Universal Instantiation
The Universal Instantiation (UI) rule states that by replacing a ground word (a term without variables) for the variable, we can infer any sentence. We employ the notion of replacements to formalize the inference rule. Let denote the result of putting the substitution to work on the sentence . The rule is then expressed as \frac{\forall v \alpha}{\operatorname{SUBST}(\{v / g\}, \alpha)}.
For every variable and ground term . For example, the substitutions
get the three phrases shown above.
Prepositional Inference in Artificial Intelligence
Let’s start with quantifiers that are universal. Assume we have in our knowledge base the conventional folklore axiom that All Greedy Kings Are Bad:
Then it appears that inferring any of the following sentences is perfectly acceptable:
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