In the book Discrete Mathematical Structures with Applications to Computer Science by J.P. Tremblay and R. Manohar, there's an example question in the section on Predicate Calculus.
Symbolize the expression "All the world loves a lover".
My solution is:
Rewrite it in the logical form as:
Given any $x$ and $y$, if $x$ is in the world and $y$ is a lover, then $x$ loves $y$.
Then denoting predicates as:
$W(x)$ : $x$ is in the world
$L(x)$ : $x$ is a lover
$R(x,y)$ : $x$ loves y
the above statement could be written as:
$(x)(y)((W(x) \wedge L(y)) \to R(x,y)) $
Is this approach and solution correct? If so, is this solution unique, or are there other "correct" solutions?
I am self-learning Discrete Mathematics using this book, and do not have any "professor" or "mentor" to seek guidance. The below solution given in the book confused me due to the reason mentioned further down, so I am hoping to get some guidance here.
Book solution
$(x)(P(x)\to (y)(P(y) \wedge L(y) \to R(x,y))$
wherein:
$P(x)$ : $x$ is a person
$L(x)$ : $x$ is a lover
$R(x,y)$ : $x$ loves $y$
I hate to put it this way, but I am not convinced the book is right. Logical form of the statement shouldn't be biased by real world experiences. It is nowhere given or implied that "all the world" refers to people only (for example, it could include computers, robots, animals, plants, aliens - logic doesn't care), and logic-wise, it is even less convincing to assume that "a lover is (necessarily) a person".
Formal logic does not (or should not) depend on knowledge of the real world.
Natural language intrinsically does depend on a lot of knowledge of the real world in order to be understood.
When you're translating a natural-language claim to logic, it is part of the task to identify world knowledge that the original claim implicitly depends on, and decide on a reasonable way to represent that explicitly in the logical formalism.
Threre's not necessarily a unique correct way to do this.