Morphology and Finite-State Transducers

Morphological analysis: Finding morphological constituents

1. angrily = angry + ly
2. proven = prove + en
3. * haven = have + en
4. ducks = duck + pl
5. ducks = duck + 3rdsg
6. ground = ground (N, sg)
7. ground = grind + pst
8. undeniability = un + deny + able + ity

Part of speech: a class of words that share many properties. (more later). Examples: Nouns, verbs

Inflection vs. derivation

1. duck vs ducks, cat vs. cats, ox vs. oxen: All nouns have plural forms (almost?: equipment, apparatus, furniture, infantry)
2. walk vs walking, talk vs talking, smoke vs smoking: All nouns have -ing forms (gerund, present participle)
3. Spanish verb amare ("to love")

walking = walk + ing
Form = Stem + Suffix

Sound system versus spelling

1. English consonants
2. English vowels

Allomorphy: plural s

1. fox: foxes, /f aa k s/ + /ax z/
2. dog: dogs, /d ao g/ + /z/
3. duck: ducks, /d uh k/ + /s/
4. lilly: lillies, /l ih l i/ + /z/

In this chapter we deal with spelling. This means we are concerned with spelling rules instead of phonological rules for allomorphy. We operate on orthographic representations not phonetic representations.

Productive ending: [s] (the morpheme s, with its phonologically predictable allomorphs) versus irregular forms. Notice that many of the irregular forms are not formed by affixation.

Regular	Irregular
ducks = duck + PL lillies = lilly + PL fox = fox + PL hogs = hog + PL houses = house + PL cups = cup + PL bellies = belly + PL	oxen = ox + PL children = child + PL deer = deer + PL mice = mouse + PL geese = goose + PL men = man + PL cacti = cactus + PL

Morphological analysis of a word:
The stem plus the various morphological features of the word, whether or not they are signaled by affixation.

We assume the category is a morphological feature.

Parsing versus Recognition

Morphological recognition: Accepts and rejects forms:

Accept: geese
Reject: gooses

Morphological parsing produces a morphological analysis (stem first, followed by category of stem, followed by all affixes):

geese: goose + N + PL
goose: goose + N + SG, goose +V +3SG
ground: ground +N +SG, grind +V +PPart

Relating surface and "underlying" forms

Morphotactic recognition

Morphotactics is the syntax of morphemes: what order they come in, what kind of units they make.

A basic morphotactic fact about affixes is where they attach with respect to the stem.

Prefix* + Stem + Suffix*
An affix is either a prefix or a suffix (English)

doability = do + able + ity
*doityable = do + ity + able

Using FSAs to do recognition

• Word-class automaton: The morphotactics
• Lexicon assumed for recognition
  1. All stems, with word-class info attached
     • fox, wine: reg-noun
     • geese, fish, pants: irreg-pl-noun
     • goose, fish, equipment, kindling: irreg-sg-noun
  2. All affixes
• Word automaton: A recognizer
• Recognizes "morphotactic strings", not surface strings of English ("foxs", not "foxes"). A missing kind of information.
• We need realizational rules that tell us: fox + s => foxes.
  On phonological representations these would be allomorphy rules. On graphic representations they're spelling rules.

Finite-State transducers

We introduce Finite-state transducers, an augmentation of FSAs in which there are two tapes

• A two-tape automaton, the upper tape an "underlying representation" tape and the lower a "surface representation"

  The main idea: The FST is just as FSA on which the arcs are labeled by pairs of symbols, an underlying symbol and a surface symbol. An arc a can be taken just in case the current symbol on the top tape matches the underlying representation symbol on a and the current symbol on the bottom tape matches the surface representation symbol on a.

  • A transition labeled a:e means "a" as underlying representation corresponds to "e" as surface representation
  • A transition "a" (with no colon) is an abbreviation for "a:a", meaning "a" as underlying representation corresponds to "a" as surface representation.

  Finite-State transducers(FSTs) give us the technology to do parsing.

  We imagine we start with the surface representation tape containing a surface word as input. Our job is to fill in an underlying representation licensed by the FST. Or, in ambiguous cases, to fill in ALL underlying representations licensed by the FST.

  Finite-State transducers give us the technology to do generation of surface forms

  We imagine we start with the underlying representation tape containing an underlying representation as input. This may consist of a sequence of affixes and stems and morphological features taken from the lexicon:
  do ity able
  Our job is to find a corresponding surface representation licensed by the FST, if there is one. For this example there isn't, but for
  do able ity
  there is.

  We will relate surface to underlying forms via an "intermediate" morphotactic representation. This will take two separate FSTs, one relating furface to intermediate representations, one relating intermediate to underlying representations.

  Relating underlying to intermediate (morphotactic) representation:

  1. The morphological lexicon is just a large FST relating stems to morphological word classes
     1. Stems related to word-class info
        • fox, wine; reg-noun
        • geese, fish, pants; irreg-pl-noun
        • fish, equipment, kindling; irreg-sg-noun
     2. The complication is irregular plurals related to an unpredictable singular:
        
        g   o:e   o:e   s   e   irreg-pl-noun
        m   o:i   u:eps   s:c   e   irreg-pl-noun
        
        
  2. The FST that captures this information
  3. We also need to relate word-class information to morphological features and morphotactic information:The word-class transducer
  4. The "composition" of these two transducers
  5. Linguistically the picture is nice:
     The underlying-to-intermediate transducer is itself composed out of two transducers, a large one that captures morphological word classes for stems, and a small one that that captures the morphotactics of the word classes.

Relating intermediate (morphotactic) representation to surface (speeling rules).

The problem

1. beg + ing = begging: Consonant doubling
2. mak + ing = making: e-deletion
3. watch + s = watches: e-insertion

E-insertion: insert an e after a morpheme ending in x, s, or z and before a word-final s.

Chomsky/Halle style "rewrite" rules:

E-insertion

Eps => e /{x,s,z}^ ____ s#

This can be modeled with an FST.

Interpreting the rule:

• ^ means a morpheme boundary.
• # means a word boundary.
• We assume word boundaries are "found" on the surface, but morpheme boundaries are not (written language: English). Thus every # transition is default (#:#), and every ^ transition is ^:eps.
• Other means, basically, not {s,x,z}, not ^, not #.
• This machine is designed to leave every word that the rule does NOT apply to unchanged.
• State 0 is the irrelevant input state. We stay in state 0 until we see something relevant. State 0 is a final state.
• State 1 means we found an {s,x,z}. State 2 means we've gone on to find a morpheme boundary.
• State 2 is the rule-ready state. We've seen a morpheme end in {s,x,z}.
• The FST incorporates ONLY the information in our rewrite rule (as written). It doesn't "know" anything else about English. Some strange cases:
  1. The ^:eps transition from state 5 to state 2.
     The rule requires e-insertion only before word-final s. We reach state 5 having seen a morpheme ending in {s,x,z} followed by a surface s. This is okay (by the rule) as long as that s isn't followed by a word boundary(#). So when in state 5 we fail for word boundary. But a morpheme boundary (^) is okay. And seeing a morpheme boundary, we go back to state 2 because that's the rule-ready state, appropriate when we've seen a morpheme ending in s.
  2. The {z,s,x} transition from 5 to 1. This is exercise 3.10.

Using the E-insertion rule when parsing:

• The correct parse
   

  Underlying
  State
  Surface	a	s	s	e	s	s	#

  Underlying	a	s	s	e	s	s	#
  State	0	1	1	0	1	1	0
  Surface	a	s	s	e	s	s	#

• A false path

  Underlying	a	s	s	^	eps	s
  State	0	1	1	2	3	4	fail
  Surface	a	s	s	eps	e	s	s	#