The Comparative Linguistics of Knowledge Representation

We develop a methodology for comparing knowledge representation formalisms in terms of their "representational succinctness," that is, their abi l i ty to express knowledge situations relatively efficiently. 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 fo rm, and conjunctive nor­ mal form. We also show that adding new vari­ ables improves the effective expressibility of certain knowledge representation formalisms.