:
Department of Education, University of Cagliari, Italy;Department of Education, University of Cagliari, Italy;Department of Education, University of Cagliari, Italy;Department of Education, University of Cagliari, Italy
Venue:
Fuzzy Sets and Systems
Year:
2009

Citing 6
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Quantum computation and quantum information

Quantum computation and quantum information
Algebraic Structures Related to Many Valued Logical Systems. Part I: Heyting Wajsberg Algebras

Fundamenta Informaticae
Algebraic Structures Related to Many Valued Logical Systems. Part II: Equivalence Among some Widespread Structures

Fundamenta Informaticae
On some properties of quasi-MV algebras and √{'} quasi-MV algebras. Part II

Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue (pp 315-357) "Ordered structures in many-valued logic"
Categorical Equivalences for ' quasi-MV Algebras*

Journal of Logic and Computation

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Abstract

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 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 Godel quantum computational algebras form a discriminator variety and we point out some consequences thereof.