In predicate logic there are two types of signs denoting individuals.

Constants are represented by the lower case English letters a ... w
Variables are represented by the lower case English letters x, y, and z

A constant is like a proper noun or a name. It represents a specific individual like JOHN, MARY, or JOHN AND MARY'S DOG.

A variable is like a pronoun except that the English pronouns are gender or human specific while the logical variables are not. The individuals represented by a variable will require logical analysis to be identified. So too for the pronouns in HE IS THE ONE.

A capital letter represents a specific property, relation, or predicate. The suggested notation defines the meaning of the capital letters. The suggested notation also defines the meaning of the individual constants.

A well formed simple proposition consists of a capital letter followed by 1 or more little letters such as Ma and Pab

Sample notation:

  a: Ann

  b: Bob

  Mx: x is a mother

  Pxy: x is a parent of y

  Ma means Ann is a mother, and

  Pab means Ann is a parent of Bob.

In the suggested notation the little letters after a capital are ALWAYS xyz but in forming the translation YOU have to decide which little letters to use.

Examples:

  Cx: x is a child

  Dx: x is a dog

  Px: x is a pet

  Hxy: x has y

In the first example it is important that x is used for both kids and dogs to get across the idea that if Cx then not Dx. In the second example y has to be used for dogs to say that the dogs (not the children) are the pets.