WHAT IS A RULE OF INFERENCE?

DOI10.1017/s1755020320000441OpenAlexW3114529159MaRDI QIDQ6193397

Neil Tennant

Publication date: 16 March 2024

Published in: The Review of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1755020320000441

zbMATH Keywords

Horn clausesintuitionistic logicself-referenceproof systemsclassical logicmodus ponensminimal logicrules of inferenceimpredicative definitionscore logicparallelized elimination rulesclassical rules of negationdischarge of assumptionsinductive definition of proof

Mathematics Subject Classification ID

Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47) Proof theory in general (including proof-theoretic semantics) (03F03) Subsystems of classical logic (including intuitionistic logic) (03B20)

Cites Work

• Advances in proof-theoretic semantics
• The intended interpretation of intuitionistic logic
• On the idea of a general proof theory
• On the rules of suppositions in formal logic
• The seeming interdependence between the concepts of valid inference and proof
• Validity concepts in proof-theoretic semantics
• CUT FOR CORE LOGIC
• THE RELEVANCE OF PREMISES TO CONCLUSIONS OF CORE PROOFS
• A natural extension of natural deduction
• Rules and Derived Rules
• What Negation is not: Intuitionism and '0=1'
• CUT FOR CLASSICAL CORE LOGIC
• Core Logic
• The independence of connectives
• Kreisel’s Theory of Constructions, the Kreisel-Goodman Paradox, and the Second Clause
• The consistency of arithmetics
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