Categorical Logic

1
Categorical Logic

• A useful type of real world logic commonly used
  for characterizing relationships
• Applications in law, business contracts, natural
  and social sciences

2
Categorical Claims

• Categorical claims relate two different concepts
  to each other.
• Each concept must be expressed as a noun or noun
  phrase.
• Standard form claims are the simplest way to
  express categorical relationships.

3
Categorical Claims

• Many natural language statements can be expressed
  as standard form categorical claims.
• There are only four forms or statement types in
  which standard form categorical claims occur.
  They are designated A, E, I, and O.

4
Categorical Claims

• A All X are Y

5
Categorical Claims

• A All X are Y

In natural language Every X is a Y. Each X is
a Y. If it is an X, then it is a Y. All Xs are
Ys. Any X is a Y. All non-Ys are non-Xs. Only
Ys are Xs The only Xs are Ys
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Categorical Claims

• A All X are Y

In natural language Every X is a Y. Each X is
a Y. If it is an X, then it is a Y. All Xs are
Ys. Any X is a Y. All non-Ys are non-Xs. Only
Ys are Xs The only Xs are Ys Note X and Y must
be nouns or noun phrases.
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Categorical Claims

• A All X are Y
• E No X are Y

8
Categorical Claims

• A All X are Y
• E No X are Y
• I Some X are Y

9
Categorical Claims

• A All X are Y
• E No X are Y
• I Some X are Y

Note The range of some in categorical logic is
from as few as one to as many as all of the
things in the category.
10
Categorical Claims

• A All X are Y
• E No X are Y
• I Some X are Y
• O Some X are not Y

11
A-claim
E-claim
I-claim
O-claim
The Square of Opposition Claims of different
types with the same subject and predicate terms
are corresponding claims.