# PREDICTION AND DISCOVERY

Minimal prediction is an artificial intelligence technique defined since the author’s model-theoretic planning project. It is a cumulative non-mono?tonic approximation attained with completing model diagrams on what might be true in a model or knowledge base. A predictive diagram for a theory T is a diagram D (M), where M is a model for T, and for any formula q in M, either the function f: q{0,1} is defined, or there exists a formula p in D(M), such that T U {p} proves q; or that T proves q by minimal prediction. A generalized predictive diagram, is a predictive diagram with D(M) defined from a minimal set of functions. The predictive diagram could be minimally represented by a set of functions {f1, ..., fn} that inductively define the model. The free trees we had defined by the notion of provability implied by the definition, could consist of some extra Skolem functions {g1, ..., gl} that appear at free trees. The f terms and g terms, tree congruences. Predictive diagrams then characterize partial deduction with free trees. The predictive diagrams are applied to discover models for the intelligent game trees. Prediction is applied to plan goal satisfiability and can be combined with plausibility (Nourani, 1991), probabilities, and fuzzy logic to obtain, for example, confidence intervals. The author has applied minimal prediction to simply encode knowledge with model diagrams to carry on automated deduction as Loveland and Poole’s automated deduction system intended. Modeling with virtual tree planning (Nourani, 1999f) is applied where uncertainty, including effector and sensor uncertainty, are relegated to agents, where competitive learning on game trees determines a confidence interval. The incomplete knowledge modeling is treated with KR on predictive model diagrams. Model discovery at KB’s are with specific techniques defined for trees. Model diagrams allow us to model-theoretically characterize incomplete KR. To key into the incomplete knowledge base we apply generalized predictive diagrams whereby specified diagram functions a search engine can select onto localized data fields. The predictive model diagrams could be minimally represented by the set of functions {f1, ., fn} that inductively define the model. Data discovery from KR on diagrams might be viewed as satisfying a goal by getting at relevant data which instantiates a goal. The goal formula states what relevant data is sought. We propose methods that can be applied to planning (Nourani, 1991) with diagrams to implement discovery planning. In planning with G-diagrams that part of the plan that involves free Skolemized trees is carried along with the proof tree for a plan goal. Computing with diagram functions allows us to key to active visual databases.