Abstract: An expert system shell efficiently computes functions of variables in response to numeric or symbolic data values input by a user. The system comprises a Knowledge Base in the form of a network of functions, an Inference Engine for efficiently updating values in the knowledge base in response to changes in entered data, and a Forms System that manages interaction with the user. A knowledge engineer creates the network of functions, and defines the user screens and the connection between screen objects and variables in the function network. The system allows many different types of variables, including numeric and symbolic types. The system associates a probability distribution with every variable, and computes the probability distributions for the dependent variables from the probability distributions for the independent variables. A variable can store multiple values as tables of probability distributions keyed by one or more key variables.