I am still learning first-order logic and needed some help understanding these s
ID: 3596483 • Letter: I
Question
I am still learning first-order logic and needed some help understanding these sentences.
Translate each of the following English sentences into rst-order logic, using only the following constants and predicates ...
Constants:
• Emily — a person named Emily
• Joe — a person named Joe
• Actor — the occupation of being an actor
• Doctor — the occupation of being a doctor
• Lawyer — the occupation of being a lawyer
• Surgeon — the occupation of being a surgeon
Predicates:
• Occupation(x,y) — person x has occupation y
• Customer(x,y) — person x is a customer of person y
• Boss(x,y) — person x is a boss of person y
• Equal(x,y) — x and y are the same object
Exercises:
1. “Emily is either a surgeon or a lawyer.”
2. “Joe is an actor, but he also holds another job.”
3. “All surgeons are doctors.”
4. “Joe does not have a lawyer.” (He is not the customer of any lawyer.)
5. “Emily has a boss who is a lawyer.”
6. “There exists a lawyer all of whose customers are doctors.”
7. “Every surgeon has a lawyer.”
Explanation / Answer
Solution:
EMILY IS EITHER A SURGEON OR A LAWYER:
ans:Occupation(Emily, Surgeon) V Occupation(Emily, Lawyer)
2)Joe is an actor, but he also holds another job.
ans:Occupation(Joe, Actor) ^ ( Occupation(Joe, Doctor) V Occupation(Joe, Surgeon) V Occupation(Joe, Lawyer) )
3)All surgeons are doctors:
ans:p Occupation(p, Surgeon) --> Occupation(p, Doctor)
4) Joe does not have a lawyer." (He is not the customer of any lawyer.)
ans:~Customer(Joe, Lawyer)
5)Emily bas a boss who is a lawyer.
ans:Boss(Emily, Lawyer)
6)'There exists a lawyer all of whose customers are doctors."
ans:p1p2 Occupation(p1, Lawyer) --> Customer ( p2, p1 ) ^ Occupation (p2, Doctor)
7)Every surgeon has a lawyer:
ans:p1p2 Occupation(p1, Surgeon) -->Customer(p1, p2) ^ Occupation(p2, Lawyer)
Please, please upvote and ask your doubts in the comments.
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