Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Sequent_calculus> ?p ?o }
- Sequent_calculus abstract "Sequent calculus is, in essence, a style of formal logical argumentation where every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology is inferred from other conditional tautologies on earlier lines in a formal argument according to rules and procedures of inference, giving a better approximation to the style of natural deduction used by mathematicians than David Hilbert's earlier style of formal logic where every line was an unconditional tautology. There may be more subtle distinctions to be made; for example, there may be non-logical axioms upon which all propositions are implicitly dependent. Then sequents signify conditional theorems in a first-order language rather than conditional tautologies.Sequent calculus is one of several extant styles of proof calculus for expressing line-by-line logical arguments. Hilbert style. Every line is an unconditional tautology (or theorem). Gentzen style. Every line is a conditional tautology (or theorem) with zero or more conditions on the left. Natural deduction. Every (conditional) line has exactly one asserted proposition on the right. Sequent calculus. Every (conditional) line has zero or more asserted propositions on the right.In other words, natural deduction and sequent calculus systems are particular distinct kinds of Gentzen-style systems. Hilbert-style systems typically have a very small number of inference rules, relying more on sets of axioms. Gentzen-style systems typically have very few axioms, if any, relying more on sets of rules.Gentzen-style systems have significant practical and theoretical advantages compared to Hilbert-style systems. For example, both natural deduction and sequent calculus systems facilitate the elimination and introduction of universal and existential quantifiers so that unquantified logical expressions can be manipulated according to the much simpler rules of propositional calculus. In a typical argument, quantifiers are eliminated, then propositional calculus is applied to unquantified expressions (which typically contain free variables), and then the quantifiers are reintroduced. This very much parallels the way in which mathematical proofs are carried out in practice by mathematicians. Predicate calculus proofs are generally much easier to discover with this approach, and are often shorter. Natural deduction systems are more suited to practical theorem-proving. Sequent calculus systems are more suited to theoretical analysis.".
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- Sequent_calculus wikiPageExternalLink tutorial.
- Sequent_calculus wikiPageExternalLink handbookI.
- Sequent_calculus wikiPageExternalLink a-brief-diversion-sequent-calc.
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- Sequent_calculus wikiPageWikiLink Argument.
- Sequent_calculus wikiPageWikiLink Artificial_intelligence.
- Sequent_calculus wikiPageWikiLink Atomic_formula.
- Sequent_calculus wikiPageWikiLink Automated_theorem_proving.
- Sequent_calculus wikiPageWikiLink Category:Automated_theorem_proving.
- Sequent_calculus wikiPageWikiLink Category:Logical_calculi.
- Sequent_calculus wikiPageWikiLink Category:Proof_theory.
- Sequent_calculus wikiPageWikiLink Classical_logic.
- Sequent_calculus wikiPageWikiLink Completeness_(logic).
- Sequent_calculus wikiPageWikiLink Completeness_of_atomic_initial_sequents.
- Sequent_calculus wikiPageWikiLink Computer_science.
- Sequent_calculus wikiPageWikiLink Consistency.
- Sequent_calculus wikiPageWikiLink Cut-elimination_theorem.
- Sequent_calculus wikiPageWikiLink David_Hilbert.
- Sequent_calculus wikiPageWikiLink De_Morgans_laws.
- Sequent_calculus wikiPageWikiLink Deduction_theorem.
- Sequent_calculus wikiPageWikiLink Disjunction_and_existence_properties.
- Sequent_calculus wikiPageWikiLink First-order_logic.
- Sequent_calculus wikiPageWikiLink Formal_system.
- Sequent_calculus wikiPageWikiLink Free_variables_and_bound_variables.
- Sequent_calculus wikiPageWikiLink Gentzens_consistency_proof.
- Sequent_calculus wikiPageWikiLink Gerhard_Gentzen.
- Sequent_calculus wikiPageWikiLink Gxc3xb6dels_incompleteness_theorems.
- Sequent_calculus wikiPageWikiLink Higher-order_logic.
- Sequent_calculus wikiPageWikiLink Hilbert_system.
- Sequent_calculus wikiPageWikiLink If_and_only_if.
- Sequent_calculus wikiPageWikiLink Inference.
- Sequent_calculus wikiPageWikiLink Intuitionistic_logic.
- Sequent_calculus wikiPageWikiLink Judgment_(mathematical_logic).
- Sequent_calculus wikiPageWikiLink Law_of_excluded_middle.
- Sequent_calculus wikiPageWikiLink Mathematical_logic.
- Sequent_calculus wikiPageWikiLink Metatheory.
- Sequent_calculus wikiPageWikiLink Modal_logic.
- Sequent_calculus wikiPageWikiLink Multiset.
- Sequent_calculus wikiPageWikiLink Natural_deduction.
- Sequent_calculus wikiPageWikiLink Principle_of_explosion.
- Sequent_calculus wikiPageWikiLink Proof_calculus.
- Sequent_calculus wikiPageWikiLink Proof_theory.
- Sequent_calculus wikiPageWikiLink Propositional_calculus.
- Sequent_calculus wikiPageWikiLink Quantifier_(logic).
- Sequent_calculus wikiPageWikiLink Resolution_(logic).
- Sequent_calculus wikiPageWikiLink Rule_of_inference.
- Sequent_calculus wikiPageWikiLink Semantics.
- Sequent_calculus wikiPageWikiLink Sequence.
- Sequent_calculus wikiPageWikiLink Sequent.
- Sequent_calculus wikiPageWikiLink Sequent_calculus.
- Sequent_calculus wikiPageWikiLink Set_(mathematics).
- Sequent_calculus wikiPageWikiLink Soundness.
- Sequent_calculus wikiPageWikiLink Substructural_logic.
- Sequent_calculus wikiPageWikiLink Tautology_(logic).
- Sequent_calculus wikiPageWikiLink Theorem.
- Sequent_calculus wikiPageWikiLink Turnstile_(symbol).
- Sequent_calculus wikiPageWikiLink Well-formed_formula.
- Sequent_calculus wikiPageWikiLinkText "LK system".
- Sequent_calculus wikiPageWikiLinkText "LK".
- Sequent_calculus wikiPageWikiLinkText "Sequent calculus".
- Sequent_calculus wikiPageWikiLinkText "Structural Rules".
- Sequent_calculus wikiPageWikiLinkText "inference rules".
- Sequent_calculus wikiPageWikiLinkText "sequent calculi".
- Sequent_calculus wikiPageWikiLinkText "sequent calculus inference rules".
- Sequent_calculus wikiPageWikiLinkText "sequent calculus".
- Sequent_calculus wikiPageWikiLinkText "sequent systems".
- Sequent_calculus wikiPageWikiLinkText "sequent".
- Sequent_calculus id "p/s084580".
- Sequent_calculus title "Sequent calculus".
- Sequent_calculus wikiPageUsesTemplate Template:Cite_book.
- Sequent_calculus wikiPageUsesTemplate Template:Cite_journal.
- Sequent_calculus wikiPageUsesTemplate Template:Main.
- Sequent_calculus wikiPageUsesTemplate Template:Reflist.
- Sequent_calculus wikiPageUsesTemplate Template:Sfn.
- Sequent_calculus wikiPageUsesTemplate Template:Springer.
- Sequent_calculus subject Category:Automated_theorem_proving.
- Sequent_calculus subject Category:Logical_calculi.
- Sequent_calculus subject Category:Proof_theory.
- Sequent_calculus hypernym Tautology.
- Sequent_calculus type Method.
- Sequent_calculus type Proof.
- Sequent_calculus comment "Sequent calculus is, in essence, a style of formal logical argumentation where every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology.".
- Sequent_calculus label "Sequent calculus".
- Sequent_calculus sameAs Q1771121.
- Sequent_calculus sameAs Sequenzenkalkül.
- Sequent_calculus sameAs Sekvaĵa_kalkulo.
- Sequent_calculus sameAs Calcul_des_séquents.
- Sequent_calculus sameAs シークエント計算.
- Sequent_calculus sameAs Sekwenty_Gentzena.
- Sequent_calculus sameAs Cálculo_de_sequentes.
- Sequent_calculus sameAs m.01lfnc.
- Sequent_calculus sameAs Числення_секвенцій.
- Sequent_calculus sameAs Q1771121.
- Sequent_calculus sameAs 相继式演算.