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April 2010NL Metaphysics1 Natural Language Metaphysics.

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1 April 2010NL Metaphysics1 Natural Language Metaphysics

2 April 2010NL Metaphysics2 Outline Ontology –Time Linguistic Phenomena –Tense –Adverbial Modification

3 April 2010NL Metaphysics3 Focus Language Logic World Model

4 April 2010NL Metaphysics4 Making Model Resemble World Add more detail Semantic Repositories –Annotated databases –Ontologies CYC But apart from more detail we need...

5 April 2010NL Metaphysics5 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

6 April 2010NL Metaphysics6 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

7 April 2010NL Metaphysics7 Markup - TIMEML: http://www.timeml.org/site/index.html 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).

8 April 2010NL Metaphysics8 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...

9 April 2010NL Metaphysics9 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

10 April 2010NL Metaphysics10 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?

11 April 2010NL Metaphysics11 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

12 April 2010NL Metaphysics12 Vincent had smiled E t E r ( time(t) & time(r) & t < r & r < now & smile(vincent, t))

13 April 2010NL Metaphysics13 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.

14 April 2010NL Metaphysics14 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

15 April 2010NL Metaphysics15 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?

16 April 2010NL Metaphysics16 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-for- uzi(s)) What’s missing?

17 April 2010NL Metaphysics17 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?

18 April 2010NL Metaphysics18 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

19 April 2010NL Metaphysics19 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)

20 April 2010NL Metaphysics20 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

21 April 2010NL Metaphysics21 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....

22 April 2010NL Metaphysics22 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

23 April 2010NL Metaphysics23 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

24 April 2010NL Metaphysics24 A point-based temporal ontology For all times t, r, s: –Irreflexivity: not (t < t) –Transitivity: (t t < r –Linearity: (t ≤ s & s ≥ t) => s = t

25 April 2010NL Metaphysics25 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.

26 April 2010NL Metaphysics26 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?

27 April 2010NL Metaphysics27 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

28 April 2010NL Metaphysics28 Interval Based Ontology For all time intervals r, s and t Irreflexivity: not (t { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/13/3908712/slides/slide_28.jpg", "name": "April 2010NL Metaphysics28 Interval Based Ontology For all time intervals r, s and t Irreflexivity: not (t

29 April 2010NL Metaphysics29 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.

30 April 2010NL Metaphysics30 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.

31 April 2010NL Metaphysics31 Semantics of Events

32 April 2010NL Metaphysics32 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.

33 April 2010NL Metaphysics33 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)

34 April 2010NL Metaphysics34 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?

35 April 2010NL Metaphysics35 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.

36 April 2010NL Metaphysics36 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 eat n and all the hungry m predicates.

37 April 2010NL Metaphysics37 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...

38 April 2010NL Metaphysics38 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)

39 April 2010NL Metaphysics39 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.

40 April 2010NL Metaphysics40 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...

41 April 2010NL Metaphysics41 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.

42 April 2010NL Metaphysics42 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).

43 April 2010NL Metaphysics43 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...

44 April 2010NL Metaphysics44 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))

45 April 2010NL Metaphysics45 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))

46 April 2010NL Metaphysics46 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.

47 April 2010NL Metaphysics47 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.

48 April 2010NL Metaphysics48 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.

49 April 2010NL Metaphysics49 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.

50 April 2010NL Metaphysics50 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

51 April 2010NL Metaphysics51 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.

52 April 2010NL Metaphysics52 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.


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