We distinguish axiomatically-based expert systems, whose design and implementation are guided by one or more axiomatically-based theories of decision-making (e.g., decision theory, Bayesian probability theory, maximum entropy theory), from traditional expert systems. An analysis of the knowledge acquisition and computational needs of axiomatically-based expert systems is presented. An explicit quantitative comparison is made between the actual knowledge acquisition effort required to build an existing expert system, and the effort that would be required to build an analogous axiomatically-based advice system. The costs and benefits of the axiomatic approach are discussed. The analysis suggests that the small additional cost of knowledge acquisition for the axiomatic approach are outweighed by the long-term benefits this approach provides.