CSA4050 Advanced Topics in NLP

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CSA4050 Advanced Topicsin NLP

• Non-Concatenative Morphology
• Reduplication
• Interdigitation

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Reference

• Ken Beesely and Lauri Karttunen, Finite State
  Non-Concatenative Morphotactics, Proceedings of
  SIGPHON-2000

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Koskenniemi 1983

• "Only restricted infixation and reduplication
  can be handled adequately with the present
  system. Some extensions or revisions will be
  necessary for an adequate description of
  languages possessing extensive infixation or
  reduplication"

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Non-Concatenative Languages

• Most languages build words by stringing together
  morphemes like beads on a string.
• The word-building processes of prefixation and
  suffixation can be straightforwardly modeled in
  finite state terms by concatenation.
• But some languages also exhibit non-concatenative
  morphotactics.

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Non-Concatenative Phenomena1. Reduplication

• In Malaybagi (bag)bagi-bagi (bags)
• Although this may appear concatenative, it does
  not involve concatenating a predictible morpheme
  like "s". Instead the entire stem is copied no
  matter what its length.
• In general language class (ww w ? L) is context
  sensitive, but if L is finite, we can construct
  an FS network that encodes it.

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General Solution for Reduplication

• Therefore, assuming the number of words subject
  to reduplication is finite, it is possible to
  construct a lexical transducer for languages like
  Malay.
• To handle reduplication, a new operator n is
  introduced
• An denotes n concatenations of A.

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Remarks from Beesleyon Context Sensitivity

• finite-state grammars (cannot handle unlimited
  nesting or non-nested terminal dependencies)
• context-free (can handle unlimited nesting,
  suchas matched parentheses in arithmetic
  expressions, but cannot handle non-nested
  dependencies between terminals)
• context-sensitive (can also handle
  non-nesteddependencies between terminals, as
  indogdogwhere terminal elements 1 and 4 have
  to bethe same, 2 and 5 have to be the same,
  and3 and 6 have to be the same.  These
  dependenciescross, so they're not nested.

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Non-Concatenation 2. Interdigitation

• In Arabic and Maltese, prefixes and suffixes
  attach to stems in the usual concatenative way,
  but stems themselves are formed by a process
  known as interdigitation.
• An example of occurs with the Arabic stem "katab"
  (wrote).
• This stem is composed of three elements
• the all consonant root ktb
• an abstract consonant-vowel template CVCVC
• a vocalisation aa (in this case signifying
  perfect tense and active voice)

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Interdigitation

• The same root ktb can combine with the same
  template CVCVC and a different vocalism ui
  (signifying imperfect aspect and passive voice)
  to produce "kutib" (was written).
• The same root ktb can combine with a different
  template CVVCVC and the vocalism ui to produce
  "kuutib" another form of the verb.

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Intermediate ResultTemplate Root
d v v r v s
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Final ResultIntermediate Result Vocalism
d u u r i s
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Merge

• In this case the filler language contains an
  infinite set of strings (i, ui, uui ) but only
  one path can be constructed because all strings
  end in i. Hence the earlier vowels must be "u".
• This need not always be the case (eg if the
  filler language were ui).

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Merge Operators

• To introduce the merge operation into the Xerox
  calculus new operators, .ltm. and .mgt. have been
  introduced.
• These differ only in the order of arguments.
• T .ltm. F and F .mgt. T represent the same
  merge operation with F and T as filler and
  template respectively.

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The Composite Transducer

• With these operators the network above can be
  compiled by using the following expressiond r
  s .mgt. C V V C V C .ltm. u i

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Merge
template
c v v c v c
vocalism
root
d r s
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Compile-Replace

• Regular expressions are compiled into networks as
  usual, but in addition,
• the compiler is then applied to its own output.
• Central idea
• transduce to a language that has the format of
  regular expressions.
• The compile-replace algorithm then replaces the
  regular expression with the result of its own
  compilation.

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Compile Replace Simple Example
This network maps the string a to a
(i.e. the same RE but with special delimiters)
Application of CR to the lower side of
the network eliminates the markers, compile
the RE a and maps the upper side to to the
language resulting from the compilation.
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The result of compiling a

• To answer the question what does this network
  do?
• Figure out what it does in upward and downward
• directions

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The result of compiling a
When applied in the upward direction, this
transducer maps any string of the infinite a
language into the regular expression from which
it was compiled.
When applied in the downward direction, it maps
from a to all the strings in the language a,
0, a, aa, ...
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Compile-Replace 1

• Copy input path to output path until is
  encountered on indicated (in our case lower) side
  of the network.
• Extract path until closing delimiter .

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Compile-Replace 2

• Symbols along indicated side are concatenated
  into a string and eliminated from the path
  leaving just the symbols on the opposite side.
  The remaining net is
• The extracted string is compiled into a second
  network using the standard network compiler

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Compile-Replace 3

• The 2 networksare combined together using the
  cross product operator.
• The result
• is spliced between the origin and destination
  states of the regular expression path.

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Reduplication Revisited

• Applying compile-replace to this transducer
• Lexical b a g i Noun Plural
• Surface b a g i 2
• yields this one
• Lexical b a g i Noun Plural
• Surface b a g i b a g i

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Interdigitation Revisited

• Applying compile-replace to this transducerUp
  k i t e b Verb Past 3SgDok t b .mgt. C V C
  V C .ltm. i e
• yields this oneUp k i t e b Verb Past 3Sg
• Do k i t e b

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Remember Two Central Problems

• Morphotactics constraints on combinations of
  morphemes governing the formation of valid words.
  unbelievable vs. believeunable
• Phonological/Orthographical Alternation (spelling
  rules)how morphemes are realised in particular
  environmentsfly s flies

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Xerox Perspective

• Morphotactics handle with lexc
• Phonological/Orthographical Alternation (spelling
  rules)handle with xfst

lexc
Morphotactics
Lexicon FST
Lexical Transducer
.o.
xfst
Rules FST
Alternations