Finite-State Methods in Natural Language Processing

1
Finite-State Methods in Natural Language
Processing

• Lauri Karttunen
• LSA 2005 Summer Institute
• August 3, 2005

2

• August 1
• Non-concatenative morphotactics
• Reduplication, interdigitation
• Realizational morphology
• Readings
• Chapter 8. Non-Concatenative Morphotactics
• Gregory T. Stump. Inflectional Morphology. A
  Theory of Paradigm Structure. Cambridge U. Press.
  2001. (An excerpt)
• Lauri Karttunen, Computing with Realizational
  Morphology, Lecture Notes in Computer Science,
  Volume 2588, Alexander Gelbukh (ed.), 205-216,
  Springer Verlag. 2003.
• August 3
• Optimality theory
• Readings
• Paul Kiparsky Finnish Noun Inflection
  Generative Approaches to Finnic and Saami
  Linguistics, Diane Nelson and Satu Manninen
  (eds.), pp.109-161, CSLI Publications, 2003.
• Nine Elenbaas and René Kager. "Ternary rhythm and
  the lapse constraint". Phonology 16. 273-329.

3
Background

• Two old strains of finite-state (morpho)phonology
• rewrite rules (ChomskyHalle 1968)
• two-level constraints (Koskenniemi 1983)
• Optimality theory (Prince Smolensky 1993)
• two-level model with ranked, violable constraints
• Formal Power
• OT is not a finite-state system if it involves
  unlimited counting of constraint violations.
  (Ellison 1994, Eisner 1997, FrankSatta 1998)
• But a finite-state model can be useful for OT.

4
Optimality theory

• Prince Smolensky 1993
• eliminate
• rules
• derivations
• introduce
• violable ranked constraints
• Instant success!

5
Brief Introduction to OT

• Input
• A language of underlying lexical forms.
• GEN
• A function that generates alternate surface
  realizations for each input form, possibly an
  infinite set.
• Constraints
• A finite set of principles, preferrably
  universal, that filter out unwanted realizations.
• Ranking
• A language-specific ordering of the constraints.

6
Computational perspective

• Ellison 1994
• OT deals with regular sets and relations a
  finite-state system
• constraint transducers mark violations, marks
  sorted and counted
• Tesar 1995
• dynamic algorithm for optimal path computations
• Eisner 1996
• two-level typology of optimality constraints
  restrict, prohibit
• FootForm Decomposed MIT Working Papers in
  Linguistics, 31115-143 proposes Primitive
  Optimality Theory (no generalized alignment)
• Karttunen 1998
• Introduces lenient composition
• Frank Satta 1998
• Prove that OT is regular if of violations is
  bounded.

7
Comparisons
8
Finnish OT Prosody

• Lauri Karttunen
• CLS-41
• April 7, 2005

9
Finnish Prosody basic facts

• The nucleus of a Finnish syllable must consist of
  a short vowel, a long vowel, or a diphthong.
• Main stress is always on the first syllable,
  secondary stress occurs on non-initial syllables.
• Adjacent syllables are never stressed.
• Stressed syllable is initial in the foot.
• ilmoittautuminen registering (Nom Sg)
• (íl.moit).(tàu.tu).(mì.nen)

10
Ternary feet in Finnish

• Stress that would fall on a light syllable shifts
  on the following heavy syllable creating a
  ternary foot.
• (ká.las).te.(lèm.me) we are fishing
• (íl.moit).(tàu.tu).mi.(sès.ta) registering (Ela
  Sg)
• (rá.kas).ta.(jàt.ta).ri.(àn.sa) his mistresses
  (Par Pl)
• Can we get these facts to come out for free,
  from the interaction of independently motivated
  principles?
• Yes!
• Paul Kiparsky Finnish Noun Inflection
  Generative Approaches to Finnic and Saami
  Linguistics, Diane Nelson and Satu Manninen
  (eds.), pp.109-161, CSLI Publications, 2003.
• Nine Elenbaas and René Kager. "Ternary rhythm and
  the lapse constraint". Phonology 16. 273-329.

11
Non-OT and OT solutions

• It is possible to define a cascade of replace
  rules that produce the desired result.
• http//www.stanford.edu/laurik/fsmbook/examples/F
  innishProsody.html
• But, following Kiparsky, we are going to do OT
  today, and in a more elegant way than is shown
  at
• http//www.stanford.edu/laurik/fsmbook/examples/F
  innishOTProsody.html

12
Prelude Built-in Functions in fst

• Case conversion
• UpCase( OptUpCase(
• DownCase( OptDownCase(
• Cap( OptCap(
• AnyCase(
• Cap(hello) is equivalent to Hello
• OptUpCase(ab, L) is equivalent to aB ab
  
• Symbol manipulation
• Explode( Implode(
• regex Explode("Test") is equivalent to regex
  Test

13
Functions User-defined

• The function definition is attached to a symbol
  ending with (
• The definition is any regular expression.
• There may be any number of arguments.
• define Redup(X) X X
• define Apply(X, Y) X .o. Y.l
• When the function is used in a regular
  expression, the arguments are bound and the
  function is evaluated.
• regex Apply(abc, a -gt x _ b)
• print words
• xbc
• The definition of a function may contain other
  functions.

14
Pig Latin

• This script creates a function for translating
  from English to Pig Latin
• pig -gt igpay, brown -gt ownbray, script -gt
  iptscray

define C bcdfghjklmnpqrstvwxy
z define V aeiou
define Redup(X) X "." X define DelCons(X) X
.o. C _at_-gt 0 .. _ define TailToAy(X) X
.o. V ? _at_-gt ay "." C _ define
DelMiddle(X) X .o. "." -gt 0
define Pig(X) DelMiddle(TailToAy(DelCons(Redup(X)
)))
15
Demo!

• fst -l piglatin.script

16
Computing with OT
By what finite-state operation?
17
Priority union .P.
All pairs from R and those pairs from Q that do
not conflict with the mapping established by R.
R .P. Q R R.u .o. Q
Kaplan 1987
18
Lenient Composition .O.

• Let R be a relation that maps each input string
  to one or more outputs.
• Let C be a constraint that eliminates some
  outputs.
• R .O. C is the relation that maps each input
  string that can meet the constraint C to the
  outputs that meet C and leaves the rest of the
  relation R unchanged. (Karttunen 1998)
• R .O. C R .o. C .P. R
• Is constraint ranking rule ordering in disguise?
  Yes.

19
Need a prolific GEN

• ka.la
• ka.lá
• ka.là
• ka.(là)
• ka.(lá)
• ká.la
• ká.lá
• ká.là
• ká.(là)
• ká.(lá)
• kà.la

• (kà.la)
• (ká).la
• (ká).lá
• (ká).là
• (ká).(là)
• (ká).(lá)
• (ká.là)
• (ká.lá)
• (ká.la) ?
• (ka.là)
• (ka.lá)

kà.lá kà.là kà.(là) kà.(lá) (kà).la (kà).lá (kà).
là (kà).(là) (kà).(lá) (kà.là) (kà.lá)
kala fish (Nom Sg) 33 candidates
20
Basic definitions 1

• Using Parc/XRCE regular expression syntax
• define C b c d f g h j k l m
• n p q r s t v w x z
  Consonant
• define HighV u y i High
  vowel
• define MidV e o ö Mid
  vowel
• define LowV a ä Low
  vowel
• define USV HighV MidV LowV
  Unstressed Vowel
• define MSV á é í ó ú ý ä ö
• define SSV à è ì ò ù y ä ö
• define SV MSV SSV Stressed
  vowel
• define V USV SV Vowel

21
Basic definitions 2

• define P V C
  Phone
• define B \P ..
  Boundary
• define E .. "."
  Edge
• define Light C V
  Light syllable
• define Heavy Light P
  Heavy syllable
• define S Heavy Light Syllable
• define SS S SV Stressed
  syllable
• define US S SV Unstressed
  syllable
• define MSS S MSV Syllable with
  main stress

22
GEN 1

• define MarkNonDiphthongs
• . . -gt "." HighV MidV _ LowV, i.a,
  e.a
• LowV _ MidV, a.e
• i _ MidV - e,
  i.o, i.ö
• u _ MidV - o,
  u.e
• y _ MidV - ö,
  y.e
• V i _ e,
  poiki.en
• V u _ o,
  
• V y _ ö
  
• Insert a syllable boundary between vowels that
  cannot form
• a diphtong i.a, e.a, a.e, i.o, u.e, y.e, etc.
• define Syllabify C V C _at_-gt ... "." _ C V
• Insert a syllable boundary after a maximal C
  V C pattern that is followed by C V. For
  example, strukturalismi -gt struk.tu.ra.lis.mi.

23
GEN 2

• define Stress a (-gt) áà, e (-gt) éè, i (-gt) íì,
• o (-gt) óò, u (-gt) úù, y (-gt)
  "y""y",
• ä (-gt) "ä""ä", ö (-gt) "ö""ö"
• Optionally stress any vowel with a primary or
  secondary stress.
• define Scan S ("." S ("." S)) SS (-gt) "("
  ... ")" E _ E
• Optionally group syllables into unary, binary, or
  ternary feet when there is at least one stressed
  syllable.
• define Gen MarkNonDiphthongs .o. Syllabify .o.
• Stress .o. Scan

24
Demo!

• fst -utf8 -l gen.script
• regex kala .o. Gen (compose)
• print lower-words (show output candidates)
• print size (count them)

25
Kiparsky's nine constraints

• Clash
• AlignLeft
• MainStress
• FootBin
• Lapse
• NonFinal
• StressToWeight
• Parse
• AllFeetFirst

26
Counting constraint violations

• We use asterisks to mark constraint violations.
  We need a way to prefer candidates with the least
  number of violation marks.
• define Viol
• define Viol0 Viol No violations
• define Viol1 Viol2 At most one violation
• define Viol2 Viol3 At most two violations
• define Viol3 Viol4
• This eliminates the violation marks after the
  candidate set has been pruned by a constraint.
• define Pardon -gt 0

27
Defining OT Constraints

• Three types
• Unviolable constraints
• Primary stress in Finnish
• Ordinary violable constraints
• Lapse
• Gradient alignment constraints
• All-Feet-First
• Strategy
• We define an evaluation template for each of the
  three types and then define the individual
  constraints with the help of the templates.

28
Evaluation Template for Unviolable Constraints

• define Unviolable(Candidates, Constraint)
• Candidates
• .o.
• Constraint
• Example
• define MainStress(X) Unviolable(X, B MSS MSS)
• B is the left edge of the word or "(".
• MSS is a syllable with a primary stress.

29
Evaluation Template for Ordinary Constraints

• define Eval(Candidates, Violation, Left, Right)
• Candidates
• .o.
• Violation -gt ... Left _ Right
• .O.
• Viol3 .O. Viol2 .O. Viol1 .O. Viol0
• .o.
• Pardon
• where Viol0 is , Viol2 is 2, etc.
  and
• Pardon is -gt 0 deleting all violation marks.

30
Evaluation Template for Left-Oriented Gradient
Alignment

• define EvalGradientLeft(Candidates, Violation,
  Left, Right)
• Candidates .o.
• Violation -gt ... .. Left _ Right
• .o.
• Violation -gt 2 ... .. Left2 _ Right
• .o.
• Violation -gt 3... .. Left3 _ Right
• .o.
• Violation -gt 4 ... .. Left4 _ Right
• .o.
• Violation -gt 5 ... .. Left5 _ Right
• .o.
• Violation -gt 6 ... .. Left6 _ Right
• .o.
• Violation -gt 7 ... .. Left7 _ Right
• .o.
• Violation -gt 8 ... .. Left8 _ Right
• .O.
• Viol12 .O. Viol11 .O. Viol10 .O. Viol9 .O.
  Viol8 .O. Viol7 .O.

31
Clash, AlignLeft, MainStress

• Clash
• No stress on adjacent syllables.
• define Clash(X) Eval(X, SS, SS B, ?)
• Align-Left
• The stressed syllable is initial in the foot.
• define AlignLeft(X) Eval(X, SV, .. ? "(" C,
  ?)
• Main Stress
• The primary stress in Finnish is on the first
  syllable.
• define MainStress(X) Unviolable(X, B MSS MSS)

32
FootBin, Lapse, NonFinal

• Foot-Bin
• Feet are minimally bimoraic and maximally
  bisyllabic.
• define FootBin(X) Eval(X, "( Light ") "
  ("S"." Sgt1,
• ? ,?)
• Lapse
• Every unstressed syllable must be adjacent to a
  stressed syllable or to the word edge.
• define Lapse(X) Eval(X, US, B US B, B US B)
• Non-Final
• The final syllable is not stressed.
• define NonFinal(X) Eval(X, SS, ?, S ..)

33
StressToWeight, Parse, AllFeetFirst

• Stress-To-Weight
• Stressed syllables are heavy.
• define StressToWeight(X) Eval(X, SS Light, ?,
  ")" E)
• License-s
• Syllables are parsed into feet.
• define Parse(X) Eval(X, S, E, E)
• All-Ft-Left
• The left edge of every foot coincides with the
  left edge of some prosodic word.
• define AllFeetFirst(X)
• EvalGradientLeft(X, "(", ".", ?)

34
Finnish Prosody

• Kiparsky 2003
• define FinnishProsody(Input)
• AllFeetFirst( Parse( StressToWeight(
• NonFinal( Lapse( FootBin( MainStress(
• AlignLeft( Clash( Input .o. Gen)))))))))

35
FinnWords

• regex FinnishProsody( kalastelet
  kalasteleminen
• ilmoittautuminen järjestelmättömyydestänsä
  
• kalastelemme ilmoittautumisesta
• järjestelmällisyydelläni järjestelmällistämä
  töntä
• voimisteluttelemasta opiskelija
  opettamassa
• kalastelet strukturalismi
  onnittelemanikin
• mäki perijä repeämä ergonomia
• puhelimellani matematiikka
  puhelimistani
• rakastajattariansa kuningas
  kainostelijat
• ravintolat merkonomin )
• Demo!

36
Result

• (ér.go).(nò.mi).a
• (íl.moit).(tàu.tu).mi.(sès.ta)
• (íl.moit).(tàu.tu).(mì.nen)
• (ón.nit).(tè.le).(mà.ni).kin
• (ó.pis).(kè.li).ja
• (ó.pet).ta.(màs.sa)
• (vói.mis).te.(lùt.te).le.(màs.ta)
• (strúk.tu).ra.(lìs.mi)
• (rá.vin).(tò.lat)
• (rá.kas).ta.(jàt.ta).ri.(àn.sa)
• (ré.pe).(ä.mä)
• (pé.ri).jä
• (pú.he).li.(mèl.la).ni

• (pú.he).li.(mìs.ta).ni
• (mä.ki)
• (má.te).ma.(tìik.ka)
• (mér.ko).(nò.min)
• (kái.nos).(tè.li).jat
• (ká.las).te.(lèm.me)
• (ká.las).te.(lè.mi).nen
• (ká.las).(tè.let)
• (kú.nin).gas
• (jär.jes).tel.(mäl.li).syy.(dèl.lä).ni
• (jär.jes).(tèl.mät).tö.(myy.des).(tän.sä)
• (jär.jes).(tèl.mäl).(lìs.tä).mä.(tön.tä)

37
Two Errors

• (ká.las).te.(lè.mi).nen
• (jär.jes).tel.(mäl.li).syy.(dèl.lä).ni
• The interaction of Lapse and StressToWeight does
  not produce the desired result in these cases.

38
What is wrong?

• define Debug(Input)
• DebugStressToWeight(
• NonFinal( Lapse( FootBin( MainStress(
  AlignLeft(
• Clash( Input .o. Gen)))))))
• regex Debug(kalasteleminen)
• (ká.las).te.(lè.mi).nen lt-- actual winner
• (ká.las).(tè.le).(mì.nen) lt-- desired output
• (jär.jes).tel.(mäl.li).syy.(dèl.lä).ni lt--
  actual winner
• (jär.jes).(tèl.mäl).li.(syy.del).(lä.ni) lt--
  desired output
• The StressToWeight constraint eliminates some of
  the desired winning candidates.

39
Nine Elenbaas

• A unified account of binary and ternary stress.
  Ph.D. dissertation. University of Utrecht. 1999.
  Based on KiparskyHanson 1996. The only
  difference is that Elenbaas has a special
  constraint (L H) or AntiLStressH( in place of
  Kiparskys more general StressToWeight
  constraint.
• define FinnishProsody(Input)
• AllFeetFirst( Parse( AntiLStressH(
• NonFinal( Lapse( AlignLeft( FootBin(
• MainStress( Clash( Input .o. Gen)))))))))
• define AntiLStressH(X) Eval(X, SS Light, "(" ,
  "." Heavy)

40
Result

• (ér.go).(nò.mi).a
• (íl.moit).(tàu.tu).mi.(sès.ta)
• (íl.moit).(tàu.tu).(mì.nen)
• (ón.nit).(tè.le).(mà.ni).kin
• (ó.pis).(kè.li).ja
• (ó.pet).ta.(màs.sa)
• (vói.mis).te.(lùt.te).le.(màs.ta)
• (strúk.tu).ra.(lìs.mi)
• (rá.vin).(tò.lat)
• (rá.kas).ta.(jàt.ta).ri.(àn.sa)
• (ré.pe).(ä.mä)
• (pé.ri).jä
• (pú.he).li.(mèl.la).ni

• (pú.he).li.(mìs.ta).ni
• (mä.ki)
• (má.te).ma.(tìik.ka)
• (mér.ko).(nò.min)
• (kái.nos).(tè.li).jat
• (ká.las).te.(lèm.me)
• (ká.las).te.(lè.mi).nen
• (ká.las).(tè.let)
• (kú.nin).gas
• (jär.jes).(tèl.mäl).li.(syy.del).(lä.ni)
• (jär.jes).(tèl.mät).tö.(myy.des).(tän.sä)
• (jär.jes).(tèl.mäl).(lìs.tä).mä.(tön.tä)

41
Did She Know?
Six syllables (Appendix of Elenbaas thesis) X X L
L L L áterìanàni áteriànani 'meal (Ess
1SG)' érgonòmiàna 'ergonomics
(Ess)' káinostèlijàna 'shy person
(Ess)' káinostèlijàni 'shy person (Nom
1SG)' kúnnallìsenàni 'council (Ess
1SG)' kúnnallìsiàni councils (Part
1SG)' kúnnallìsinàni 'councils (Ess
1SG)' mérkonòmiàni 'degree in economics (Part
1SG)' mérkonòminàni 'degree in economics (Ess
1SG)' ópiskèlijàni 'student (Nom
1SG)' púhelìmenàni 'telephone (Ess
1SG)' púhelìmiàni telephone (Part
1SG) Missing pattern X X L L L H
42
Conclusion

• Can we get ternary feet in Finnish for free,
  from the interaction of independently motivated
  principles?
• We dont know.
• We know that the Kiparsky and Elenbaas accounts
  fail.
• Optimality Prosody is computationally very
  difficult.
• The number of initial candidates is huge
• kalasteleminen 70653
• järjestelmällisyydelläni 21767579
• Simple tableau methods do not work.
• Finite-state implementation guards against errors
  made by a human GEN and EVAL.
• But even when an error can be pinpointed, the fix
  is not obvious.
• Debugging OT constraints is as hard as debugging
  two-level rules, in practice more difficult than
  rewrite systems.

43
Final Thoughts

• Morphology is a regular relation.
• The composition of words (morphosyntax),
  morphological alternations, and prosody can be
  described in finite-state terms.
• A complex relation can be decomposed in different
  ways.
• There are many flavors of finite-state
  morphology Item-and-Arrangement, Rewrite rules,
  Two-level rules, Realizational Morphology,
  Classical optimality constraints.
• Computing with finite-state tools is fun and
  easy.
• We have sophisticated formalism for describing
  regular relations, efficient compilers and
  runtime software.
• Pen-and-pencil morphology badly needs
  computational support.
• It is difficult to get globally correct results
  relying on a handful of interesting words, rules,
  and constraints.