# Proof-theoretic semantics

**Proof-theoretic semantics**is an approach to the semantics of logic that attempts to locate the meaning of propositions andlogical connective s not in terms ofinterpretation s, as inTarski an approaches to semantics, but in the role that the proposition or logical connective plays within the system of inference.Gerhard Gentzen is the founder of proof-theoretic semantics, providing the formal basis for it in his account ofcut-elimination for thesequent calculus , and some provocative philosophical remarks about locating the meaning of logical connectives in their introduction rules withinnatural deduction . It is not a great exaggeration that the history of proof-theoretic semantics since then has been devoted to exploring the consequences of these ideas.Dag Prawitz extended Gentzen's notion ofanalytic proof tonatural deduction , and suggested that the value of a proof in natural deduction may be understood as its normal form. This idea lies at the basis of theCurry-Howard isomorphism , and ofintuitionistic type theory . Hisinversion principle lies at the heart of most modern accounts of proof-theoretic semantics.Michael Dummett introduced the very fundamental idea oflogical harmony , building on a suggestion ofNuel Belnap . In brief, a language, which is understood to be associated with certain patterns of inference, has logical harmony if it is always possible to recover analytic proofs from arbitrary demonstrations, as can be shown for the sequent calculus by means of cut-elimination theorems and for natural deduction by means of normalisation theorems. A language that lacks logical harmony will suffer from the existence of incoherent forms of inference: it will likely be inconsistent.**References*** [

*http://www.iep.utm.edu/l/logcon-d.htm Logical Consequence, Deductive-Theoretic Conceptions*] , at theInternet Encyclopedia of Philosophy .**ee also***

Inferential role semantics

*Truth-conditional semantics **External links*** [

*http://arche-wiki.st-and.ac.uk/~ahwiki/bin/view/Arche/ProofTheoreticSemantics Arché Bibliography on Proof-Theoretic Semantics.*]

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