Distributed Morphology As a Regular Relation Marina Ermolaeva University of Chicago, Mermolaeva@Uchicago.Edu

Proceedings of the Society for Computation in Linguistics

Volume 1 Article 20

2018 Distributed Morphology as a regular relation Marina Ermolaeva University of Chicago, [email protected]

Daniel Edmiston University of Chicago, [email protected]

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Recommended Citation Ermolaeva, Marina and Edmiston, Daniel (2018) "Distributed Morphology as a regular relation," Proceedings of the Society for Computation in Linguistics: Vol. 1 , Article 20. DOI: https://doi.org/10.7275/R51834PC Available at: https://scholarworks.umass.edu/scil/vol1/iss1/20

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Marina Ermolaeva and Daniel Edmiston University of Chicago {mermolaeva,danedmiston}@uchicago.edu

1 Introduction structure (FS). An FS F is defined as a pair M,E , h i where the feature bundle M = feat(F ) is a sub- This research reorganizes the Distributed Morphol- set of some finite set of features (including syntac- ogy (DM, (Halle and Marantz, 1993)) framework tic category labels) and the phonological exponent to work over strings. That the morphological mod- E = exp(F ) (Σ None, ), where Σ is a fi- ule should operate over strings is desirable, since it ∈ ∪ { } nite set of phonemes. The default exponent of each is assumed that most (arguably all) morphological syntactic unit is None, a place-holder to be replaced processes can be modelled with regular languages by vocabulary insertion (VI) in the morphological (Karttunen et al. 1992). As is, DM typically op- module; None is distinct from the null exponent . erates on binary trees, with the syntax- morphol- An example derivation and its yield serving as in- ogy interface implicitly treated as a tree-transducer. put to the morphology are shown in (1); we assume We contend that using (binary) trees is overpowered, that word boundaries (denoted by #) are part of the and predicts patterns which are unattested in natu- linearized representation. ral language (e.g. iterable nested dependencies). If however, we restrict the morphological component (1) > to working on strings, we correctly predict that morphology can be modelled with regular string lan- D, JOHN, 3, SG { None } < guages, and so we treat the morphological compo- D E T, PAST, 3, SG nent as a finite-state string-transducer, i.e. as a regu- { } > lar relation. None D E Assuming the Y-model, standard DM operating V, SLEEP { } on trees presumes that the flattening of the derivation None D E for PF takes place post-morphology. We push this flattening of the structure to above the morphologi- ⇓ D, JOHN, 3, SG # V, SLEEP # T, PAST, 3, SG cal module, between the syntax and morphology. { None } { None } { None } D E D E D E 2 Syntax-morphology interface 3 Morphology as regular relations We use a modified version of Minimalist Grammars As in standard DM, our operations are context- (Stabler, 1997) as our syntactic framework. We en- dependent. Context-dependent rewriting rules have hance the formalism with the notion of node strength the form A B/C D, where A, B, C, D are → imported from Mirror Theory (Brody, 1997; Kobele, regular expressions over some alphabet. With a few 2002) to implement both Head Movement and Low- caveats, such rules (and ordered finite sequences ering as mechanisms for constructing morphological thereof) have been shown to define regular relations words. Following (Trommer, 1999), we assume that on strings (Kaplan and Kay, 1994). Assuming that the basic unit of syntactic computation is a feature morphology can be modelled by regular relations, it

178 Proceedings of the Society for Computation in Linguistics (SCiL) 2018, pages 178-181. Salt Lake City, Utah, January 4-7, 2018 should be possible to state morphological rules in a 4 Cyclicity and Rewriting way compatible with this format. We take A, B to be sequences of FSs and C, D to be regular expres- As we have proposed a move away from tree- sions over FSs. As a proof of concept, we deﬁne VI structures and toward strings, it is worth revisiting and Readjustment as follows. VI rewrites a single one of the primary motivations behind tree struc- node as a sequence of FSs which can be thought of tures in the literature, namely Cyclicity/Rewriting as morphophonemes and can be further manipulated (Bobaljik, 2000). by Readjustment rules: (6) Cyclicity: VI starts at the root and proceeds outwards (2) A rule r of the form A B/C D is a VI rule → Rewriting: VI deletes morphosyntactic fea- iff: tures it expresses A = 1, B 1; | | | | ≥ exp(A ) = None for 1 i A ; i ≤ ≤ | | The two constraints in (6) make strong predictions exp(B ) = None for 1 j B ; j 6 ≤ ≤ | | concerning possible contexts for VI rules. In par- 1 i A feat(Ai) = 1 j B feat(Bj) ≤ ≤| | (r is≤ feature-preserving≤| | ); ticular, Cyclicity predicts that phonologically condi- S S tioned allomorphy can only be inward-sensitive, and feat(A1) = ... = feat(A A ) = feat(B1) = | | ... = feat(B B ) (r is set-preserving). Rewriting only allows outward-sensitivity for mor- | | phosyntactic features. One motivating example be- (3) A rule r of the form A B/C D is a Read- → hind Cyclicity comes from Itelmen, where it appears justment rule iff: that dependencies are sensitive to embedding-depth exp(A ) = None for 1 i A ; i 6 ≤ ≤ | | exp(B ) = None for 1 j B ; rather than linear ordering. Consider the follow- j 6 ≤ ≤ | | r is feature-preserving and set-preserving. ing schematic of an Itelmen example adapted from Bobaljik 2000.

For instance, the root alternation in sleep/slept can (7) be captured by the VI and Readjustment rules in (4), represented as rewriting rules in (5), with ? as short- A, SUBJ-AGR { } hand for “any exponent”: None D E B, OBJ-AGR (4)[ SLEEP] sli:p { None } → i: E /X Y[PAST], where X Y {CREEP, D E → ∈ SLEEP, WEEP, ...} VERB C, CLASS(II) {None} { None }

SLEEP SLEEP SLEEP SLEEP SLEEP D E D E (5) { } { } { } { } None → { s } l i: p In (7), the surface form B is dependent upon the D SLEEP E D SLEEPED EDSLEEP ED∗ PAST E { } { } / { } { } morphosyntantic features of A, and the the form of C i: → E ? ? D E D E hD Ei D E is dependent upon the features of B and A. Given the Importantly, morphological rules – both in tradi- tree structure above, there is a clear pattern of more- tional DM and in our formalism – are stated over embedded items being dependent on less-embedded underspecified feature structures: they apply to any items morphosyntactically; however, such depen- item whose features match the structural descrip- dencies cannot be reduced to linear order. tion. Put in practice, each underspecified rule like Such effects in morphology are handled by ap- the ones in (5) can be converted, via a well-defined plying VI rules from the root outwards – which is procedure, into a set of instances – regular relations impossible after linearization. Fortunately, using over the alphabet of fully specified FSs. This alpha- transducer composition to build our morphology out bet is guaranteed to be finite, as the set of features of individual rules imposes a strict rule ordering. and Σ are finite by definition. Relations encoding For this ordering, we can follow the standard or- rules are then composed into a single regular rela- der of projections, working from bottom to top (e.g. tion (transducer), following the procedure laid out V T C in the clausal domain). In this way, we re- → → in (Kaplan and Kay, 1994). produce Cyclicity effects over strings. For example,

179 with cases of phonologically conditioned allomor- (12) > phy like English DPs of the form [DPD[NPN]], we can T, PRS > { } capture the a/an allomorphy by having rules that ap- None

SPACE,D E ply to FSs containing N precede rules that target FSs { > TRANSLOC containing D. Likewise for examples like (7) above, None } ASP, P,D E { arranging VI in the C B A order yields the right < S-CLASS → → None } pattern with no need for tree structure. D E V, 3, SG Thus, trees are not necessary to produce Cyclic- { None } > ity effects. However, it is not even clear that D E FIND, µ, { { C-CLASS S-CLASS Cyclicity/Rewriting are desirable constraints for our None } None } D E D E grammar, as there are numerous apparent counter- The solution proposed by Deal and Wolf (2017) examples to Rewriting (Gribanova and Harizanov, involves weakening of both Rewriting and Cyclicity. 2017) and Cyclicity (Svenonius, 2012). The former is replaced with Monotonicity: instead An interesting case is Nez Perce (Deal and Wolf, of deleting morphosyntactic features, VI strictly 2017). The verb suffix denoted as µ exhibits al- adds information. The latter is restated in terms of lomorphy conditioned by the class feature of the cycles, roughly corresponding to syntactic phases. root, as exemplified by the so-called ‘S-class’ verb Within a cycle, lexical items can be inserted in any eat in (8) and the ‘C-class’ verb find in (9). This order, constrained only by their phonological con- is an instance of inward sensitivity and, since class text requirements. Cycles themselves are spelled out membership is a morphosyntactic feature, a counter- in an inside-out fashion, one at a time. As there is example to Rewriting: a phase boundary above Aspect, the realization of µ can depend on the phonological exponent of Aspect, (8) ’aw- ’ap- an’y- o’- qa 3OBJ- eat- µ- PROSP.ASP- PST but not of a morpheme belonging to the higher cycle. This can be straightforwardly translated into our (9) ’aw- ’yáx-ˆ nan’y- o’- qa formalism. The contexts for -nay’ (10) and -nan’i 3OBJ- find- µ- PROSP.ASP- PST (11) are shown in (13a) and (13b) respectively: Moreover, µ appears in the long form (9) if the fol- C-CLASS (13) a. { ? } {}C {}V lowing suffix is smaller than a sequence of one con- D C-CLASS E D ED E sonant and one vowel (CV). The short form (10) is b. { ? } realized when µ is followed by a CV (or longer) Our definitionD of VIE in (2) already conforms to morpheme. Suffixes that appear to the right of µ, Monotonicity rather than Rewriting. The weaken- such as Aspect, attach outside µ, making this al- ing of Cyclicity pushes the responsibility for the cor- ternation a case of outward-looking phonologically- rect order of VI steps inside a cycle to the ordering conditioned allomorphy – contrary to Cyclicity. of VI rules; the correct choice of µ allomorphs can (10) ’aw- ’yáx-ˆ nay’- sa- qa be ensured by placing all VI rules realizing Aspect 3OBJ- find- µ- IPFV.ASP- PST before those realizing µ. Finally, the locality restric- tion that prompted the adoption of weakened Cyclic- Importantly, this alternation is conditioned only by ity can be stated in terms of linear adjacency. One the suffix immediately following µ; if that suffix is way to achieve this on strings is to incorporate phase realized by a null exponent (11), µ will appear in the boundaries into the linearized input to morphology. long form, even if the material further to the right is This would prevent the right context in (13a) from CV in form: crossing the phase boundary. To summarize, the string-based formalism can be (11) ’aw- ’yáx-ˆ nan’i- - ki- ∅ ∅ used both to capture patterns that require VI to (ap- 3OBJ- find- µ- P.ASP- TRANSLOC- PRS parently) make reference to word-internal tree struc- Using our feature structure notation, the structure ture, and to handle counter-examples to Cyclicity in of (11) can be represented as follows: a simple and natural way.

180 5 Inching toward Word & Paradigm DM closer to certain instantiations of W&P morphology, particularly Stump’s PFM. We believe this What we find when we simplify DM as we have, bringing together of frameworks is enlightening, as is that we reveal how DM and certain models of it shows the cores of each are more similar than they W&P end up looking a lot alike. Per Karttunen at first appear to be. (2003), Stump’s (2003) Paradigm Function Mor- Assuming that running DM over strings does not phology (PFM) can also be recast as regular rela- cost us empirical coverage, we contend that DM tions. That both PFM and DM can be recast as regu- should be run on strings, providing a direct explana- lar relations means that whatever dress these frame- tion for the generalization that morphology appears works may be adorned with, they are in some fun- to be regular, and allows for efficient parsing and damental and real ways the same. For a direct com- generation of surface forms (Kaplan and Kay, 1994). parison, consider the PFM-style realization (15) of a Swahili example (14): (14) ni-ta-taka References 1SG-FUT-want Jonathan David Bobaljik. 2000. The ins and outs of con- textual allomorphy. In University of Maryland Work- (15) PF( TAKA, σ: 1sg fut ) = h { }i ing Papers in Linguistics, pages 35–71. [II: [I: Stem( TAKA, σ )]] h i Michael Brody. 1997. Mirror theory. a. [I: taka, σ: 1sg fut ] = tataka, σ Amy Rose Deal and Matthew Wolf. 2017. Outwards- h { }i h i b. [II: tataka, σ: 1sg fut ] = sensitive phonologically-conditioned allomorphy in h { }i nitataka, σ Nez Perce. In The morphosyntax-phonology connec- h i tion: locality and directionality at the interface. Ox- This style of analysis is clearly just a series of ford University Press. rewrite rules, where the ordering of the blocks is Vera Gribanova and Boris Harizanov. 2017. Locality and handled as composition of VI-rules in our frame- directionality in inward-sensitive allomorphy: Russian work. Compare with our formulation. and Bulgarian. In The morphosyntax-phonology con- nection: locality and directionality at the interface. D, 1, SG T, FUT V,TAKA Oxford University Press. (16) { } { } { } None None None Morris Halle and Alec Marantz, 1993. Distributed Mor-

TAKA TAKA TAKA TAKA TAKA phology and the pieces of inflection, pages 111–176. (17) D{ } {ED} ED{ } E None → t { a } k { a } The MIT Press. D E D ED ED ED E Ronald M. Kaplan and Martin Kay. 1994. Regular mod- FUT FUT FUT { } { } None → t { a } els of phonological rule systems. Computational Lin- D E D ED E guistics, 20(3):331–378. 1SG 1SG 1SG { } Lauri Karttunen, 2003. Computing with Realizational None { n } { i } → Morphology, pages 203–214. Springer Berlin Heidel- D E D ED E 6 Discussion berg, Berlin, Heidelberg. Gregory M. Kobele. 2002. Formalizing mirror theory. Above, we defined a portion of DM over strings and Grammars, 5(3):177–221. gave examples as a proof of concept. Given recent Jason Merchant. 2015. How much context is enough? work in DM which seeks to limit the size of context Two cases of span-conditioned stem allomorphy. Lin- available to morphological rules (Merchant, 2015), guistic Inquiry, 46(2):273–303. we believe that limiting DM to strings is a step in Edward P. Stabler. 1997. Derivational Minimalism. In Christian Retoré, editor, LACL ’96 Selected Papers, the right direction. Rather than limit the size of the pages 68–95. Springer Berlin Heidelberg. relevant windows over trees, restricting ourselves to Peter Svenonius. 2012. Look both ways: Outward- regular relations over strings gives us a solid formal looking allomorphy in icelandic participles. grounding to limit contexts. Restrictions on context Jochen Trommer. 1999. Morphology consuming syntax’ can be naturally stated by regular expressions, and resources: generation and parsing in a minimalist ver- the formal properties of these systems are well un- sion of Distributed Morphology. In Proceedings of the derstood. As a final plus, in eliminating tree struc- ESSLLI Workshop on Resource Logics and Minimalist ture from DM and relying on rule-ordering, we bring Grammars.

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