Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

original expression:
( ¬ P11 ∨ ¬ P12 ...∨ ¬ P1n ∨ Q11 ∨ Q12.... ∨ Q1m ) ∧
(¬ P21 ∨ ¬ P22 ... ∨ ¬ P2n ∨ Q21 ∨ Q22 ... ∨ Q2m) ∧
....
(¬ Pt1 ∨ ¬ Pt2 ... ∨ ¬ Ptn ∨ Qt1 ∨ Qt2 .... ∨ Qtm).
After writing one clause per line, the resulting expressions become as follows.
P11, P12,..., P1n → Q11, Q12,... ,Q1m
P21 , P22 ,...,P2n → Q21, Q22,..., Q2m
... … … … …. …. …
Pt1, Pt2,..., Ptn → Qt1, Qt2,.…., Q tm
With reference to the above, we get the following line as the final expression.
Child (X), Takes (X, Y), Biscuit (Y) → Loves (john, X).
It may be noted that the resulting expression, derived above, is not much
different from the expression (3). This, however, is not the case for all
complex sentences. For example, let us consider the following complex
sentence and the clause forms corresponding to that.
Expression: ∀ X ( Loves (john, X) → Female (X) )
∧ ∃ X ( ¬ Loves (X, Brother-of (X) ∧ Female (X)))
The clause forms for the above expression are:
a) Loves (john, X) → Female (X)
b) Loves (s(X), Brother-of (s (X))), Female (X) → _|_
where the meaning of the first clause is obvious, while the second clause
means that it is impossible that there exists a female X, who loves her
brother. The inverted T is called a Falsum operator, which is opposite to
Truam (T), meaning that the expression is true [2]. The symbol s(X) denotes a
Skolem function of X, which may be read as some of X.