enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Proof theory - Wikipedia

    en.wikipedia.org/wiki/Proof_theory

    Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much research also focuses on applications ...

  3. Structural proof theory - Wikipedia

    en.wikipedia.org/wiki/Structural_proof_theory

    The notion of analytic proof was introduced into proof theory by Gerhard Gentzen for the sequent calculus; the analytic proofs are those that are cut-free.His natural deduction calculus also supports a notion of analytic proof, as was shown by Dag Prawitz; the definition is slightly more complex—the analytic proofs are the normal forms, which are related to the notion of normal form in term ...

  4. Category:Proof theory - Wikipedia

    en.wikipedia.org/wiki/Category:Proof_theory

    Download as PDF; Printable version; In other projects Wikimedia Commons; Wikidata item; Appearance. ... In mathematics, Proof theory is the study of formalized arguments.

  5. Kruskal's tree theorem - Wikipedia

    en.wikipedia.org/wiki/Kruskal's_tree_theorem

    The theorem was conjectured by Andrew Vázsonyi and proved by Joseph Kruskal (); a short proof was given by Crispin Nash-Williams ().It has since become a prominent example in reverse mathematics as a statement that cannot be proved in ATR 0 (a second-order arithmetic theory with a form of arithmetical transfinite recursion).

  6. Curry–Howard correspondence - Wikipedia

    en.wikipedia.org/wiki/Curry–Howard_correspondence

    In programming language theory and proof theory, the Curry–Howard correspondence is the direct relationship between computer programs and mathematical proofs.It is also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions-or formulae-as-types interpretation.

  7. Hilbert system - Wikipedia

    en.wikipedia.org/wiki/Hilbert_system

    In logic, more specifically proof theory, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style system, Hilbert-style proof system, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of formal proof system attributed to Gottlob Frege [1] and David Hilbert. [2]

  8. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Kinoshita–Lee–Nauenberg theorem (quantum field theory) Kirby–Paris theorem (proof theory) Kirchberger's theorem (discrete geometry) Kirchhoff's theorem (graph theory) Kirszbraun theorem (Lipschitz continuity) Kleene fixed-point theorem (order theory) Kleene's recursion theorem (recursion theory) Knaster–Tarski theorem (order theory)

  9. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    Proofs employ logic expressed in mathematical symbols, along with natural language which usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic language without the involvement of natural language, are considered in proof theory.