From owner-cse191-sp08-list@LISTSERV.BUFFALO.EDU Wed Jan 30 13:35:01 2008 Date: Wed, 30 Jan 2008 13:34:44 -0500 From: "William J. Rapaport" Subject: 191: TRANSLATION OF ENGLISH IN THE LANGUAGE OF LOGIC -- Part II To: CSE191-SP08-LIST@LISTSERV.BUFFALO.EDU ------------------------------------------------------------------------ Subject: 191: TRANSLATION OF ENGLISH IN THE LANGUAGE OF 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. 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 Note: I'll also use "Ax" and "Ex" for "for all x" and "for some x", respectively. Translation of the above logical argument (or "syllogism"): Ax[Baby(x) -> -Logical(x)] Ax[Manages-Crocs(x) -> -Despised(x)] Ax[-Logical(x) -> Despised(x)] Therefore, -Ex[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" at: http://www.cse.buffalo.edu/~rapaport/191/S08/logic.html or directly at: http://www.math.hawaii.edu/~hile/math100/logice.htm