Natural Language
Metaphysics
April 2010
NL Metaphysics
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Outline
• Ontology
– Time
• Linguistic Phenomena
– Tense
– Adverbial Modification
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Focus
Model
Logic
Language
April 2010
World
NL Metaphysics
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Making Model
Resemble World
• Add more detail
• Semantic Repositories
– Annotated databases
– Ontologies
• CYC
• But apart from more detail we need ...
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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
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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
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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).
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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 . . .
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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
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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?
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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
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Vincent had smiled
EtEr
( time(t) &
time(r) &
t<r&
r < now &
smile(vincent, t))
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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.
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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/Michaeliste
nseHEL.pdf
• Hackmack, S., Reichenbach’s theory of tense
and its application to English
http://www.fb10.unibremen.de/khwagner/verb
/pdf/Reich.pdf
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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?
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Tense in Text
• Vincent woke up
Et(t < now & vincent-wake-up(t))
• Something felt very wrong
Eu(u < now & something-feel-very-wrong(u))
• Vincent reached under his pillow for his Uzi
Es(s < now & vincent-reach-under-pillow-foruzi(s))
• What’s missing?
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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-foruzi(s))
• What’s missing?
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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-foruzi(s))
• These representations do not capture the
desired discourse interpretation
• The relation between the three timepoints is not
captured
• Quantifier scoping
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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-foruzi(s) & u < s)
April 2010
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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
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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 ....
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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
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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
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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
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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.
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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?
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An interval based temporal
ontology: constraints
• For all times t, r, s:
• Reflexivity inclusion: t  t
• Transitivity inclusion:
(t s & sr) → t  r
• Antisymmetry inclusion:
(t  s & s  t) → t = s
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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?
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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 subinterval.
• Achievement verbs: John crossed the road at
some interval implied that he did not do so at
a smaller interval.
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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.
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Semantics of Events
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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.
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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)
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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?
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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.
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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.
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Attempt 2: quantifying out
• Basic idea. make use of one eat predicate,
with enough arguments to cover everything
we need. For example
eat(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. . .
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Quantifying Out
• Vincent ate a big Kahuna burger with his hands for
breakfast (location missing
El 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)
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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.
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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 . . .
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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-whosename-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.
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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).
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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 . . .
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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))
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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))
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We win because ...
• We can handle adverbs
Vincent 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.
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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
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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. 48
April 2010
NL Metaphysics
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.
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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
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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.
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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 2010
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Natural Language Metaphysics