Translating Lewis Carroll into First-Order Logic

Part II

Here is an answer to the translation example inspired by a puzzle by Lewis Carroll:

All babies are illogical.
Anyone who can manage a crocodile is not despised.
All illogical people are despised.
Therefore, no baby can manage a crocodile.

Here is the syntax and semantics of the representation in FOPL:

Baby(x)	:	x is a baby
Logical(x)	:	x is logical (or: x is a logical person)
Manages-Crocs(x)	:	x can manage a crocodile
Despised(x)	:	x is despised

Here, finally, is a translation of the above logical argument (or "syllogism"):

∀x[Baby(x) → ¬Logical(x)]
∀x[Manages-Crocs(x) → ¬Despised(x)]
∀x[¬Logical(x) → Despised(x)]
Therefore, ¬∃x[Baby(x) ∧ Manages-Crocs(x)]

Note, by the way, that FOPL is not needed for this example. It could be represented in propositional logic.

For more information on this puzzle, look at "Lewis Carroll Puzzles".

For more information on Lewis Carroll as a logician, look at Lewis Carroll, Logician