Clausal-Form Logic (2)

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There are some alternative classifications of clauses:

• Indefinite clauses are called non-Horn clauses (all others are Horn clauses).
• In the logic programming context, positive unit clauses are also called assertions.
• All other definite clauses are called conditional clauses.
• In the Prolog context, positive unit clauses are called facts.
• All other definite clauses are called rules.
• Negative clauses are called either queries or goal clauses in logic programming or Prolog.

A set of clauses can also be classified.

• A program is a set of non-negative clauses. (a.k.a. A database, a knowledge base or a rule base).
• A set of definite clauses whose positive literals all share the same predicate symbol is referred to as either a definition or as a procedure for that symbol.

Clausal Form	Prolog equivalent	Classification
a	a.	Fact
a ¬b ¬c	a :- b, c	Rule

The second example can be clarified as follows

a ¬b ¬c
 = a ¬(b c)
 = (b c) a
 = a (b c)
 = a :- b, c.     (reads as "a if b and c")

Programs can be separated into two parts, definite and indefinite. A program consisting of only definite clauses is a definite program. Any other program is an indefinite program. Indefinite programs are much more complicated to implement. The following is an example of a definite program, it is a definition for 'likes':

likes(sim, X) likes(X, logic)
likes(sim, logic)
likes(max, logic)
likes(X, Y) loves(X, Y)

In some cases, sentences are naturally written down in unrestricted first order logic. They then need to be converted into clausal form. This can be done using a sequence of steps, that can be defined in an algorithm.

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