april 2010nl metaphysics1 natural language metaphysics

April 2010 NL Metaphysics 1

Natural Language Metaphysics


Outline

• Ontology– Time

• Linguistic Phenomena– Tense– Adverbial Modification


Focus

Language

Logic

World

Model


Making ModelResemble World

• Add more detail

• Semantic Repositories– Annotated databases– Ontologies

• CYC

• But apart from more detail we need ...


Abstract Entities

• .... what Emmon Bach called Natural Language Metaphysics.

• That is: what kinds of things need to be in the world for natural language to work the way it does? In particular regarding

• Time• Events • Agents


Language and Time

• Temporal Reference: Yesterday, now, 16.45, three days ago, when the bus arrived, 12th July 1959, after the goldrush, Monday

• Tense: markings on the verb that (among other things) serve to locate some state or happening relative to the time of utterance.

• Aspect: verbal indications of the status of a happening. e.g. whether it is completed or ongoing


Markup - TIMEML: http://www.timeml.org/site/index.html

• TimeML is a robust specification language for events and temporal expressions in NL– Time stamping of events– Ordering events with respect to one another

(lexical versus discourse properties of ordering); – Reasoning with contextually underspecified

temporal expressions (temporal functions such as 'last week' and 'two weeks before');

– Reasoning about the persistence of events (how long does an event or the outcome of an event last).

http://www.timeml.org/site/index.html

http://www.timeml.org/site/index.html


Past Tense

• Consider the sentence: Vincent smiled

• What does it mean?

• How can we represent its meaning in first-order logic?

• We can do so quite easily if we are prepared to allow ourselves to admit times into our view of the world . . .


Et (time(t) & t < now & smile(vincent, t))

• one-place predicate time to indicate that something is a time,

• a two-place binary relation smile involving both an ordinary individual and a time.

• < to indicate the relation of temporal precedence between times

• a constant now to single out a special time, namely the time of utterance.

• Class Exercise: a man smiled


Two Time Points

• Note that this representation essentially involves two points of time– speech time (that is, now ) – event time (that is, the t when the smiling

happened).

• Past tense is being explained in terms of the relationship between two points of time

• Can the meaning of all tenses of English be explained as a relation between two points of time?


Past Perfect (or Pluperfect)

• Consider Vincent had smiled

• Hans Reichenbach said that this tense (the past perfect tense) asserts that there was some past time r, and that before that time r, Vincent smiled.

• Class exercise: translate into FOL


Vincent had smiled

E t E r

( time(t) &

time(r) &

t < r &

r < now &

smile(vincent, t))


Reichenbach

• Reichenbach claimed that three points of time were sufficient for the semantics of natural language tenses:– speech time, – event time, and – reference time.

• His ideas (usually modified in various ways) continue to be influential.


Riechenbach Links

• Reichenbach, Hans. 1947. Elements of Symbolic Logic. New York: Macmillan.

• Michaelis L, Time and Tense in B. Aarts and A. McMahon, (eds.), The Handbook of English Linguistics. Oxford:http://spot.colorado.edu/~michaeli/MichaelistenseHEL.pdf

• Hackmack, S., Reichenbach’s theory of tense and its application to Englishhttp://www.fb10.unibremen.de/khwagner/verb/pdf/Reich.pdf


Tense in Text

• Vincent woke up. Something felt very wrong. Vincent reached under his pillow for his Uzi.

• How many events?

• What temporal relations exist between them?


Tense in Text

• Vincent woke upEt(t < now & vincent-wake-up(t))

• Something felt very wrongEu(u < now & something-feel-very-wrong(u))

• Vincent reached under his pillow for his UziEs(s < now & vincent-reach-under-pillow-for-uzi(s))

• What’s missing?


Tense in Text

Et(t < now & vincent-wake-up(t)) &Eu(u < now & something-feel-very-wrong(u)) & Es(s < now & vincent-reach-under-pillow-for-uzi(s))

• What’s missing?


Tense in Text

Et(t < now & vincent-wake-up(t)) &Eu(u < now & something-feel-very-wrong(u)) & Es(s < now & vincent-reach-under-pillow-for-uzi(s))

• These representations do not capture the desired discourse interpretation

• The relation between the three timepoints is not captured

• Quantifier scoping


Tense in Text

Et(t < now & vincent-wake-up(t)) ∧Eu(u < now & something-feel-very-wrong(u)& u=t) ∧∃s(s < now ∧ vincent-reach-under-pillow-for-uzi(s) & u < s)


A Good Argument?

Mia fainted before Vincent got in the car

Vincent got in the car before Butch killed the boxer

|=

Mia fainted before Butch killed the boxer


A Good Argument?

Mia fainted before Vincent got in the car

Vincent got in the car before Butch killed the boxer

|=

Mia fainted before Butch killed the boxer

• However it is not valid because ....


A Countermodel

• Assume there are 3 time points: t, u and s.– faint(Mia, t)– get_in_car(Vincent,u)– kill(Butch, Boxer, s)

• t < u• u < s• not t < s


A Countermodel

• Assume there are 3 time points: t, u and s.– faint(Mia, t)– get_in_car(Vincent,u)– kill(Butch, Boxer, s)

• t < u• u < s• not t < s• transitivity of < needs to be stated to exclude

such a model


A point-based temporal ontology

• For all times t, r, s:– Irreflexivity: not (t < t)– Transitivity: (t < s & s < r) => t < r– Linearity: (t ≤ s & s ≥ t) => s = t


Are points really enough?

• Handling words like during and while• Handling progressive tenses of English (this

is, the -ing tenses) require access to intervals?

• Both seem to require reference to intervals.• A lot of this has to do with what linguists call

aspect.• There are many interesting constraints here,

involving both points and intervals.


Present Progressive

• John is running

Et (interval(t) & now t & run(vincent, t))• One-place predicate interval, • Two-place predicate for inclusion.• Quantification over intervals. • We also need some constraints. • What aspects of reality should it reflect?


An interval based temporal ontology: constraints

• For all times t, r, s:

• Reflexivity inclusion: t t

• Transitivity inclusion: (t s & sr) → t r

• Antisymmetry inclusion:(t s & s t) → t = s


Interval Based Ontology

• For all time intervals r, s and t

• Irreflexivity: not (t<t)

• Transitivity (t < s) & (s < r) => (t < r)

• Note that we no longer demand linearity. Why not?


Linguistically inspired temporal-constraints

• Some verbs (process verbs) require downwards persistence.

• Other verbs (achievement verbs) can't have this.

• Process verb: John is running at an interval implies that John is running over all its sub-interval.

• Achievement verbs: John crossed the road at some interval implied that he did not do so at a smaller interval.


Points and Intervals?

• Perhaps we should have both points and intervals

• Interesting work on making points out of intervals and intervals out of point; see The Logic of Time, by Johan van Benthem.

• But key point is that we probably do want to work with models in which both are present (in some form or another) as things we can quantify across.


Semantics of Events


Problem: How to represent meanings of• Vincent ate.• Vincent ate a big Kahuna burger.• Vincent ate a big Kahuna burger with

his hands.• Vincent ate a big Kahuna burger with

his hands for breakfast.• Key point: we are using eat with varying

numbers of arguments and modifiers.


Attempt 1:Multiple eat relations

• Vincent ate: ate1(vincent)• Vincent ate a big Kahuna burger:

ate2 (vincent,big-k-burger)• Vincent ate a big Kahuna burger with his hands:

ate3 (vincent,big-k-burger,his-hands)• Vincent ate a big Kahuna burger with his hands

for breakfast: ate4 (vincent,big-k-burger,his-hands,breakfast)


Problems• Ugly. Must remember, e.g. that the third slot

represents the implement used to perform the eating, and that the fourth slot is used to represent the meal/

• eat1 and eat2 are two wholly distinct symbols.• So what?


Problems• Ugly. Must remember, e.g. that the third slot

represents the implement used to perform the eating, and that the fourth slot is used to represent the meal/

• eat1 and eat2 are two wholly distinct symbols.• fundamental inferences are lost:

eat2(vincent,big-k-burger) /|= eat1(vincent).• This is because in some model they will have

no connection with one another.


Quick Fix

• Add appropriate axioms: e.g.AxAy (eat2 (x,y) => eat1 (x))

• But such axioms are merely there to do a certain (boring) job.

• Lots of axioms required . For example, instead of axioms linking eats and hunger we need to be carefully to add axioms linking all the eatn and all the hungrym predicates.


Attempt 2: quantifying out

• Basic idea. make use of one eat predicate, with enough arguments to cover everything we need. For exampleeat(agent,patient,instrument,meal,location )

• Then, to represent sentences that don't need all this information, we simply quantify out all the redundant slots using the existential quantifier. . .


Quantifying Out

• Vincent ate a big Kahuna burger with his hands for breakfast (location missingEl ate(vincent,big-k-burger,his-hands,breakfast,l)

• Vincent ate a big Kahuna burger with his hands: EmEl ate(vincent,big-k-burger,his-hands,m,l)

• Vincent ate a big Kahuna burger:Ei Em El ate(vincent,big-k-burger,i,m,l)

• Vincent ate: Ep Ei Em El ate(vincent,p,i,m,l)


This is an improvement because

• We have recovered the missing inferences without needing to add axioms.

• e.g. if Vincent ate a big kahuna burger it follows that Vincent ate something.

• In this case Ei Em El ate(vincent,big-k-burger, i ,m,l)|= Ep Ei Em El ate(vincent,p,i,m,l)

• The required inference follows directly from the semantics of the existential quantifier.


Still no good ...

• One obvious problem, How do we know we've got all the slots in the predicate we need?

• In fact,eat(agent,patient,instrument, meal,location )is probably insufficient.

• We will need at least eat(agent,patient,instrument,meal,location,time)

• But even if we get this completely correct, we're still in trouble . . .


Problem: Adverbial Modification

• All the sentences we have been discussing can be modified by adverbs such as greedily, slowly, rapidly, piggishly, fastidiously, ceremoniously, ravenously, a-bit-like-Bogart-in-that-film-whose-name-I-forget-ily, surreptitiously, etc.

• That is, adverbial modification works in a potentially unlimited way that we can modify the sentence.

• This casts strong doubt on the previous approach.


Concretely

• How should we represent the following sentences?

• Vincent ate - greedily.• Vincent ate a big Kahuna burger - greedily.• Vincent ate a big Kahuna burger with his

hands - greedily. • Intuition: Underlying all these sentences is

something: and we are ascribing the greedilyproperty to that thing (whatever it is).


The concrete strategy

• OK, so we'll hold onto our intuition that there is a thing out there that is being modified.

• We will call these things events.• We will work with models containing

certain special kinds of entities called events.

• This lets us do some useful things . . .


Our Sentences Revisited• Vincent ate:

Ee (eating(e) & agent(e,vincent))• Vincent ate a big Kahuna burger:

Ee (eating(e) & agent(e,vincent) & patient(e,big-k-burger))

• Vincent ate a big Kahuna burger at three o'clock in the room where the suitcase was hidden: Ee (eating(e) & agent(e,vincent) ∧ patient(e,big-k-burger) & time(e,3.00) & location(e,room-suitcase-hidden))


We win because

• from Vincent ate a big kahuna burger we want it to follow that Vincent ate something.

• As with the previous solution, we have recovered the missing inferences without needing to add axioms: Ee (eating(e) & agent(e,vincent) ∧ patient(e,big-k-burger)) |= Ee (eating(e) & agent(e,vincent))


We win because ...

• We can handle adverbsVincent ate Ee (eating(e) & agent(e,vincent))

• Vincent ate greedily: Ee (eating(e) & agent(e,vincent) & greedy(e))

• The point is, we now have something at our disposal (namely e) of which we can say it is greedy.


Inferences follow naturally

• Vincent ate greedily |= Vincent ate • Ee (eating(e) & agent(e,vincent) &

greedy(e)) |= Ee (eating(e) & agent(e,vincent))

• The required inference follow directly from the semantics of the existential quantifier and conjunction.


Reification

• Wikipedia: (Lat. res thing + facere to make) n. the turning of something into a thing or ob ject; the error which consists in treating as a thing something which is not one.

• Reification (knowledge representation), used to represent facts that must then be manipulated in some way.

• Reification (linguistics), in natural language processing, where a natural language statement is transformed so actions and events in it become quantifiable variables.


Publication

• Of course, when we insist that our models contain events (or times or whatever) we should describe their properties. That is, we should impose constraints on our new ontology.

• The Proper Treatment of Events, Michiel van Lambalgen and Fritz Hamm, Explorations in Semantics, Blackwell Publishing, 2005.


Further Work Required

• Natural language semantics seems to require many kinds of entities, and semanticists have not been slow to develop them.

• Plural entities: Johan and Mary lifted the piano

• Stuff of various kinds (for mass terms among other things).

• Possible worlds: It's possible that Mary will come today

• The Naïve Physics Manifesto - Patrick Hayes


Remarks

• We accept that there are such things as electrons, magnetic fields, genes, phonemes.

• We accept them Because such items play an important role in explanatory theories.

• Most scientists would not be dogmatic about the existence of these entities

• They know full well that the best scientific theories of today many well turn out to be inadequate. ･ Nonetheless, these items play a crucial role in our intellectual economy.


Conclusions

• The sort of entities proposed in semantics don't yet have the same status, according to Blackburn

• Semantics is too young a subject to have created such rich theories.

• The items proposed by semanticists are the building blocks of our concepts.

april 2010nl metaphysics1 natural language metaphysics

Documents

nl time

time points

event time

points of time speech

reference time

time of utterance

special time

past time r