Categorical Logic l A useful type of “real world” logic commonly used for characterizing relationships l Applications in law, business contracts, natural and social sciences

Categorical Claims l A: All X are Y

Categorical Claims l 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 XsThe only Xs are Ys

Categorical Claims l 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 XsThe only Xs are Ys Note: X and Y must be nouns or noun phrases.

Categorical Claims l A: All X are Y l E: No X are Y

Categorical Claims l A: All X are Y l E: No X are Y l I: Some X are Y

Categorical Claims l A: All X are Y l E: No X are Y l 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.

Categorical Claims l A: All X are Y l E: No X are Y l I: Some X are Y l O: Some X are not Y

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