4 Unification

• Unification: Determine whether the following two sentences are similar ornot.

• Propositional calculus → very trivial.

• Predicate calculus → very difficult (variables).

• X/Y means X is substituted for the variable Y .

• Substitution → Binding.

• Examples: What is the final value of Y and Z?{X/Y, W/Z}, {V/X}, {a/V, f(b)/W}

• Predicate calculus expression should be transformed to list syntax.• p(a,b) → (p a b).

• p(f(a),g(X,Y)) → (p (f(a)) (g(X,Y))).

• equal(eva, mother(sara)) → (equal eva (mother(sara))).

Skolemization

• Skolemization is a process of replacing each existentially quantified variablewith a function that returns the appropriate constant.

• Eliminating existentially quantified variable is complicated due to the de-pendency of this variable on another variables.

• ∀X∃Y mother(X, Y ) It is equivalent to ∀Xmother(X, f(X))

• ∀X ∀Y ∃Z m(X, Y, Z) ⇒ ∀X ∀Y m(X,Y, f(X, Y ))

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Question:- A logical_Based Financial Advisor?

where minincome(X) = 15000 + (4000 ∗ X)

and minisaving(X) = 5000 ∗ X

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