Standard Form

A formula is in standard form after it has been converted to prenex normal form, Skolemized, and converted into conjunctive normal form. The result is a conjunction of clauses, each of which is a disjunction of literals.

Example: ``Every man loves some woman.''

&forall x [Man(x) &rarr &exist y [Woman(y) &and Loves(x,y)]]

This is Skolemized as:

Man(x) &rarr [Woman(lover(x)) &and Loves(x,lover(x))]

Converted to CNF, it becomes:

(¬ Man(x) &or Woman(lover(x))) &and
(¬ Man(x) &or Loves(x,lover(x)))

Since we know where the &and and &or are in CNF, we can eliminate them and represent clauses in list form in Lisp. Note that we have eliminated all of the algebraic structure in the formulas except for ¬.

( ( (not (man x)) (woman (lover x)) )
  ( (not (man x)) (loves x (lover x)) ) )

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