Consider this first-order logic knowledge base: In this first-order logic knowle
ID: 3598018 • 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
Mechanized derivation utilizing FOL is harder than utilizing PL in light of the fact that factors can go up against conceivably a limitless number of conceivable esteems from their space. Thus there are conceivably a limitless number of approaches to apply Universal-Elimination govern of deduction
Godel's Completeness Theorem says that FOL entailment is just semidecidable. That is, if a sentence is genuine given an arrangement of adages, there is a method that will decide this. Be that as it may, if the sentence is false, at that point there is no assurance that a method will ever decide this. As it were, the technique may never stop for this situation.
The Truth Table technique for derivation isn't finished for FOL in light of the fact that reality table size might be limitless
Regular Deduction is finished for FOL yet isn't useful for computerized induction on the grounds that the "spreading factor" in a hunt is too vast, caused by the way that we would need to conceivably attempt each derivation run in each conceivable way utilizing the arrangement of known sentences
Summed up Modus Ponens isn't finished for FOL
Summed up Modus Ponens is finished for KBs containing just Horn conditions
A Horn proviso is a sentence of the frame:
(Hatchet) (P1(x) ^ P2(x) ^ ... ^ Pn(x)) => Q(x)
where there are at least 0 Pi's, and the Pi's and Q are sure (i.e., un-nullified) literals
Horn provisos speak to a subset of the arrangement of sentences representable in FOL. For instance, P(a) v Q(a) is a sentence in FOL yet isn't a Horn statement.
Normal derivation utilizing GMP is finished for KBs containing just Horn provisos. Evidences begin with the given sayings/premises in KB, inferring new sentences utilizing GMP until the objective/question sentence is determined. This characterizes a forward fastening surmising strategy since it moves "forward" from the KB to the objective.