• Premise 1: All (A) is (B)
  This forces any region with (A) and (¬ B) to be (0). These are the 3rd and 4th slots ((A¬ BC) and (A¬ B ¬ C)).

  V_{All B is C} = (1, 1, 0, 0, 1, 1, 1, 1)

• Premise 2: All (B) is (C)
  This forces any region with (B) and (¬ C) to be (0). These are the 2nd and 6th slots ((AB¬ C) and (¬ AB¬ C)).

  V_{All B is C} = (1, 0, 1, 0, 1, 0, 1, 1)

• Conclusion: All (A) is (C)
  This forces any region with (A) and (¬ C) to be (0). These are the 2nd and 4th slots ((AB¬ C) and (A¬ B¬ C)).

  V_{All A is C} = (1, 0, 1, 0, 1, 1, 1, 1)

[ Premise Intersection Vector ] ===> ( 1, 0, 0, 0, 1, 0, 1, 1 ) [Weight 4]
                                       │  │  │  │  │  │  │  │ 
                                       ▼  ▼  ▼  ▼  ▼  ▼  ▼  ▼
[ Target Conclusion Vector ] ===>    ( 1, 0, 1, 0, 1, 1, 1, 1 ) [Weight 6]

                                 (Upward Lattice Flip)

• Map out a negative syllogism (like Celarent: No B is C, All A is B, therefore No A is C) [1].
• See how invalid syllogistic fallacies (like the Undistributed Middle) manifest as broken or disconnected geometric paths where you get trapped on an adjacent vertex. [1, 2]

3 sites

• Establishing Validity | Introduction to Philosophy

  Although the modern interpretation of categorical logic provides an easier method for determining the validity of categorical syll…

  
  Lumen Learning
   
• Alice, Aristotle’s Syllogisms & Boole’s AND, OR & NOT

  CELARENT, the Negative Universal Syllogism: If All A is B, and No B is C, then No A is C.

  
  
  ericgerlach.com
   
• Categorical Syllogisms | The Logic Book: Critical Thinking | OpenALG

  It does this using the relationship those two terms have to the third term M. But if M is never distributed, then S and P can be d…

  
  
  OpenALG