Text Structure and Proof Structure

Authors:
C. F. M. Vermeulen
Affiliations:
Linguistics Department and Philosophy Department, Utrecht University, Trans 10, 3512 JK Utrecht, The Netherlands kees.vermeulen@phil.uu.nl
Venue:
Journal of Logic, Language and Information
Year:
2000

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Abstract

This paper is concerned with the structure of texts in which aproof is presented. Some parts of such a text are assumptions, otherparts are conclusions. We show how the structural organisation of thetext into assumptions and conclusions helps to check the validity of theproof. Then we go on to use the structural information for theformulation of proof rules, i.e., rules for the (re-)construction ofproof texts. The running example is intuitionistic propositional logicwith connectives ∧, → and⊥. We give new proofs of some familiar results aboutthe proof theory of this logic to indicate how the new techniques workout.