In this Section we present an inference algorithm based on the Specialisation Calculus. We are interested in obtaining the intervals of truth values for the facts deduced minimising the number of deductive steps.
In order to preserve the correctness of the inference algorithm with respect to the semantics of the Specialisation Calculus, the algorithm does not introduce any extra-logical component. Deduction is implemented by using just the axioms and inference rules presented in the previous Section.
We consider that a proposition has a definitive value when there are no rules that can contribute to its provisional value (initially [0,1]), producing a more precise one by means of applications of the Composition inference rule. We will use a proposition to specialise rules only when that proposition has a definitive value. This restriction permits that a rule be substituted by its specialised versions when no more specialisation is possible for the condition being eliminated from its premise. When there are no conditions left in the premise of a rule the conclusion of the rule is generated. The Weakening inference rule will not be used in the deductive process, it will only be used when necessary at query answering time.