On modal logics of partial recursive functions

Studia Logica 81 (3):295 - 309 (2005)
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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    Pavel Naumov (2006). On Modal Logic of Deductive Closure. Annals of Pure and Applied Logic 141 (1):218-224.
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