Consider this first-order logic knowledge base: In this first-order logic knowle
ID: 3597288 • Letter: C
Question
Consider this first-order logic knowledge base:
In this first-order logic knowledge base, taller and tall are predicates, x is a variable, and John, Bill are constants. Convert this first-order logic knowledge base into a propositional logic knowledge base, by performing the following two steps:
Define symbols for the propositional-logic version of the knowledge base, and specify what their equivalents are in the original first-order logic knowledge base.
Define the statements that should be stored in the propositional-logic version of the knowledge base.
The symbols you define should be comprehensive enough to allow us to translate any well-defined inference problem in the original knowledge base to an equivalent problem for the propositional knowledge base. Anything that we can infer from the original first-order logic knowledge base we should also be able to infer from the propositionalized knowledge base, and vice versa.
Explanation / Answer
Solution :-
The given first-order logic knowledge base -
The first-order logic knowledge base defines that "John is taller than bill".
For all x, if x is taller than bill implies that x is tall.
Now define the symbols of propositional logic knoledge base.
P defines "John is taller than bill" and Symbol Q defines "tall"
let constant "a" replace the "John" in the propositional logic knowledge base. and let "x" is a variable.
Therefore, we have the coverted propoitional logic formaula is -
P(a)
Explanation -
1) P(a) represents the fact that "john is taller than bill", where constant symbol "a" used to represent the "John".
2) (x) P(x/a) -> Q(x) represents the rule that "for all x, if x is taller than Bill then this implies that x is tall".
Here P(x/a) represents the variable "x" can be used for every occurance of constant symbol "a" and Q(x) represents the fact that "x is tall".
Therefore the conveted propositional-logic version of the knowledge base is
P(a)