Computational Morphology and its Implications for Theoretical Morphology

Computational Morphology and its Implications for Theoretical Morphology Richard Sproat University of Illinois at Urbana-Champaign PASCAL Morpho. Challenge Venice April 12, 2006 Computational Morphology/Theoretical Morphology

“Item-and-arrangement” versus “Item and process” • Charles Hockett (1954) “Two models of grammatical description”: – Item-and-arrangement: words are composed of morphemes that are put together by a kind of “word syntax” – Item-and-process: words are built up via the application of rules that add phonological and morphosyntactic information Computational Morphology/Theoretical Morphology 1

Stump’s classification Affix is a lexical entry that introduces morphosyntactic features Incremental Lexical Inferential hoot+s[3 sg] Ø’s / hoot[3 sg] Lieber Steele hoots = 3 sg because of -s Realizational -s is introduced due to 3 sg Halle&Marantz Stump, Beard’s LMBM Affix introduced because of morphosyntactic features Computational Morphology/Theoretical Morphology 2

Computational morphology • Nearly all morphological operations can be expressed in terms of regular relations. – Only possible exception is reduplication • Regular relations are relations over pairs of strings that can be constructed solely by the operations of: – Concatenation: if R, S are regular relations then so is R • S – Union: if R, S are regular relations then so is RUS – Kleene closure: if R is a regular relation then so is R* (0 or more instances of R concatenated with itself) • Regular relations are closed under composition: if R, S are regular relations, then so is R○S • Implemented with finite-state transducers Computational Morphology/Theoretical Morphology 3

Transducers and composition (Johnson, 1972; Koskenniemi, 1983; Kaplan & Kay, 1994; Mohri & Sproat, 1996) • Consider 3 -letter alphabet {a, b, c} • Given a rule a " b, the equivalent transducer is: abbca bbbcb Computational Morphology/Theoretical Morphology 4

Another rule b"c / _ b Computational Morphology/Theoretical Morphology 5

The two rules composed a"b b"c / _ b abbca ccbcb Computational Morphology/Theoretical Morphology 6

Composition and morphology • Composition is the most general computational mechanism that handles morphological operations (Roark and Sproat, 2006) • Affixation (which is more typically handled using concatenation) can also be handled using composition • Composition, and other closure properties of regular relations imply that there is no fundamental difference between morphological theories. Computational Morphology/Theoretical Morphology 7

Affixation as composition Any string over the alphabet Insert b Computational Morphology/Theoretical Morphology 8

Is this Rube-Goldbergesque? • No! Because many affixes either impose requirements on their base or modify their base. • Cf. Yowlumne (aka Yawelmani) (Archangeli, 1984) Computational Morphology/Theoretical Morphology 9

Yowlumne gerundial -inay • -inay requires the template CVC(C) Composing the base with k 1 will modify the base and add [+GER] Computational Morphology/Theoretical Morphology 10

CVC(C) Computational Morphology/Theoretical Morphology 11

Some morphological operations • • Subsegmental morphology Truncation Infixation Root-and-pattern morphology Reduplication Morphomic requirements (Aronoff, 1994) All of these can be handled using composition Computational Morphology/Theoretical Morphology 12

German diminutives Computational Morphology/Theoretical Morphology 13

Koasati truncation (Lombardi & Mc. Carthy, 1991) Computational Morphology/Theoretical Morphology 14

Two kinds of infixation • Extrametrical infixation – E. g. Bontoc • Positively circumscribed infixation – E. g. Ulwa Computational Morphology/Theoretical Morphology 15

Bontoc infixation (Seidenadel, 1907) Computational Morphology/Theoretical Morphology 16

Ulwa infixation (CODIUL, 1989) Computational Morphology/Theoretical Morphology 17

Root & pattern morphology (Mc. Carthy 1979) k t b Computational Morphology/Theoretical Morphology 18

Root & pattern morphology Computational Morphology/Theoretical Morphology 19

Root & pattern morphology: related approaches • Beesley & Karttunen (2000) merge propose an approach using compile-replace plus dd Vu Vu rr Vi Ss • Surface form is a regular expressionsolution Kiraz (2000) proposes a multitape • But all of these are equivalent to composition Computational Morphology/Theoretical Morphology 20

Reduplication: Gothic (Wright 1910) • Prefix a syllable of the form (A)Cai to the stem, where C is a consonant position and A is an optional appendix • Copy the onset of the stem to the C position. If there is a pre-onset appendix /s/, copy this to the appendix position Computational Morphology/Theoretical Morphology 21

Bambara reduplication (Culy, 1985) This is apparently beyond the power of finite-state methods. Computational Morphology/Theoretical Morphology 23

Factoring reduplication • Prosodic constraints • Copy verification transducer C Computational Morphology/Theoretical Morphology 24

Gothic index transducer Computational Morphology/Theoretical Morphology 25

Factoring reduplication • Then reduplication in Gothic can be modeled as: αo C • More generally, one can model reduplication as the following composition, where P implements the prosodic constraints, C the copy constraints, and A optional phonological adjustments: Po Co. A Computational Morphology/Theoretical Morphology 26

Other approaches • Walther (2000 a, 2000 b) proposes a special kind of transducer involving – Repeat arcs: move backwards in a string and repeat – Skip arcs: skip over portions of the string • Cohen-Sygal & Wintner (forthcoming) introduce finite state registered automata, extending FSA’s with registers • These methods generally seem to presume exact copies Computational Morphology/Theoretical Morphology 27

Non-exact copies • Dakota (Inkelas & Zoll, 1999): Computational Morphology/Theoretical Morphology 28

Non-exact copies • Basic and modified stems in Sye (Inkelas & Zoll, 1999): “they will fall over” Computational Morphology/Theoretical Morphology 29

Morphological Doubling Theory (Inkelas & Zoll, 1999) • In contradistinction to the more common “correspondence” theory: – Reduplication involves doubling at the morphosyntactic level – Phonological doubling is thus expected, but not required Computational Morphology/Theoretical Morphology 30

Gothic reduplication under Morphological Doubling Theory Computational Morphology/Theoretical Morphology 31

More • Composition also elegantly accounts for other phenomena such as prosodic circumscription (Mc. Carthy and Prince, 1990) or morphomic requirements (Aronoff, 1994). • Composition of regular relations can model rules • It can also model affixation • It doesn’t matter if you describe affixation as lexical-incremental or inferential-realizational Computational Morphology/Theoretical Morphology 32

Morphomic requirements (Aronoff, 1994) Latin 3 rd Stem Computational Morphology/Theoretical Morphology 33

So? • 3 rd stem is not morphologically uniform: – It differs across different verb classes and some verbs have idiosyncratic third stems • It is not semantically coherent: – Forms that require the 3 rd stem are a motley crew • Yet there is clearly a notion of 3 rd stem: – If you tell me the 3 rd stem of a verb, I can tell you how the agentive noun, the supine, the perfect participle … are formed • 3 rd stem has a purely morphological function Computational Morphology/Theoretical Morphology 34

3 rd stem is just prosodically induced affixation • Assume we have a transducer T that forms the 3 rd stem of a verb: – of course, T will have to allow for a lot of idiosyncratic changes Σ* >3 st: ε Σ* Computational Morphology/Theoretical Morphology 35

Summary so far • Most or all morphological operations can be handled with composition • We wish to show next that this fact, along with general properties of regular languages and relations, allows us to dispense with distinctions between morphological theories. Computational Morphology/Theoretical Morphology 37

Return to Stump (2001) • In (Roark & Sproat, 2006) we reanalyze Stump’s analyses of: – Sanskrit nominal declensions – Swahili verbal declensions – Breton double plurals • All of which purport to show the need for an realizational-inferential account. • Here we will consider: – A simple example from Beard & Volpe’s analysis of English agentive nominals – A quick overview of the Sanskrit case. Computational Morphology/Theoretical Morphology 38

English Agentive Nominals (cf. Beard & Volpe, 2005) • read-er, stand-ee, correspond-ent, record-ist, cook • e " ent / [+ent][+noun, +agentive] S* __ $ • Call the set of all agentive rules R • We can define a new ‘metarule’ R′ that is the union of all rules in R: Computational Morphology/Theoretical Morphology 39

Feature [+noun, +agentive] • Presumably this is also introduced by rule: call this rule M • Then given a base B, the base with that feature specification added is given by B○M • Then the appropriate suffixed form is given by [B○M]○R′ • But this can be written, by associativity, as B○[M○R′] • Finally, [M○R′] can be precomposed; call this R′′ Computational Morphology/Theoretical Morphology 40

So what? • R′′: – Introduces the morphosyntactic feature [+noun, +agentive] – Introduces the affixal morphology as appropriate to the base • In short, R′′ encodes a lexicalincremental model of morphology. Computational Morphology/Theoretical Morphology 41

Sanskrit declensions Computational Morphology/Theoretical Morphology 42

Sanskrit declensions Computational Morphology/Theoretical Morphology 43

Issues with Sanskrit • Nouns have two or three stems – strong, middle and (optionally) weakest • A different series of stem alternations crosscuts this: guna, vrddhi, and zero: – “foot”: pād-, pad-, pd– strong stems may be guna or vrddhi – middle stems may be zero, or a lexeme-specific stem – weakest stems may be zero or lexeme-specific stem Computational Morphology/Theoretical Morphology 44

Sanskrit declensions guna zero Computational Morphology/Theoretical Morphology 45

Sanskrit declensions vrddhi lexeme-class particular Computational Morphology/Theoretical Morphology 46

Further issues • Stump argues for Indexing Autonomy Hypothesis: – A stem’s index is independent of the form used for the stem – Sanskrit nominal declensions are morphomic in Aronoff’s sense • Also involved are rules of referral whereby a particular form is systematically used to represent more than one slot in the paradigm. – For example, in Latin the ablative and dative plural in nominal paradigms are identical no matter what form is used for the particular paradigm • So we have several layers of complexity here, which would seem to make an “item-and-arrangement” approach impossible Computational Morphology/Theoretical Morphology 47

Computational analysis Computational Morphology/Theoretical Morphology 48

Refactoring But this is just an item-and-arrangement analysis Computational Morphology/Theoretical Morphology 49

Summary • Theoretical distinctions between different approaches to morphology seem to the issue of how cleanly one can describe a given phenomenon. • But it is not clear that they relate to important differences in underlying mechanisms. Computational Morphology/Theoretical Morphology 50

Why morphological theory? • Morphology has tended to develop highly articulated theories that are (often) intended to represent the morphological component of some putative ‘language faculty’. • Need a set of mechanisms to account for complex morphological systems – e. g. Sanskrit. • Need to account for observed universals – These might related to built-in predispositions, but equally well might relate to historical change; cf. Blevins (2004) • Linguistic phenomena are complex: how can children learn them? – Clearly relates to learning mechanisms Computational Morphology/Theoretical Morphology 51

Whither morphological theory? • Assumptions underlying linguistic theory have not changed much in the last 50 years – Arguments against statistical learning methods are based on antiquated notions of what statistical methods are capable of • Meanwhile there have been significant advances in machine learning over the past 10 -20 years. • Some of this has made it into computational linguistics in the form of grammar induction methods (cf. Klein and Manning, 2004; Smith 2006) Computational Morphology/Theoretical Morphology 52

Morphological theory redux • Computational arguments (above) suggest there may not be as much difference between morphological theories as people like to think • Recent work on induction of morphology suggests that we need to revisit our assumptions. • Issues of the future will likely be: – What historical mechanisms explain the observed patterns across the world’s languages? – What general learning mechanisms can account for children’s learning of morphology? Computational Morphology/Theoretical Morphology 53