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**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… … Wikipedia**proof theory**— The study of the relations of deducibility among sentences in a logical calculus . Deducibility is defined purely syntactically, that is, without reference to the intended interpretation of the calculus. See also model theory … Philosophy dictionary**Structural proof theory**— In mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof. Contents 1 Analytic proof 2 Structures and connectives 3 Cut elimination in the sequent… … Wikipedia**Proof**— may refer to: * A rigorous, compelling argument ** Formal proof ** Mathematical proof ** Proof theory, a branch of mathematical logic that represents proofs as formal mathematical objects ** Logical argument ** Evidence (law), tested evidence or… … Wikipedia**Theory (mathematical logic)**— This article is about theories in a formal language, as studied in mathematical logic. For other uses, see Theory (disambiguation). In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. Usually… … Wikipedia**Proof calculus**— In mathematical logic, a proof calculus corresponds to a family of formal systems that use a common style of formal inference for its inference rules. The specific inference rules of a member of such a family characterize the theory of a… … Wikipedia**Theory**— The word theory has many distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion.In science a theory is a testable model of the manner of interaction of a set of natural phenomena,… … Wikipedia**Proof mining**— In proof theory (a branch of mathematical logic), proof mining is a research program [cite book title = Applied Proof Theory: Proof Interpretations and Their Use in Mathematics author = Ulrich Kohlenbach publisher = Springer Verlag, Berlin year … Wikipedia**Proof complexity**— In computer science, proof complexity is a measure of efficiency of automated theorem proving methods that is based on the size of the proofs they produce. The methods for proving contradiction in propositional logic are the most analyzed. The… … Wikipedia**Proof procedure**— In logic, and in particular proof theory, a proof procedure for a given logic is a systematic method for producing proofs in some proof calculus of (provable) statements.There are several types of proof calculi. The most popular are natural… … Wikipedia