Clausal Normal Form - Conversion To Clausal Normal Form

Conversion To Clausal Normal Form

The procedure to convert a formula into clausal form can destroy the structure of the formula, and naive translations often causes exponential blowup in the size of the resulting formula.

The procedure begins with any formula of classical first-order logic:

  1. Put the formula into negation normal form.
  2. Standardize variables
    • becomes, where is new
  3. Skolemize -- replace existential variables with Skolem constants or Skolem functions of universal variables, from the outside inward. Make the following replacements:
    • becomes, where is new
  4. Discard the universal quantifiers (which are implicit in CNF).
  5. Put the formula into conjunctive normal form.
  6. Replace with . Each conjunct is of the form, which is equivalent to .

When n ≤ 1 for all clauses, the logic is called Horn clause logic and is equivalent in computational power to a universal Turing machine. Horn logic is the basis of Prolog, the most widely used logic programming language.

Often it is sufficient to generate an equisatisfiable (not an equivalent) CNF for a formula. In this case, the worst-case exponential blow-up can be avoided by introducing definitions and using them to rename parts of the formula.

Read more about this topic:  Clausal Normal Form

Famous quotes containing the words conversion, normal and/or form:

    “The conversion of a savage to Christianity is the conversion of Christianity to savagery.”
    —George Bernard Shaw (1856–1950)

    “You know that fiction, prose rather, is possibly the roughest trade of all in writing. You do not have the reference, the old important reference. You have the sheet of blank paper, the pencil, and the obligation to invent truer than things can be true. You have to take what is not palpable and make it completely palpable and also have it seem normal and so that it can become a part of experience of the person who reads it.”
    —Ernest Hemingway (1899–1961)

    “Self-esteem is the real magic wand that can form a child’s future. A child’s self-esteem affects every area of her existence, from friends she chooses, to how well she does academically in school, to what kind of job she gets, to even the person she chooses to marry.”
    —Stephanie Martson (20th century)