Modularity and relevant logic

Abstract

A practical system of reasoning must be both correct and efficient. An efficient system which contains a large body of information can not search for the proof of a conclusion from all information available. Efficiency requires that deduction of the conclusion be carried out in a modular way using only a relatively small and quickly identified subset of the total information. One might assume that data modularity is incompatible with correctness, where a system is correct for a logic L iff it proves exactly what is valid in L. We point out that modularity and correctness are indeed incompatible if the logic in question is classical. On the other hand, the two desiderata are compatible for relevance logic. Furthermore, Horn clause resolution theorem proving is modular (this helps explain its relative efficiency) and the logic for which it is correct is relevance logic not classical logic. © 1989 by the University of Notre Dame. All rights reserved.