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- Proof-theoretic_semantics abstract "Proof-theoretic semantics is an approach to the semantics of logic that attempts to locate the meaning of propositions and logical connectives not in terms of interpretations, as in Tarskian approaches to semantics, but in the role that the proposition or logical connective plays within the system of inference.Gerhard Gentzen is the founder of proof-theoretic semantics, providing the formal basis for it in his account of cut-elimination for the sequent calculus, and some provocative philosophical remarks about locating the meaning of logical connectives in their introduction rules within natural deduction. The history of proof-theoretic semantics since then has been devoted to exploring the consequences of these ideas.Dag Prawitz extended Gentzen's notion of analytic proof to natural deduction, and suggested that the value of a proof in natural deduction may be understood as its normal form. This idea lies at the basis of the Curry–Howard isomorphism, and of intuitionistic type theory. His inversion principle lies at the heart of most modern accounts of proof-theoretic semantics.Michael Dummett introduced the very fundamental idea of logical harmony, building on a suggestion of Nuel Belnap. In brief, a language, which is understood to be associated with certain patterns of inference, has logical harmony if it is always possible to recover analytic proofs from arbitrary demonstrations, as can be shown for the sequent calculus by means of cut-elimination theorems and for natural deduction by means of normalisation theorems. A language that lacks logical harmony will suffer from the existence of incoherent forms of inference: it will likely be inconsistent.".
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- Proof-theoretic_semantics wikiPageExternalLink proof-theoretic-semantics.
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- Proof-theoretic_semantics wikiPageWikiLink Analytic_proof.
- Proof-theoretic_semantics wikiPageWikiLink Category:Philosophical_logic.
- Proof-theoretic_semantics wikiPageWikiLink Category:Proof_theory.
- Proof-theoretic_semantics wikiPageWikiLink Curry–Howard_correspondence.
- Proof-theoretic_semantics wikiPageWikiLink Curry–Howard_isomorphism.
- Proof-theoretic_semantics wikiPageWikiLink Cut-elimination.
- Proof-theoretic_semantics wikiPageWikiLink Cut-elimination_theorem.
- Proof-theoretic_semantics wikiPageWikiLink Dag_Prawitz.
- Proof-theoretic_semantics wikiPageWikiLink Formal_semantics_(logic).
- Proof-theoretic_semantics wikiPageWikiLink Formal_system.
- Proof-theoretic_semantics wikiPageWikiLink Gerhard_Gentzen.
- Proof-theoretic_semantics wikiPageWikiLink Inferential_role_semantics.
- Proof-theoretic_semantics wikiPageWikiLink Internet_Encyclopedia_of_Philosophy.
- Proof-theoretic_semantics wikiPageWikiLink Interpretation_(logic).
- Proof-theoretic_semantics wikiPageWikiLink Intuitionistic_type_theory.
- Proof-theoretic_semantics wikiPageWikiLink Inversion_principle.
- Proof-theoretic_semantics wikiPageWikiLink Logica_Universalis.
- Proof-theoretic_semantics wikiPageWikiLink Logical_connective.
- Proof-theoretic_semantics wikiPageWikiLink Logical_harmony.
- Proof-theoretic_semantics wikiPageWikiLink Michael_Dummett.
- Proof-theoretic_semantics wikiPageWikiLink Natural_deduction.
- Proof-theoretic_semantics wikiPageWikiLink Nuel_Belnap.
- Proof-theoretic_semantics wikiPageWikiLink Sequent_calculus.
- Proof-theoretic_semantics wikiPageWikiLink Stanford_Encyclopedia_of_Philosophy.
- Proof-theoretic_semantics wikiPageWikiLink Tarski.
- Proof-theoretic_semantics wikiPageWikiLink Tarsky.
- Proof-theoretic_semantics wikiPageWikiLink Truth-conditional_semantics.
- Proof-theoretic_semantics wikiPageWikiLinkText "Proof-theoretic semantics".
- Proof-theoretic_semantics wikiPageWikiLinkText "Proof-theoretic".
- Proof-theoretic_semantics wikiPageWikiLinkText "proof-theoretic semantics".
- Proof-theoretic_semantics hasPhotoCollection Proof-theoretic_semantics.
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- Proof-theoretic_semantics wikiPageUsesTemplate Template:Doi.
- Proof-theoretic_semantics wikiPageUsesTemplate Template:Logic-stub.
- Proof-theoretic_semantics subject Category:Philosophical_logic.
- Proof-theoretic_semantics subject Category:Proof_theory.
- Proof-theoretic_semantics hypernym Approach.
- Proof-theoretic_semantics type ProgrammingLanguage.
- Proof-theoretic_semantics type Proof.
- Proof-theoretic_semantics comment "Proof-theoretic semantics is an approach to the semantics of logic that attempts to locate the meaning of propositions and logical connectives not in terms of interpretations, as in Tarskian approaches to semantics, but in the role that the proposition or logical connective plays within the system of inference.Gerhard Gentzen is the founder of proof-theoretic semantics, providing the formal basis for it in his account of cut-elimination for the sequent calculus, and some provocative philosophical remarks about locating the meaning of logical connectives in their introduction rules within natural deduction. ".
- Proof-theoretic_semantics label "Proof-theoretic semantics".
- Proof-theoretic_semantics sameAs Semântica_Prova-Teórica.
- Proof-theoretic_semantics sameAs m.03p2gz.
- Proof-theoretic_semantics sameAs Q7249983.
- Proof-theoretic_semantics sameAs Q7249983.
- Proof-theoretic_semantics wasDerivedFrom Proof-theoretic_semantics?oldid=650356165.
- Proof-theoretic_semantics isPrimaryTopicOf Proof-theoretic_semantics.