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Categories – relations or individuals?. What are the differences in representing collie as a relation vs. an individual? As a relation: collie(lassie)

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Categories relations or individuals
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

  • 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
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
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
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
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
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
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
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
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
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.

Examples


Aspect
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 – 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
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 – 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
Activities - II

  • Examples:

    • John is kicking.

    • John is studying.

  • Diagnostics:

    • fine in progressive (see above!)

    • fine in imperatives:

      • Kick harder!

      • Study longer!


Accomplishments i
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
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
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
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
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
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
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
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
How do we deal with this?

  • Modal logic is a typical approach.

  • Extends FOPC with a belief operator which takes a proposition.


Referential transparency
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
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.


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