A Specialisation Calculus to Improve Expert Systems Communication

The motivation of this work is the improvement of the classical input/output expert systems behaviour. In an uncertain reasoning context this behaviour consists of just getting certainty values for propositions. Instead, the answer of an expert system will be a set of formulas: a set of propositions and a set of specialised rules containing unknown propositions in their left part. This type of behaviour is much more informative than the classical one because gives to users not only the answer to a query but all the relevant information to improve the solution. A family of propositional rule-based languages founded on multiple-valued logics is presented and formalised. The deductive system defined on top of it is based on a Specialisation Inference Rule (SIR): (A1 ∧ A2 · · · ∧ An → P, V ), (A1, V ) ` (A2 ∧ . . . ∧ An → P, V ), where V , V ′ and V ′′ are uncertainty intervals. This inference rule provides a way of obtaining rules containing unknown conditions in their premise as the result of the deductive process. The soundness and literal completeness of the deductive system are proved. The implementation of this deductive calculus is based on techniques of partial evaluation. Moreover, the specialisation mechanism provides an interesting way of validating knowledge bases.