The Comparative Linguistics of Knowledge

We develop a methodology for comparing knowledge representation formalisms in terms of their \representational succinctness," that is, their ability to express knowledge situations relatively eeciently. We use this framework for comparing many important formalisms for knowledge base representation: propositional logic, default logic, circumscription, and model preference defaults; and, at a lower level, Horn formulas, characteristic models, decision trees, disjunctive normal form, and conjunctive normal form. We also show that adding new variables improves the eeective expressibility of certain knowledge representation formalisms.