Slide 14.3: An example of first-order predicate calculus

Slide 14.2: First-order predicate calculus
Slide 14.4: Inference rules
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An Example of First-order Predicate Calculus

The following are logical statements in English:

A horse is a mammal.
A human is a mammal.
Mammals have four legs and no arms, or two legs and two arms.
A horse has no arms.
A human has arms.
A human has no legs.

A possible translation of these statements into first-order predicate calculus is as follows:

   mammal( horse ).
   mammal( human ).
     for all x, mammal( x )
   → legs(x, 4) and arms(x, 0) or legs(x, 2) and arms(x, 2).
   arms( horse, 0).
   not arms( human, 0 ).
   legs( human, 0 ).

In this example,

The constants are the integers 0, 2, and 4 and names horse and human.
The predicates are mammal, arms, and legs.
The only variable is x.
The first five statements are axioms.
arms(human,2) becomes provable from the axioms.
legs(human,2) is true also, so the last statement is false.

Precedence can be used to leave out many parentheses. For example,

 legs(x,4) and arms(x,0) or legs(x,2) and arms(x,2)

is the same as

 (legs(x,4) and arms(x,0)) or (legs(x,2) and arms(x,2))