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.
"The logic of interactive Turing reduction." J. Symbolic Logic 72 (1) 243 - 276, March 2007. https://doi.org/10.2178/jsl/1174668394