Proof theory (nonfiction)

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.

In the News

• 

  Set theorist and crime-fighter John Venn uses Proof theory to detect and prevent crimes against mathematical constants.

Fiction cross-references

• Crimes against mathematical constants
• Gnomon Algorithm
• Mathematics

Nonfiction cross-reference

• Nonfiction (nonfiction)
• Logic (nonfiction)
• Mathematics (nonfiction)
• Method of analytic tableaux (nonfiction)

External links:

• Proof theory @ Wikipedia