Linneus Quiz on Transivity of isa and hasa Rules
Answers

Rule 1: if X is a Y  and Z has a X, then Z has a Y  (hasa - isa --> hasa)

Rule 2: if X is a Y and Y has a Z, then X has a Z  (isa - hasa --> hasa)

Rule 3: if X is a Y and Y is a Z, then X is a Z  (isa - isa --> isa)

Rule 4: if X has a Y and Y has a Z, then X has a Z (hasa - hasa --> hasa)

(a turbot is a fish)
(a fish is an animal)
(an animal has a heart)
(a heart is an organ)
(an organ has a cell)

therefore: (has a turbot a cell) is true


                                      organ (has a cell)  (Rule 4) hasa - hasa, 
                                       /                      turbot has a cell
                                    isa     Rule 1: hasa - isa, turbot has an
                                     /                            organ
                     animal (has a heart)    Rule 2: isa - hasa, turbot has a 
                     /                                           heart
                  isa
                  /
                fish      Rule 3: isa - isa, turbot is an animal
               / 
             isa 
             /
          turbot

1. (Rule 3) use the transitivity of "isa": a turbot is a fish and a fish is an 
   animal, so a turbot is an animal.
2. use Rule 2, because a turbot is an animal and an animal has a heart, then
   a turbot has a heart.
3. use Rule 1, because a turbot has a heart, and a heart is an organ, then
   a turbot has an organ.
4. (Rule 4) use transitivity of "hasa", if a turbot has an organ and an organ 
   has a cell, then a turbot has a cell.