Implications-as-rules vs. implications-as-links: an alternative implication-left schema for the sequent calculus

DOI10.1007/s10992-010-9149-zzbMath1228.03039OpenAlexW2061849418MaRDI QIDQ626494

Peter Schroeder-Heister

Publication date: 18 February 2011

Published in: Journal of Philosophical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10992-010-9149-z

zbMATH Keywords

cut eliminationsequent calculusimplication

Mathematics Subject Classification ID

Cut-elimination and normal-form theorems (03F05)

Related Items

The categorical and the hypothetical: a critique of some fundamental assumptions of standard semantics ⋮ Paradox and Inconsistency: Revising Tennant’s Distinction Through Schroeder-Heister’s Assumption Rules ⋮ PROOF-THEORETIC SEMANTIC VALUES FOR LOGICAL OPERATORS ⋮ Eight inference rules for implication ⋮ Generalized Elimination Inferences, Higher-Level Rules, and the Implications-as-Rules Interpretation of the Sequent Calculus ⋮ Proof-theoretic semantics, self-contradiction, and the format of deductive reasoning ⋮ On a distinction of two facets of meaning and its role in proof-theoretic semantics

Uses Software

• Pesca

Cites Work

• Gentzenizing Schroeder-Heister's natural extension of natural deduction
• Display logic
• A Proof-Theoretic Approach to Logic Programming. I. Clauses as Rules
• A natural extension of natural deduction
• Lambda terms for natural deduction, sequent calculus and cut elimination
• Generalized Elimination Inferences, Higher-Level Rules, and the Implications-as-Rules Interpretation of the Sequent Calculus
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