In mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof.
Other articles related to "proof, structural proof theory, structural, proof theory, structural proof, proofs":
... The most widely known proof calculi are those classical calculi that are still in widespread use The class of Hilbert systems, of which the most famous example is the 1928 ... Many other proof calculi were, or might have been, seminal, but are not widely used today ... Modern research in logic teems with rival proof calculi Several systems have been proposed which replace the usual textual syntax with some graphical syntax ...
... The term structure in structural proof theory comes from a technical notion introduced in the sequent calculus the sequent calculus represents the judgement made at any stage of an inference using special, extra-logical ... the logical connectives they are interpreted by in the sequent calculus the structural operators are used in every rule of the calculus, and are not considered when asking whether the subformula property applies ... logical structure is introduced by logical rules, and cannot be eliminated once created, while structural operators can be introduced and eliminated in the course of a ...
... In proof theory, the notion of analytic proof provides the fundamental concept that brings out the similarities between a number of essentially distinct proof calculi, so defining the subfield of structural proof ... There is no uncontroversial general definition of analytic proof, but for several proof calculi there is an accepted notion ... In Gerhard Gentzen's natural deduction calculus the analytic proofs are those in normal form that is, no formula occurrence is both the principal premise of an elimination rule and ...
Famous quotes containing the words theory, structural and/or proof:
“Many people have an oversimplified picture of bonding that could be called the epoxy theory of relationships...if you dont get properly glued to your babies at exactly the right time, which only occurs very soon after birth, then you will have missed your chance.”
—Pamela Patrick Novotny (20th century)
“The reader uses his eyes as well as or instead of his ears and is in every way encouraged to take a more abstract view of the language he sees. The written or printed sentence lends itself to structural analysis as the spoken does not because the readers eye can play back and forth over the words, giving him time to divide the sentence into visually appreciated parts and to reflect on the grammatical function.”
—J. David Bolter (b. 1951)
“The chief contribution of Protestantism to human thought is its massive proof that God is a bore.”
—H.L. (Henry Lewis)