April 2010NL Metaphysics1 Natural Language Metaphysics.
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Transcript of April 2010NL Metaphysics1 Natural Language Metaphysics.
April 2010 NL Metaphysics 2
Outline
• Ontology– Time
• Linguistic Phenomena– Tense– Adverbial Modification
April 2010 NL Metaphysics 4
Making ModelResemble World
• Add more detail
• Semantic Repositories– Annotated databases– Ontologies
• CYC
• But apart from more detail we need ...
April 2010 NL Metaphysics 5
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
April 2010 NL Metaphysics 6
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
April 2010 NL Metaphysics 7
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).
April 2010 NL Metaphysics 8
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 . . .
April 2010 NL Metaphysics 9
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
April 2010 NL Metaphysics 10
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?
April 2010 NL Metaphysics 11
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
April 2010 NL Metaphysics 12
Vincent had smiled
E t E r
( time(t) &
time(r) &
t < r &
r < now &
smile(vincent, t))
April 2010 NL Metaphysics 13
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.
April 2010 NL Metaphysics 14
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
April 2010 NL Metaphysics 15
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?
April 2010 NL Metaphysics 16
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?
April 2010 NL Metaphysics 17
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?
April 2010 NL Metaphysics 18
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
April 2010 NL Metaphysics 19
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)
April 2010 NL Metaphysics 20
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
April 2010 NL Metaphysics 21
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 ....
April 2010 NL Metaphysics 22
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
April 2010 NL Metaphysics 23
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
April 2010 NL Metaphysics 24
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
April 2010 NL Metaphysics 25
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.
April 2010 NL Metaphysics 26
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?
April 2010 NL Metaphysics 27
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
April 2010 NL Metaphysics 28
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?
April 2010 NL Metaphysics 29
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.
April 2010 NL Metaphysics 30
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.
April 2010 NL Metaphysics 32
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.
April 2010 NL Metaphysics 33
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)
April 2010 NL Metaphysics 34
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?
April 2010 NL Metaphysics 35
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.
April 2010 NL Metaphysics 36
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.
April 2010 NL Metaphysics 37
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. . .
April 2010 NL Metaphysics 38
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)
April 2010 NL Metaphysics 39
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.
April 2010 NL Metaphysics 40
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 . . .
April 2010 NL Metaphysics 41
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.
April 2010 NL Metaphysics 42
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).
April 2010 NL Metaphysics 43
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 . . .
April 2010 NL Metaphysics 44
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))
April 2010 NL Metaphysics 45
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))
April 2010 NL Metaphysics 46
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.
April 2010 NL Metaphysics 47
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.
April 2010 NL Metaphysics 48
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.
April 2010 NL Metaphysics 49
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.
April 2010 NL Metaphysics 50
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
April 2010 NL Metaphysics 51
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.