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Epistemic Quantum Computational Structures in a Hilbert-space Environment

Beltrametti E., Dalla Chiara M. L., Giuntini R., Leporini R., Sergioli G.

Fundamenta Informaticae

2012

Vol. 115, nr 1

1-14

Quantum computation and quantum computational logics are intrinsically connected with some puzzling epistemic problems. In the framework of a quantum computational approach to epistemic logic we investigate the following question: is it possible to interpret the basic epistemic operations (having information, knowing) as special kinds of Hilbert-space operations? We show that non-trivial knowledge operations cannot be represented by unitary operators. We introduce the notions of strong epistemic quantum computational structure and of epistemic quantum computational structure, where knowledge operations are identified with special examples of quantum operations. This represents the basic tool for developing an epistemic quantum computational semantics, where epistemic sentences (like "Alice knows that the spin-value in the x-direction is up") are interpreted as quantum pieces of information that may be stored by quantum objects.

Algebraic Structures Related to Many Valued Logical Systems. Part 2, Equivalence Among some Widespread Structures

Cattaneo G., Ciucci D., Giuntini R., Konig M.

Fundamenta Informaticae

2004

Vol. 63, nr 4

357--373

Several algebraic structures (namely HW, BZMVdM, Stonean MV and MVΔ algebras) related to many valued logical systems are considered and their equivalence is proved. Four propositional calculi whose Lindenbaum-Tarski algebra corresponds to the four equivalent algebraic structures are axiomatized and their semantical completeness is given.

Algebraic Structures Related to Many Valued Logical Systems. Part 1, Heyting Wajsberg Algebras

Cattaneo G., Ciucci D., Giuntini R., Konig M.

Fundamenta Informaticae

2004

Vol. 63, nr 4

331--355

A bottom-up investigation of algebraic structures corresponding to many valued logical systems is made. Particular attention is given to the unit interval as a prototypical model of these kind of structures. At the top level of our construction, Heyting Wajsberg algebras are defined and studied. The peculiarity of this algebra is the presence of two implications as primitive operators. This characteristic is helpful in the study of abstract rough approximations.