Qubit Semantics and Quantum Trees

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.