"Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques."
Study of proofs and their properties.
"Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system."
"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 in computer science, linguistics, and philosophy."
"Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques."
"Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees."
"Proofs are constructed according to the axioms and rules of inference of a given logical system."
"Proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature."
"Proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature."
"Much research also focuses on applications in computer science, linguistics, and philosophy."
"Some of the major areas of proof theory include structural proof theory..."
"Some of the major areas of proof theory include... provability logic..."
"Some of the major areas of proof theory include... proof mining..."
"Some of the major areas of proof theory include... proof complexity."
"Some of the major areas of proof theory include... automated theorem proving."
"Some of the major areas of proof theory include... ordinal analysis."
"Some of the major areas of proof theory include... reverse mathematics."
"Much research also focuses on applications in computer science, linguistics, and philosophy."
"Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques."