Further Connections
Axioms P1, P2 and P3, with the deduction rule modus ponens (formalising intuitionistic propositional logic), correspond to combinatory logic base combinators I, K and S with the application operator. Proofs in the Hilbert system then correspond to combinator terms in combinatory logic. See also Curry-Howard correspondence.
Read more about this topic: Hilbert System
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—Jane Mersky Leder (20th century)
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—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)