First Order Logic and Knowledge Representation: Some Problems of Incomplete Systems
It is arguable that knowledge representation and use should be founded on a complete system. For example, if the knowledge representation language is to be first order logic, then we would like to express knowledge K under the assumption that we have available a sequenthood procedure which is complete in the sense that any true sequent K → G (G follows from K) is demonstrably true by the procedure. For example, our knowledge system might be based on finite clausal sequents for which there is indeed a procedure using resolution which has the completeness property.
Over the last decade an incomplete resolution system called Prolog has been elaborated and has become widely used. Prolog has intriguing analogies with Absys - an assertive programming system developed in 1968. Some issues of incompleteness important for knowledge manipulation are illustrated by comparing some aspects of the two systems.
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