1 / 11

Categorical Logic

Categorical Logic. A useful type of “real world” logic commonly used for characterizing relationships Applications in law, business contracts, natural and social sciences. Categorical Claims. A: All X are Y All means “Every single one, no exceptions.” “And there is at least one.”.

betsy
Download Presentation

Categorical Logic

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 • A: All X are Y All means “Every single one, no exceptions.” “And there is at least one.”

  3. 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

  4. 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.

  5. Categorical Claims • A: All X are Y • E: No X are Y

  6. Categorical Claims • A: All X are Y • E: No X are Y • I: Some X are Y

  7. 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.

  8. Categorical Claims • A: All X are Y • E: No X are Y • I: Some X are Y • O: Some X are not Y

  9. Categorical Claims The direct way of reasoning with ALL All S are P A is s VALID Therefore, a is P

  10. Categorical Claims Reasoning in a chain with All All S are P All P are Q VALID Therefore, all S are Q (This works with All not Some)

  11. Categorical Claims Direct way of reasoning with NO All S are P No Q is a P VALID Therefore, no Q is a S

More Related