Normal natural deduction proofs (in classical logic)

Studia Logica 60 (1):67-106 (1998)

Authors
Wilfried Sieg
Carnegie Mellon University
Abstract
Natural deduction (for short: nd-) calculi have not been used systematically as a basis for automated theorem proving in classical logic. To remove objective obstacles to their use we describe (1) a method that allows to give semantic proofs of normal form theorems for nd-calculi and (2) a framework that allows to search directly for normal nd-proofs. Thus, one can try to answer the question: How do we bridge the gap between claims and assumptions in heuristically motivated ways? This informal question motivates the formulation of intercalation calculi. Ic-calculi are the technical underpinnings for (1) and (2), and our paper focuses on their detailed presentation and meta-mathematical investigation in the case of classical predicate logic. As a central theme emerges the connection between restricted forms of nd-proofs and (strategies for) proof search: normal forms are not obtained by removing local "detours", but rather by constructing proofs that directly reflect proof-strategic considerations. That theme warrants further investigation.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/A:1005091418752
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Automated Search for Gödel’s Proofs.Wilfried Sieg & Clinton Field - 2005 - Annals of Pure and Applied Logic 133 (1):319-338.
1999 Spring Meeting of the Association for Symbolic Logic.Charles Parsons - 1999 - Bulletin of Symbolic Logic 5 (4):479-484.

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