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On Modal Logics of Partial Recursive Functions

Pavel Naumov
Studia Logica: An International Journal for Symbolic Logic
Vol. 81, No. 3 (Dec., 2005), pp. 295-309
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016752
Page Count: 15
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On Modal Logics of Partial Recursive Functions
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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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