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Definability of Boolean Functions in Kripke Semantics
Notre Dame Journal of Formal Logic 64 (3):363-376 (2023)
Abstract
A set F of Boolean functions is said to be functionally complete if every Boolean function is definable by combining functions in F. Post clarified when a set of Boolean functions is functionally complete (with respect to classical semantics). In this paper, by extending Post’s theorem, we clarify when a set of Boolean functions is functionally complete with respect to Kripke semantics.Links
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References found in this work
Semantical Analysis of Intuitionistic Logic I.Saul A. Kripke, J. N. Crossley & M. A. E. Dummett - 1970 - Journal of Symbolic Logic 35 (2):330-332.
Effect of the Choice of Connectives on the Relation between Classical Logic and Intuitionistic Logic.Tomoaki Kawano, Naosuke Matsuda & Kento Takagi - 2022 - Notre Dame Journal of Formal Logic 63 (2).
Logical connectives for intuitionistic propositional logic.Dean P. McCullough - 1971 - Journal of Symbolic Logic 36 (1):15-20.
Proof of the independence of the primitive symbols of Heyting's calculus of propositions.J. C. C. McKinsey - 1939 - Journal of Symbolic Logic 4 (4):155-158.
Post's functional completeness theorem.Francis Jeffry Pelletier & Norman M. Martin - 1990 - Notre Dame Journal of Formal Logic 31 (3):462-475.
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