The rules If x is A then y is C are of two types:
- Conjunctive rules: In this case the rule represents positive knowledge, inputs (A) and output (C) represent pairs of conjunctly possible values. The rule semantic is: If Input is of type A Then a possible output value is C. The rule relationship between inputs and outputs is modelled by a conjunction (t-norm). These rules are inspired from the data base paradigm it is possible because it has been observed, and implement reasoning through similarities. The inferred output is a guaranteed possibility distribution.
- Implicative rules: The rule represents negative knowledge and
its semantic becomes: If Input is of type A Then Output must
be in C. This more formal expression is issued from the Logic
research branch of Artificial Intelligence and Computer Science. Instead of cumulating possible values, it works by successive elimination, and removes all values that do not satisfy the rule constraints. The rule relationship between inputs and outputs is modelled by an implication, which may or may not be fuzzy. The inferred output is a (usual) potential possibility distribution.
For an expert, the passage from positive to negative knowledge requires a modelling step.
For a detailed comparison between conjunctive and implicative rules, please refer to .