Abstract
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.
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Naumov, P. On Modal Logics of Partial Recursive Functions. Stud Logica 81, 295–309 (2005). https://doi.org/10.1007/s11225-005-4646-8
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DOI: https://doi.org/10.1007/s11225-005-4646-8