The logic of interactive Turing reduction

The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic reduction. This concept — more precisely, the associated concept of reducibility — is a generalization of Turing reducibility from the traditional, input/output sorts of problems to computational tasks of arbitrary degrees of interactivity. MSC: primary: 03B47; secondary: 03F50; 03B70; 68Q10; 68T27; 68T30; 91A05