Two Types of Updating of Probabilities
In sect. 2.1 we saw that the change of the state of a knowledge base through new information supply can be looked upon as the updating of the information already existing in the knowledge base by a conjunction (AND composition) with the newly supplied information. We have also seen that the representation of information in the form of a chain set declares a probability distribution over all possible 0–1 chains over the ground universe, the ground universe being determined by the statements supplied to the knowledge base. The updating of chain-set-formed information in a knowledge base can therefore be looked upon as an updating of the values of the probability row of the knowledge base chain set. For example, when the knowledge base information is A ORA B, and the new information supply to the knowledge base is A ORE B,then the new information updates the probability value m of the (lA 1B) chain to 0; the m probability values of the other two chains (as well as the 0 probability value of the missing (0A 0B) chain) are left unchanged. If the new information had been A AND B, then the m probability values of the chains (lA 0B), (0A 1B) would be updated to 0, and the m probability value of the (lA 1B) chain to 1. When the ground universe of the knowledge base chain set is not identical with the ground universe of the chain set of the new information, then the chain sets must be prolonged (and expanded, see sections 3.6, 3.7.1) before the updating.
KeywordsKnowledge Base Propositional Calculus Inductive Reasoning Information Supply Deductive Reasoning
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