2015•The Review of Symbolic LogicRequires access

ON THE NOTION OF CANONICAL DERIVATIONS FROM OPEN ASSUMPTIONS AND ITS ROLE IN PROOF-THEORETIC SEMANTICS

Nissim Francez

Abstract

Abstract The paper proposes an extension of the definition of a canonical proof, central to proof-theoretic semantics, to a definition of a canonical derivation from open assumptions. The impact of the extension on the definition of (reified) proof-theoretic meaning of logical constants is discussed. The extended definition also sheds light on a puzzle regarding the definition of local-completeness of a natural-deduction proof-system, underlying its harmony.

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Key concepts: Proof-theoretic semantics, Extension (predicate logic), Completeness (order theory), Proof theory, Mathematics, Semantics (computer science), Meaning (existential), Operational semantics