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. Together with
model theory,
axiomatic set theory, and
recursion theory, proof theory is one of the so-called four pillars of the
foundations of mathematics. 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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<
logic> The branch of
logic describing procedures for combining logical statements to show, by a series of truth-preserving transformations, that one statement is a consequence of some other statement or group of statements.
(1994-10-31)
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