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- Hilbert_system abstract "In mathematical physics, Hilbert system is an infrequently used term for a physical system described by a C*-algebra.In logic, especially mathematical logic, a Hilbert system, sometimes called Hilbert calculus 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 first-order logic, but are of interest for other logics as well.Most variants of Hilbert systems take a characteristic tack in the way they balance a trade-off between logical axioms and rules of inference. Hilbert systems can be characterised by the choice of a large number of schemes of logical axioms and a small set of rules of inference. Systems of natural deduction take the opposite tack, including many deduction rules but very few or no axiom schemes. The most commonly studied Hilbert systems have either just one rule of inference — modus ponens, for propositional logics — or two — with generalisation, to handle predicate logics, as well — and several infinite axiom schemes. Hilbert systems for propositional modal logics, sometimes called Hilbert-Lewis systems, are generally axiomatised with two additional rules, the necessitation rule and the uniform substitution rule.A characteristic feature of the many variants of Hilbert systems is that the context is not changed in any of their rules of inference, while both natural deduction and sequent calculus contain some context-changing rules. Thus, if we are interested only in the derivability of tautologies, no hypothetical judgments, then we can formalize the Hilbert system in such a way that its rules of inference contain only judgments of a rather simple form. The same cannot be done with the other two deductions systems: as context is changed in some of their rules of inferences, they cannot be formalized so that hypothetical judgments could be avoided — not even if we want to use them just for proving derivability of tautologies.".
- Hilbert_system thumbnail Deduction_architecture.png?width=300.
- Hilbert_system wikiPageExternalLink 02-prop-logic.pdf.
- Hilbert_system wikiPageExternalLink view1-deductive-system.pdf.
- Hilbert_system wikiPageID "8529655".
- Hilbert_system wikiPageLength "15239".
- Hilbert_system wikiPageOutDegree "58".
- Hilbert_system wikiPageRevisionID "697912470".
- Hilbert_system wikiPageWikiLink Alfred_North_Whitehead.
- Hilbert_system wikiPageWikiLink Alfred_Tarski.
- Hilbert_system wikiPageWikiLink Axiom.
- Hilbert_system wikiPageWikiLink Axiom_schema.
- Hilbert_system wikiPageWikiLink Bertrand_Russell.
- Hilbert_system wikiPageWikiLink C*-algebra.
- Hilbert_system wikiPageWikiLink Category:Automated_theorem_proving.
- Hilbert_system wikiPageWikiLink Category:Logical_calculi.
- Hilbert_system wikiPageWikiLink Category:Proof_theory.
- Hilbert_system wikiPageWikiLink Combinatory_logic.
- Hilbert_system wikiPageWikiLink Conservative_extension.
- Hilbert_system wikiPageWikiLink Curry–Howard_correspondence.
- Hilbert_system wikiPageWikiLink David_Hilbert.
- Hilbert_system wikiPageWikiLink Deduction_theorem.
- Hilbert_system wikiPageWikiLink Deductive_reasoning.
- Hilbert_system wikiPageWikiLink First-order_logic.
- Hilbert_system wikiPageWikiLink Formal_system.
- Hilbert_system wikiPageWikiLink Free_variables_and_bound_variables.
- Hilbert_system wikiPageWikiLink Freges_propositional_calculus.
- Hilbert_system wikiPageWikiLink Generalization.
- Hilbert_system wikiPageWikiLink Gottlob_Frege.
- Hilbert_system wikiPageWikiLink Group_theory.
- Hilbert_system wikiPageWikiLink Hilbert-Lewis_system.
- Hilbert_system wikiPageWikiLink Intuitionistic_logic.
- Hilbert_system wikiPageWikiLink Intuitionistic_predicate_logic.
- Hilbert_system wikiPageWikiLink Intuitionistic_propositional_logic.
- Hilbert_system wikiPageWikiLink Jan_Łukasiewicz.
- Hilbert_system wikiPageWikiLink Judgment_(mathematical_logic).
- Hilbert_system wikiPageWikiLink Logic.
- Hilbert_system wikiPageWikiLink Logical_equivalence.
- Hilbert_system wikiPageWikiLink Mathematical_logic.
- Hilbert_system wikiPageWikiLink Mathematical_physics.
- Hilbert_system wikiPageWikiLink Minimal_logic.
- Hilbert_system wikiPageWikiLink Modal_logic.
- Hilbert_system wikiPageWikiLink Modus_ponens.
- Hilbert_system wikiPageWikiLink Natural_deduction.
- Hilbert_system wikiPageWikiLink Necessitation_rule.
- Hilbert_system wikiPageWikiLink Predicate_logic.
- Hilbert_system wikiPageWikiLink Propositional_calculus.
- Hilbert_system wikiPageWikiLink Rule_of_inference.
- Hilbert_system wikiPageWikiLink Semantic_theory_of_truth.
- Hilbert_system wikiPageWikiLink Sequent_calculus.
- Hilbert_system wikiPageWikiLink Set_theory.
- Hilbert_system wikiPageWikiLink Springer_Science+Business_Media.
- Hilbert_system wikiPageWikiLink Tautology_(logic).
- Hilbert_system wikiPageWikiLink Trade-off.
- Hilbert_system wikiPageWikiLink Uniform_substitution.
- Hilbert_system wikiPageWikiLink File:Deduction_architecture.png.
- Hilbert_system wikiPageWikiLinkText "Hilbert calculi".
- Hilbert_system wikiPageWikiLinkText "Hilbert style".
- Hilbert_system wikiPageWikiLinkText "Hilbert system".
- Hilbert_system wikiPageWikiLinkText "Hilbert-style axiom system".
- Hilbert_system wikiPageWikiLinkText "Hilbert-style".
- Hilbert_system wikiPageWikiLinkText "axiomatic system".
- Hilbert_system wikiPageUsesTemplate Template:Citation_needed.
- Hilbert_system wikiPageUsesTemplate Template:Cite_book.
- Hilbert_system wikiPageUsesTemplate Template:Cite_web.
- Hilbert_system wikiPageUsesTemplate Template:Expert-subject.
- Hilbert_system wikiPageUsesTemplate Template:Further.
- Hilbert_system subject Category:Automated_theorem_proving.
- Hilbert_system subject Category:Logical_calculi.
- Hilbert_system subject Category:Proof_theory.
- Hilbert_system hypernym System.
- Hilbert_system type Method.
- Hilbert_system type Proof.
- Hilbert_system comment "In mathematical physics, Hilbert system is an infrequently used term for a physical system described by a C*-algebra.In logic, especially mathematical logic, a Hilbert system, sometimes called Hilbert calculus or Hilbert–Ackermann system, is a type of system of formal deduction attributed to Gottlob Frege and David Hilbert.".
- Hilbert_system label "Hilbert system".
- Hilbert_system sameAs Q910361.
- Hilbert_system sameAs Hilbertovský_kalkulus.
- Hilbert_system sameAs Hilbert-Kalkül.
- Hilbert_system sameAs Système_à_la_Hilbert.
- Hilbert_system sameAs System_Hilberta.
- Hilbert_system sameAs Sistema_de_Hilbert.
- Hilbert_system sameAs m.0276sb2.
- Hilbert_system sameAs Q910361.
- Hilbert_system sameAs 希尔伯特演绎系统.
- Hilbert_system wasDerivedFrom Hilbert_system?oldid=697912470.
- Hilbert_system depiction Deduction_architecture.png.
- Hilbert_system isPrimaryTopicOf Hilbert_system.