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Inflectional learning as local optimization

Abstract

Formal descriptions of inflectional systems face three interrelated problems: (1) the Meaning Assignment Problem: Which morphosyntactic feature specification should be assigned to a given affix? (2) the Imperfect Distribution Problem: To what degree can the paradigmatic distribution of an affix deviate from its morphosyntactic specification? and (3) the Subsegmentation Problem: Does a given string of segments consist of one or more affixes? What makes the analysis of complex inflectional systems potentially intractable is the accumulative effect of all three problems, which results in an unwieldy amount of analytic options. Existing approaches to these problems are either incompatible with standard analyses in theoretical morphology (e.g. Harris 1955; Goldsmith 2010) or address only a subset of these problems (e.g. Pertsova 2011). In this paper, we propose a unified approach to all three problems by outlining a learning algorithm that uses optimal patterns of paradigmatic distribution of potential affixes as the main criterion for computing morpheme meaning and subsegmentation of affix strings. The central idea is that learners apply local optimization in the sense of the Harmonic Serialism version of Optimality Theory (McCarthy 2010): Every optimization step identifies the affix with the optimal distribution in a paradigm, assigning a morpheme entry to it, and ‘freezes’ the substrings corresponding to the newly learned affix in the paradigm for further learning. Different constraint rankings result naturally in affix lexica optimized for specific theoretical approaches to morphology.

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Notes

  1. 1.

    The paradigm table omits the indefinite subject/object forms which largely result from adding a- to the left of the 3rd person subject and i- to the right of the 3rd person object forms.

  2. 2.

    A relative explicit proposal in this context is the Syncretism Principle proposed by Müller (2005, 2003).

  3. 3.

    Requiring that the function mapping affix hypotheses to paradigm cells is injective (i.e., that every feature structure of the affix is mapped to maximally one feature structure of the cell) amounts to a ban against overlapping exponence. Thus, without the injectivity requirement an affix hypothesis specified as {[+1],[+2]} would not only subsume a transitive cell with one 1st person argument and a distinct 2nd person argument (say [Nom Erg +1 −pl][Acc Abs +2 +pl]), but also intransitive cells with a first person inclusive argument specified as [+1 +2] (a standard representation for inclusive, cf. Noyer 1992). We explicitly exclude this possibility because it leads to a proliferation of counterintuitive affix hypotheses.

  4. 4.

    Stemming is a relatively well-understood classical task in information retrieval (Lovins 1968; Porter 1980). Most current work on morpheme segmentation in computational linguistics is in fact restricted to Stemming (cf. Goldsmith 2010).

  5. 5.

    Note that candidate meaning could also be restricted to specifications with zero, one, and two feature structures as more of them will not introduce (extensionally) different meanings in the (mono-)transitive agreement paradigm.

  6. 6.

    We take it for granted that unfilled (‘blind’) cells such as the 1→1 and 2→2 cells in Ainu agreement (the shaded cells in (5)) are formally not part of the paradigm, and therefore not taken into account for computing constraint violations.

  7. 7.

    It might seem that the effects of MaximalCoverage and MinimalCoverage can be derived from FeatureMinimality and FeatureMaximality respectively, but minimizing feature cardinality does not necessarily lead to larger paradigmatic coverage, compare e.g. [Acc Abs +1 −pl] which covers four cells and [Nom Abs +1 −pl] which covers one cell, while both have the same number of features.

  8. 8.

    This again leaves open the question how to account for the surface distribution of ci-. One option in DM is blocking of ci- by other markers or by impoverishment rules, the other option is to assign a context restriction resulting in an entry as ci-:[Nom +1pl] / [Acc +3], which is an asymmetric version of the portmanteau candidate in (28). More generally, one might speculate that context restrictions in morphemes depending on two input heads correspond to the additional feature structures introduced by the optimal portmanteau candidate under the ranking in (26). This would for portmanteau environments provide a solution to the arbitrariness problem for deciding which features in a DM vocabulary item are substantial and which are contextual (cf. Stump 2001a, 41–42).

  9. 9.

    If the insertion is restricted to one exponent, markers with identical meaning are predicted to be in free variation, yielding a random distribution.

  10. 10.

    This is one of the rankings we have tested with the computational implementation described in Sect. 5. The full resulting affix lexicon is identical to the one given in Appendix A.3.

  11. 11.

    This holds only for Rules of Referral which refer to entire inflectional strings. In the major implementation of Rules of Referral in PFM (Stump 2001b,a), Rules of Referral refer to affixes, hence logically presuppose segmentation.

  12. 12.

    In that sense, zero marking of inflectional categories like 3rd person or present tense can guide the subsegmentation necessary where multiple categories are marked on the same side of the stem, by providing independent evidence for e.g. agreement markers where tense is zero-marked or tense markers in 3rd person contexts (see Bank and Trommer 2015).

  13. 13.

    A promising extension would be to assume constraints which conjoin the effects of BeFree and constraints on accuracy. For example, one might posit a version of *UnderInsertion that counts only paradigm cells as constraint violations, whose affix string is strictly identical to the string of the relevant affix hypothesis. In tandem with the standard version of *UnderInsertion (in (7b)), this would capture the intuition that an inflectional string which occurs on its own is more likely to instantiate a homophonous affix than a proper substring of an inflectional string (which is subject to potential misanalysis), and should therefore have a major impact for estimating the accuracy of an affix hypothesis.

  14. 14.

    In the Ainu paradigm, substrings like ec-, ie-, iu-, c-, i-, k-, -a, or -s have exactly the same distribution as their smallest free superstring (eci-, ecien-, etc.) yielding the same violation profile for all of the constraints except for Length, which would always choose the superstring anyway. The only ‘bound’ string with a genuine distribution is -n. Hence the only generalization missed here is the possible subsegmentation of 1st person object into e-n- and u-n-. Evidence like this if backed up by crosslinguistic data might indicate that BeFree is in fact an inviolable restriction on Gen, as we tentatively assume here.

  15. 15.

    To see this, consider potential simple and portmanteaux markers for transitive agreement: Since every feature structure of an affix hypothesis is specified for at least one non-case feature (cf. Sect. 2), a portmanteau marker (e.g. one specified as [Erg +1][Acc +3]) cannot subsume a complete row (e.g. all transitive forms with [Erg+1] subjects) or column (e.g. all transtive forms with [Acc+3] objects) of a paradigm’s transitive region. On the other hand, an intransitive affix hypothesis either subsumes entire rows (e.g. a hypothesis specified as [Erg +1]), entire columns (e.g. if specified as [Acc+1]), or no transitive cells at all (e.g. if specified as [Nom Abs +1]), whereas a portmanteau hypothesis never covers intransitive cells (since any feature structure in an affix hypothesis must subsume a distinct feature structure of a paradigm cell, cf. footnote 3).

  16. 16.

    This is partially, but not completely, due to the fact that the implementation presupposes BeFree to be invariably undominated. In principle (for other distributions of the same inflectional strings or by adding further constraints) iterative optimization could result in affixes which do not occur as free inflectional strings in the overall paradigm (the initial input to the algorithm). For example we might get the segmentation e-n- for some instance of en- by subsuming this occurrence under the meaning of e- (which occurs independently in the paradigm). After freezing e-, the algorithm would assign a marker entry to n- in one of the following optimization cycles. Thus for Ainu, the constraint inventory we use is remarkably conservative in not generating affix hypotheses which do not correspond to inflectional strings.

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Correspondence to Jochen Trommer.

Additional information

We thank Adam Albright, Gereon Müller, Daniela Henze, Eva Zimmermann, and an anonymous reviewer for helpful comments. All remaining errors are our own.

Appendix A: The factorial typology of affix lexica for Ainu

Appendix A: The factorial typology of affix lexica for Ainu

A.1 *Portmanteaux*OverInsertion*UnderInsertion ≫ …

  1. (52)

    Expansionist Grammar without Portmanteaux

  1. (53)

    Full Morpheme List

    a. en- [Acc +1 −pl] e. ku- [Nom Abs +1 −pl]
    b. un- [Acc +1 +pl] f. ci- [Nom Abs +1 +pl]
    c. eci- [+2 +pl] g. -as [Nom Abs +1 +pl]
    d. e- [Nom Abs +2 −pl]    

A.2 *Portmanteaux*UnderInsertion*OverInsertion ≫ …

  1. (54)

    Retractive Grammar without Portmanteaux

  1. (55)

    Full Morpheme List

    a. en- [Acc +1 −pl] e. ku- [Nom +1 −pl]
    b. un- [Acc +1 +pl] f. ci- [Erg +1 +pl]
    c. eci- [+2] g. -as [Nom Abs +1 +pl]
    d. e- [+2 −pl]    

A.3 *OverInsertion*Portmanteaux*UnderInsertion ≫ …

  1. (56)

    Expansionist Grammar with Dispreference for Portmanteaux

  1. (57)

    Full Morpheme List

    a. en- [Acc +1 −pl] e. ku- [Nom Abs +1 −pl]
    b. un- [Acc +1 +pl] f. ci- [Nom +1 +pl][Acc +3]
    c. eci- [+2 +pl] g. -as [Nom Abs +1 +pl]
    d. e- [Nom Abs +2 −pl]    

A.4 *OverInsertion*UnderInsertion*Portmanteaux ≫ …

  1. (58)

    Expansionist Grammar with Focus on Accuracy

  1. (59)

    Full Morpheme List

    a. en- [Acc +1 −pl] e. ku- [Nom +1 −pl][Acc  +3]
    b. un- [Acc +1 +pl] f. ci- [Nom +1 +pl][Acc +3]
    c. eci- [+2 +pl] g. -as [Nom Abs +1 +pl]
    d. e- [+2 −pl][+3]    

A.5 *UnderInsertion*Portmanteaux*OverInsertion ≫ …

  1. (60)

    Retractive Grammar with Dispreference for Portmanteaux

  1. (61)

    Full Morpheme List

    a. en- [Acc +1 −pl] e. ku- [Nom +1 −pl]
    b. un- [Acc +1 +pl] f. ci- [Erg +1 +pl]
    c. eci- [+2] g. -as [Nom Abs +1 +pl]
    d. e- [+2 −pl]    

A.6 *UnderInsertion*OverInsertion*Portmanteaux ≫ …

  1. (62)

    Retractive Grammar with Focus on Accuracy

  1. (63)

    Full Morpheme List

    a. en- [Acc +1 −pl] e. ku- [Nom +1 −pl]
    b. un- [Acc +1 +pl] f. ci- [Nom +1 +pl][Acc +3]
    c. eci- [+2] g. -as [Nom Abs +1 +pl]
    d. e- [+2 −pl]    

A.7 *OverInsertion ≫ MinimalCoverage ≫ *Portmanteaux ≫ …

  1. (64)

    Leading-Form Grammar

  1. (65)

    Full Morpheme List

    a. en- [Nom +2 −pl][Acc +1 −pl] e. ku- [Nom  Abs +1 −pl]
    b. un- [Nom +2 −pl][Acc +1 +pl] f. ci- [Nom  +1 +pl][Acc +3 −pl]
    c. eci- [Nom Abs +2 +pl] g. -as [Nom Abs +1  +pl]
    d. e- [Nom Abs +2 −pl]    

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Trommer, J., Bank, S. Inflectional learning as local optimization. Morphology 27, 383–422 (2017). https://doi.org/10.1007/s11525-017-9304-0

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Keywords

  • Morphological learning
  • Inflectional paradigms
  • Syncretism
  • Subsegmentation
  • Optimality theory
  • Harmonic serialism