Categories – relations or individuals?

What are the differences in representing collie as a relation vs. an individual?

As a relation: collie(lassie)– Can reason only about members of the category collie, not

about the category (FOPC only allows terms, not predicates, as arguments of predicates: cannot make true/false statements about predicates): goodWithKids(lassie).

As an individual: ISA(lassie,collie)– Can make statements about both categories and individual

members of categories: goodWithKids(lassie) goodWithKids(collie)

Reification

Reification is the technique we used to make collie an individual; reification is sometimes called objectification.

ISA is a member-class relationship– ISA(lassie, collie)

AKO (A Kind Of) is a subclass-superclass relationship:– AKO(collie, dog)– AKO(dog, mammal)– AKO(mammal, animal)

Events – relations or individuals?

We face the same question for events as we did for categories.

Should we represent events as relations or as individuals?

Looking at syntax it seems that representing the event as a relation is natural (think of subcategorization frames).

But, this implies we can’t reason about events! Take the same approach as with categories: reify!

Basic problem (p. 524-525)

Examples with the verb to eat:– I ate.– I ate a turkey sandwich.– I ate a turkey sandwich at my desk.– I ate at my desk.– I ate lunch.– I ate a turkey sandwich for lunch.– I ate a turkey sandwich for lunch at my desk.

All describe an event of eating. What is a reasonable representation?

Events as relations

Suppose we decide that events should be represented as relations.

Q: What is the arity (# arguments) of the predicate? A: It is different in different examples!

– Eating1(Speaker)– Eating2(Speaker, TurkeySandwich)– Eating3(Speaker, TurkeySandwich, Desk)– Eating4(Speaker, Desk)– Eating5(Speaker, Lunch)– Eating6(Speaker, TurkeySandwich, Lunch)– Eating7(Speaker, TurkeySandwich, Lunch, Desk)

Reasoning problem

While we can build such representations, they do not possess the desired characteristics.

For example, we cannot reason with these representations to learn that they all describe the same type of event (an eating event):

– Eating1 Eating2 Eating3 Eating4 Eating5 Eating6 Eating7

Can solve this problem by introducing meaning postulates, such as, w,x,y,z Eating7(w,x,y,z) Eating6(w,x,y)

Such a solution does not scale well (since these have to be explicitly encoded into knowledge base).

Additional problems

Assumes that underlying event always has four arguments (eater, food, meal, location)– but surely you can eat outside of regular meal

times

Can’t express that two (partial) descriptions are about the same event: w,x Eating(Speaker, w, x, Desk) w,x Eating(Speaker, w, Lunch, x)

w Eating(Speaker, w, Lunch, Desk)

Reification of event is a better solution

Compare the following two representations of “I ate a Turkey sandwich” w,x Eating(Speaker, TurkeySandwich, w, x) e ISA(e,Eating)Eater(e,Speaker)Eaten(e,TurkeySandwich)

Advantages:– “There is no need to specify a fixed number of arguments for a

given surface predicate, rather as many roles and fillers can be glued on as appear in the input.” [p. 527]

– “No more roles are postulated than are mentioned in the input.” [p. 527]

– “The logical connections among closely related examples is satisfied without the need for meaning postulates.” [p. 527]

Time and events

Consider the following three examples (cf examples on page 528)– I will arrive in Buffalo.– I am arriving in Buffalo.– I arrived in Buffalo.

They all describe an event of arriving: e ISA( e, Arriving ) Arriver( e, Speaker )

Destination( e, Buffalo ) What makes them different is the time of the

event.

Representing the time of an event

e,i,t ISA(e,Arriving) Arriver(e,Speaker) Destination(e,Buffalo) IntervalOf(e,i) EndPointOf(i,t) Precedes(Now,t)

e,i,t ISA(e,Arriving) Arriver(e,Speaker) Destination(e,Buffalo) IntervalOf(e,i) MemberOf(i,Now)

e,i,t ISA(e,Arriving) Arriver(e,Speaker) Destination(e,Buffalo) IntervalOf(e,i) EndPointOf(i,t) Precedes(t,Now)

Representing time

Reichenbach (1947)– E is the event time– R is the reference time– U is the utterance time

See diagram on page 530.

Examples

Simple past (R=E < U) Present (R=E=U) Simple future (R=U < E)

Past perfect (E<R<U) Present perfect (E<R=U) Future perfect (U<E<R)

I ate. I eat. I will eat.

I had eaten. I have eaten. I will have eaten.

Aspect

The aspect of an event describes:– whether event is ongoing or completed– whether it occurs at a point in time or over an

interval of time– whether its completion results in a change in the

state of the world Events are classified as one of:

– state– activity– accomplishment– achievement

States – I

“States are like snapshots of the world at a given instant. They lack a natural culmination or end point, and their subject is perceived not as an agent (as doing something) but as an experiencer (as experiencing something).”

“Meaning and Grammar: An Introduction to Semantics” by Chierchia and McConnell-Ginet, p. 353

States – II

Examples:– John is drunk.– John knows Latin.

Diagnostics:– not good in progressive:

*John is being drunk. *John is knowing Latin.

– not good in imperative: *Be drunk! *Know Latin!

Activities – I

“Activities share with states the property of lacking a natural culmination. Yet they are agentive in that they typically involve a subject doing something. They cannot in general be viewed as instantaneous snapshots of the world.”

[ibid, p. 353]

Activities - II

Examples:– John is kicking.– John is studying.

Diagnostics:– fine in progressive (see above!)– fine in imperatives:

Kick harder! Study longer!

Accomplishments – I

“accomplishment expressions describe events that have a natural end point and result in a particular state.” [p. 532]

Examples [p. 532]:– He booked me a reservation.– United flew me to New York.

Accomplishments – II

Diagnostic: stop [p. 532]:– I stopped living in Brooklyn. [activity]– She stopped booking my flight. [accomplishment]

Inferences?– I lived in Brooklyn.– but not: She booked my flight. (intended state was

not reached) Diagnostic: temporal adverbials [p.533]

– *I lived in Brooklyn in a year. [activity]– She booked a flight in a minute. [accomplishment]

Achievements – I

“[Achievement expressions] are similar to accomplishments in that they result in a state. […] Unlike accomplishments, achievement events are though of as happening in an instant, and are not equated with any particular activity leading up to the state.” [p. 533]

Achievements – II

Examples:– She found her gate.– I reached New York.

Diagnostic: temporal adverbial [p. 533]– I lived in New York for a year. [activity/accomplishment]– *I reached New York for a few minutes. [achievement]

Diagnostic: stop [p. 533]– I stopped booking my flight. [accomplishment]– *I stopped reaching New York. [achievement]

Beliefs

Up to this point we have been discussing simple utterances, with (relatively) straightforward representations.

Utterances have expressed propositions which we have represented as being either true or false.

Not all utterances are like this.

Example

Consider– John believes that Mary likes ice cream.

The utterance as a whole can be either true or false.

But, does Mary like ice cream?

How do we represent the semantics of this sentence?

Possible representation #1

u,v ISA(u,Believing) ISA(v,Liking) Believer(u,John) BelievedProp(u,v) Liker(v,Mary) Liked(v,IceCream)

Is this a good representation of the sentence?

No.

It implies that Mary likes ice cream, which may not be the case: just because someone believes something to be true does not make it so.

Possible representation #2

Believing(John,Liking(Mary,IceCream))

Is this a good representation?

It doesn’t imply that Mary likes ice cream.

No.

Its not well-formed FOPC!

How do we deal with this?

Modal logic is a typical approach.

Extends FOPC with a belief operator which takes a proposition.

Referential transparency

Consider:– Snow has delayed Flight 1045.– John’s sister’s flight serves dinner.

If John’s sister’s flight is flight 1045, then the truth conditions of the following pairs are the same:– Snow has delayed Flight 1045.– Snow has delayed John’s sister’s flight.

– John’s sister’s flight serves dinner.– Flight 1045 serves dinner.

Referential opacity

Consider:– John believes snow has delayed Flight 1045.– John believes his sister’s flight serves dinner.

If John’s sister’s flight is flight 1045, but John doesn’t know this, then the truth conditions of the following pairs are not necessarily the same:– John believes snow has delayed Flight 1045.– John believes snow has delayed John’s sister’s flight.

– John believes his sister’s flight serves dinner.– John believes Flight 1045 serves dinner.