%0 Journal Article %T On Modal Logics of Partial Recursive Functions %A Pavel Naumov %J Computer Science %D 2004 %I arXiv %X The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both of them semantically complete modal logics are described and decidability of these logics is established. %U http://arxiv.org/abs/cs/0407031v1