As was requested over email, let me provide a worked out example of something like the sentences from Part I, and a couple of notes about parts II−III.

Part I: Translating quantified arguments into FOPL

Suppose that you were asked to translate (12).

(12) Pat ate every sandwich.

What you need to do is provide a key, and a translation. Probably simplest to make a single key for everything (since at least there are a couple in there that refer to the same individuals, or use the same predicates). But here, since there’s just the one sentence, the key would include:

• EAT(x, y) : x ate y
• SANDWICH(x) : x is a sandwich
• p : Pat

Then the translation of this would use the quantifier ∀ (because the English sentence in (12) contains “every”), and what it says is basically for every x that is a sandwich, Pat ate x. Or, in FOPL:

∀x₁( SANDWICH(x) → EAT(p, x₁) )

That’s it for the sentences in Part I, just do that for each of them.

For part II, keep in mind that there’s a difference between “everything likes Bob” and “everyone likes Bob”—the latter one is only generalizing about people, so you’ll want to use the predicate PERSON (at least, in general, if there are any individuals in the domain D that are not people).

For Part III, the models M₁, M₂, etc. are setting out possible actual states of the world. That is, who the professors are and who the vain people are, etc. You won’t actually need to do anything with the assignment function g. The function g is used in the semantic interpretation of a formula with a quantifier in it by taking g and modifying it, but that’s implicit when you write ∀x₁(…). What that means “behind the scenes” is “go through all of the individuals in the domain D, one by one, and for each of them change g so that g(x₁) is the individual you’re considering. Then see if the (…) part is true (where usually the (…) part will contain at least one x₁ that will be replaced by the individual you are considering when you evaluate it). I reiterate that this is not something you need to be writing down on (this) assignment, but that’s how ∀ works. So, step by step, working out something like “everyone is a professor”, we’d translate it as ∀x₁(PROFESSOR(x)) (no need to worry about people vs. non-people, because D as defined has only people in it). To see if it is true, the procedure below is followed:

• Take the first individual in D. It’s Carol.
• Take the assignment function g and change it so that g(x₁)=Carol.
• Check to see if PROFESSOR(x₁) is true (under M₁ and g).
• This is going to be true if g(x₁) ∈ Val(PROFESSOR).
• g(x₁) is Carol according to the change we made a couple of steps ago.
• Val(PROFESSOR) is {Carol, Paul, Pete} according to the definition of model M₁.
• So Carol ∈ {Carol, Paul, Pete} is true.
• Move on to the next individual in D. It’s Paul.
• Take the assignment function g and change it so that g(x₁)=Paul.
• Check to see if PROFESSOR(x₁) is true (under M₁ and g).
• …
• Having no more individuals left, the whole formula ∀x₁(PROFESSOR(x)) is true if we got only “true”s above when we checked whether a formula was true.

So that’s “behind the scenes.” But you can kind of do this in your head. To re-reiterate, you don’t have to write down anything about g or this semantic evaluation procedure on homework 7, but what I wrote above is explaining how it works in FOPL, based on the semantics we have for FOPL. In particular, that PREDICATE(x₁) is true if g(x₁) ∈ Val(PREDICATE).

I’ve gotten a couple of questions about homework 5, but the main one so far is this one:

For part I.A., you are encouraged to “recycle” your constants “to the greatest extent possible” but you need not take this to its logical extreme. Since (1) and (2) both involve John and Mary, and some particular $10 dollars we are considering to be an individual, there’s no need to rewrite “j: John; m: Mary; t: Ten dollars” again in (2), you can use that same key for both (1) and (2). But then you can let it go, and define a new key for (3), with just Toby and the table. So, no need to have a key that defines 20 different individual constants, etc., the idea was more to use groupings of one or two, where the sentences have names or individuals in common.

Hi. Ok, this is very last-minute, but I’ve talked to a few people who don’t feel particularly confident that they are doing the homework right, so I think we’ll take this Tuesday to talk about it some more. It doesn’t really matter whether I get the homework on Tuesday or Thursday, it still won’t be back before after Spring Break, so I’m moving the due date one more time to Thu 3/6. If you’re happy with what you’ve got, great, you can give it to me today, but otherwise Thursday is fine.

Since there is still a bit to cover in class relating to the questions on homework 4, though it says on it that it is due on Thu Feb 27, it is in fact not due until Tue Mar 4. This was mentioned in class, but here it is officially on the course blog as well.

Here’s the first “homework”, just a couple of demographic questions for you. You can email your answers to me. If I did it right, you can click here to start your email with the questions already there. But the questions are:

What other Linguistics courses (or related courses) have you taken?

What are your (actual or planned) major/minors?

What languages (other than English) do you know, and how well?

What language(s) did you grow up speaking?

Do you prefer to be called something other than what I see in the class list?¹

Anything else that seems relevant?

¹Within reason, that is. “Your Excellence” is not a valid answer here.