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.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1007/s11225-005-4646-8
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References found in this work BETA

The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
Dynamic Logic.Lenore D. Zuck & David Harel - 1989 - Journal of Symbolic Logic 54 (4):1480.
Combinatory Logic, Volume I.Haskell B. Curry, Robert Feys & William Craig - 1959 - Philosophical Review 68 (4):548-550.

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On Modal Logic of Deductive Closure.Pavel Naumov - 2006 - Annals of Pure and Applied Logic 141 (1):218-224.

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