Question 1.
Translate the following English sentences into predicate calculus; choose your own variables and predicate letters, giving the key. If you think more than one translation is suitable, give the alternatives and discuss their differences. Represent as much as possible of the structure relevant to quantifiers, predicates, and arguments.
You may sometimes need to change a sentence into its paraphrase to represent it. When a part of the MEANING is lost in translation, discuss what is lost.
Example: "If John is at the party, then Mary is, too"
Key: p - the party, j - John, m - Mary, AT - at
(AT(j,p) -> AT(m,p))
a. Either John is in that room or Mary is, and possibly they both are.
b. When it rains, it pours.
c. Sam wants a dog, but Alice wants cats.
d. If Steve comes late and has not had any supper, we will reheat the stew.
e. Everything is black or white.
f. Either everything is black or it is white.
g. A dog is a quadruped.
h. Fido is a dog
i. Everybody loves somebody.
j. If you love a woman, kiss her or lose her.
k. If someone loves someone, John loves himself.
Question 2.
Partee et al. chapter 13 - exertise 6, pp.369-370. (a)-(i)
Non-graded discussion-starter Question 3.
As a translation of the sentence "Everyone answered all the questions", the statement (Every x)(Every y) Answered(x,y) is not adequate, because our universe of discourse must contain both people and questions (so, the formular means "Everything answered everything". We have to represent the two sets (the set of people and the set of questions) by two predicates in the antecedent of a conditional formula. In the light of this discussion, translate the following sentences.
(a) No one answered every question.
(b) For every question there was someone who answered it.
(c) Everyone answered at least one question.
(d) Some people didn't answer any questions.
(e) Everyone likes Mary except Mary herself.
(f) Everyone but Fred answered at least one question.
(g) Everyone who answered a question attempted some question or other.
(h) No one answered any question that everyone attempted.
(i) Everyone who attempted a question answered it.