Computing power of Turing machines in the framework of unsharp quantum logic

We present recursion theoretical characterizations of the computational power of Turing machines in the framework of unsharp quantum logic. For unsharp quantum logic, let a lattice ordered quantum multiple valued (QMV) algebra be its truth value lattice. When lattice ordered QMV algebras satisfy a locally finite condition (that is, every non-zero element has a finite order) and its meet operation, ∧, is computable, we prove that Σ10∪Π10⊆LdT(E,Σ)(or LwT(E,Σ))⊆Π20, where LdT(E,Σ)(respectively LwT(E,Σ)) denotes the class of languages accepted by these Turing machines in the depth-first method (respectively the width-first method). For sharp quantum logic, similar results are obtained for a general orthomodular truth value lattice.