Text Structure and Proof Structure

This paper is concerned with the structure of texts in which a proof is presented. Some parts of such a text are assumptions, other parts are conclusions. We show how the structural organisation of the text into assumptions and conclusions helps to check the validity of the proof. Then we go on to u...

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Bibliographic Details
Published in:Journal of logic, language, and information language, and information, 2000-07, Vol.9 (3), p.273-311
Main Author: Vermeulen, C. F. M.
Format: Article
Language:English
Subjects:
Discourse analysis
Grammatical clauses
Logic
Logical proofs
Mathematical validity
Modus ponens
Natural deduction calculus
Prolog
Proof theory
Semantics
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Summary:This paper is concerned with the structure of texts in which a proof is presented. Some parts of such a text are assumptions, other parts are conclusions. We show how the structural organisation of the text into assumptions and conclusions helps to check the validity of the proof. Then we go on to use the structural information for the formulation of proof rules, i.e., rules for the (re-)construction of proof texts. The running example is intuitionistic propositional logic with connectives Ʌ → and ┴ We give new proofs of some familiar results about the proof theory of this logic to indicate how the new techniques work out.
ISSN:0925-8531
1572-9583
DOI:10.1023/A:1008309715242