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Identity of Proofs

By Filip Widebäck

December 2001

Almqvist & Wiskell International

ISBN: 91-22-01940-5

85 pages, illustrated

$47.50 paper original

In the early seventies it was conjectured that a certain mathematically well-defined equivalence relation (bh-equivalence) on proofs in natural deduction captures the informal notion of identity of proofs. The conjecture can be divided into two parts: soundness (bh-equivalent proofs are identical) and completeness (identical proofs are bh-equivalent). It is argued that soundness cannot be mathematically proved, that it must be taken for granted or rejected. Completeness, on the other hand, must be proved or disproved, although the question is not mathematically precise. The main result of this Ph.D. thesis is that the completeness part of the conjecture is true for the system of minimal implication logic, assuming soundness. The thesis also contains a new proof of so-called confluence and a conjecture characterizing bh-equivalence in a new way.

Logic; Philosophy

Stockholm Studies in Philosophy, No. 22