# Questions tagged [hilbert-calculus]

In logic a Hilbert calculus, sometimes called Hilbert system, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of system of formal deduction attributed to Gottlob Frege and David Hilbert. These deductive systems are most often studied for propositional and first-order logic.

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### Transforming Hilbert-style Axiom Systems for Classical Propositional Logic and Retaining Soundness and Completeness

First off, I will use ~ for negation, & for conjunction, V for disjunction, -> for implication, and <-> for bi-conditional. To the question: The axioms of classical propositional logic (CPL) ...
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### Hilbert calculi for First-Order Logic

I'm a bit confused about the Hilbert-style axiomatization of first-order logic. More precisely, I am a bit confused about completeness w.r.t. to Hilbert-calculi. A complete Hilbert-style calculus I am ...
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### Axiomatic proofs in propositional logic

I have to use these three axioms (A1) $P \to (Q \to P)$ (A2) $(P \to (Q \to R)) \to ((P \to Q) \to (P \to R))$ (A3) $(\neg Q \to \neg P) \to ((\neg Q \to P) \to Q)$ along with Modus Ponens to ...
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### Sufficient condition for gradient existence in Hilbert spaces

Let $\mathbb H$ a Hilbert space and $N:\mathbb H\to \mathbb H$ a continuous nonlinear mapping. In Fonda and Mawhin (Iterative and variational methods for the solvability of some semilinear equations ...