Proof theory (nonfiction): Difference between revisions

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File:Woman teaching geometry circa 1309.jpg|link=Geometry (nonfiction)|Women geometers first to ask [[Geometry (nonfiction)|geometry]] how it feels.
File:John Venn computing diagram.jpg|link=John Venn|Set theorist and crime-fighter [[John Venn]] uses Proof theory to detect and prevent [[crimes against mathematical constants]].
File:Voronoi-diagram-color-commentators.jpg|link=Fantasy Voronoi diagram|[[Fantasy Voronoi diagram]] color commentators discussing recent scores from hotly contested [[Voronoi diagram (nonfiction)|Voronoi diagrams]].
File:Cantor set (four iterations).png|link=Set theory (nonfiction)|Crime-fighter [[The Sigil (crime fighter)|The Sigil]]'s seen wearing new [[Sigil (nonfiction)|sigil]]. "Naturally I am pleased," said [[Georg Cantor]].
File:Euclid_Lueneburg_ms_page_8.jpg|link=Mathematical diagram (nonfiction)|Artifically intelligent manuscript of Euclid's ''Elements'' needs to upgrade itself, has [[Mathematical diagram (nonfiction)|sketch on back of envelope]] it wishes to show you.
File:John Venn computing diagram.jpg|link=John Venn|[[John Venn]] computes a [[Venn diagram|Demon-repelling diagram]] for [[Roger Zelazny]] and [[William Blake]].
File:Benoit Mandelbrot.jpg|link=Benoit Mandelbrot (nonfiction)|[[Benoit Mandelbrot (nonfiction)]] survived by [[Benoit Mandelbrot]].
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* [[Logic (nonfiction)]]
* [[Logic (nonfiction)]]
* [[Mathematics (nonfiction)]]
* [[Mathematics (nonfiction)]]
* [[Method of analytic tableaux (nonfiction)]]


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Latest revision as of 12:10, 26 December 2017

Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques.

Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system.

As such, 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 in computer science, linguistics, and philosophy.

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