Translate English to First Order Logic 1. Variables: p ranges over people, v ran

Question

Translate English to First Order Logic
1. Variables: p ranges over people, v ranges over volumes, b ranges over books
2. Constants: John, Mark, Christine, Evan
3. Predicates
- Owns(p,v): person p owns volume v
- Author(p,b): person p wrote book b
- Copy(v,b): volume v is a copy of book b

Please express each of the following as a sentence in L

1. Mark owns all John’s books
2. John owns a book that is writing by Evan
3. Mark and Christine wrote a book together
4. An author does not own a copy of his/her own book
5. John and Evan did not wrote a book together
6. If Christine owns a copy of a book, then Mark owns a copy of the same book

Explanation / Answer

Using (Av) to mean "for all v" Using (Ev) to mean "there exists a v" 1. (Ab) [Author(John,b) -> (Ev) (Copy(v,b) ^ Owns(Mark,v))] 2. (Eb) (Ev) [Owns(John,v) ^ Copy(v,b) ^ Author(Evan,b)] 3. (Eb) (Author(Mark,b) ^ Author(Christine,b)) 4. This sentence is a little ambiguous. I'm interpreting it to mean "There is an author who wrote a book that he/she does not own a copy of." (Ep)(Eb) [Author(p,b) ^ -(Ev) (Copy(v,b) ^ Owns(p,v))] 5. -(Eb) (Author(John,b) ^ Author(Evan,b)) 6. (Ab) {[(Ev) (Owns(Christine,v) ^ Copy(v,b))] -> (Ev) (Owns(Mark,v) ^ Copy(v,b))}

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