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Proof theory Information (995 words) |
 | 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. |
| Proof theory can also be considered a branch of philosophical logic, where the primary interest is in the idea of a proof-theoretic semantics, an idea which depends upon technical ideas in structural proof theory to be feasible. |
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Mathematical proof - Wikipedia, the free encyclopedia (549 words) |
| In the context of proof theory, where purely formal proofs are considered, such not entirely formal demonstrations in mathematics are often called "social proofs". |
| The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language. |
| Regardless of one's attitude to formalism, the result that is proved to be true is a theorem; in a completely formal proof it would be the final line, and the complete proof shows how it follows from the axioms alone. |
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