In the qubit semantics the meaning of any sentence is represented by a quregister: a unit vector of the n-fold tensor product, where n depends on the number of occurrences of atomic sentences in a formula. The logic characterized by this semantics, called quantum computational logic (QCL), is unsharp, because the noncontradiction principle is violated. We show that QCL does not admit any logical truth. In this framework, any sentence gives rise to a quantum tree, consisting of a sequence of unitary operators. The quantum tree of a formula can be regarded as a quantum circuit that transforms the quregister associated to the occurrences of atomic subformulas of the formula into the quregister associated to the formula.

(2005). Qubit Semantics and Quantum Trees [journal article - articolo]. In INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS. Retrieved from http://hdl.handle.net/10446/19589

Qubit Semantics and Quantum Trees

Leporini, Roberto
2005-01-01

Abstract

In the qubit semantics the meaning of any sentence is represented by a quregister: a unit vector of the n-fold tensor product, where n depends on the number of occurrences of atomic sentences in a formula. The logic characterized by this semantics, called quantum computational logic (QCL), is unsharp, because the noncontradiction principle is violated. We show that QCL does not admit any logical truth. In this framework, any sentence gives rise to a quantum tree, consisting of a sequence of unitary operators. The quantum tree of a formula can be regarded as a quantum circuit that transforms the quregister associated to the occurrences of atomic subformulas of the formula into the quregister associated to the formula.
articolo
2005
Dalla Chiara, Maria Luisa; Giuntini, Roberto; Leporati, Alberto; Leporini, Roberto
(2005). Qubit Semantics and Quantum Trees [journal article - articolo]. In INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS. Retrieved from http://hdl.handle.net/10446/19589
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/19589
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