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Additional info for Application of Artificial Intelligence in Process Control. Lecture Notes Erasmus Intensive Course
However the latter can easily be expressed as: (X V Y) A - . e. "if and only if ... ". e. when X => Y is known to exist, and X is true, then Y will also be true. Note that if we think of X and X => Y as two entries in a database, the modus ponens rule allows us to replace t h e m with the single statement, Y, thus eliminating one occurrence of the connective '=^'. In what are called natural deduction systems of logic, there are typically two rules of inference for each connective, one that introduces it into expressions and one t h a t eliminates it.
3. Specificity. When still more t h a n one instantiation is candidate for being executed, the specificity of the m a t c h will have to be used for the decision. The specificity of the m a t c h is determined by the complexity of the LHS of the rule. T h e compiler will start looking for the total number of tests in the LHS of a production. T h e language specifies exactly which items are considered to be a test and which not. The production with the highest number of time tags will be executed.
A contradiction occurs when a clause becomes so restricted t h a t there is no way it can be true. This is indicated by t h e generation of the e m p t y clause. T h e tree-representation in the Figure 4 indicates the whole procedure up to the final step where an e m p t y clause is found, indicating thereby a contradiction. As this contradiction is between the negated proposition -»r and the rest of the connectives, this thereby proves r to be true. 47 -\p V -*q V r -ir - i p V -> "^9 itV q t -i* n Figure 4: Resolution Tree 4 Predicate Logic.