The computational nature of stress assignment

While computational studies of stress patterns as phonotactics have yielded restrictive characterizations of stress (Rogers et al., 2013) with provably correct learning procedures (Heinz, 2009), an outstanding question is the nature of stress assignment as a function which assigns stress to an underlying bare string of syllables. This paper fills this gap by locating stress patterns with respect to the subsequential class of functions (Mohri, 1997), which are argued to be important for phonology in that the vast majority of phonological functions fall within the subsequential boundary (Heinz & Lai, 2013; Chandlee, 2014), with the notable exception of tone and vowel harmony (Jardine, 2016; McCollum et al., under review). The main result is that – while most, if not all quantity insensitive (QI) stress systems are subsequential functions – the same does not hold for quantity sensitive (QS) systems. Counter-intuitively, so-called default-to-opposite QS patterns are subsequential, but default-to-same QS patterns are provably not. It also supports the claim of Jardine (2016) that certain tonal patterns are non-sequential because their suprasegmental nature allows for more a more powerful computation. As stress assignment is also suprasegmental, the existence of non-sequential stress functions adds evidence for this conclusion

Learning Phonological Mappings by Learning Strictly Local Functions

In this paper we identify strict locality as a defining computational property of the input-output mapping that underlies local phonological processes. We provide an automata-theoretic characterization for the class of Strictly Local functions, which are based on the well-studied Strictly Local formal languages (McNaughton & Papert 1971; Rogers & Pullum 2011; Rogers et al. 2013), and show how they can model a range of phonological processes. We then present a learning algorithm, the SLFLA, which uses the defining property of strict locality as an inductive principle to learn these mappings from finite data. The algorithm is a modification of an algorithm developed by Oncina et al. (1993) (called OSTIA) for learning the class of subsequential functions, of which the SL functions are a proper subset. We provide a proof that the SLFLA learns the class of SL functions and discuss these results alongside previous studies on using OSTIA to learn phonological mappings (Gildea and Jurafsky 1996)

Learning Local Phonological Processes

We present a learning algorithm for local phonological processes that relies on a restriction on the expressive power needed to compute phonological patterns that apply locally. Representing phonological processes as a functional mapping from an input to output form (an assumption compatible with either the SPE or OT formalism), the learner assumes the target process can be described with the functional counterpart to the Strictly Local (McNaughton and Papert 1971, Rogers and Pullum 2011) formal languages. Given a data set of input-output string pairs, the learner applies the two-stage grammatical induction procedure of 1) constructing a prefix tree representation of the input and 2) generalizing the pattern to words not found in the data set by merging states (Garcia and Vidal 1990, Oncina et al. 1993, Heinz 2007, 2009, de la Higuera 2010). The learner’s criterion for state merging enforces a locality requirement on the kind of function it can converge to and thereby directly reflects its own hypothesis space. We demonstrate with the example of German final devoicing, using a corpus of string pairs derived from the CELEX2 lemma corpus. The implications of our results include a proposal for how humans generalize to learn phonological patterns and a consequent explanation for why local phonological patterns have this property

Use It or Lose It Harmony in Komo

This paper discusses a case of putative dominance reversal in the Komo language (Otero 2015, 2019), which we analyze as a related, but distinct repair strategy called “Use it or Lose it” (Mullin & Pater 2015).Mullin & Pater (2015) argue that Use it or Lose it harmony is a pathological prediction of Agree for the same basic reason that “Sour Grapes” harmony (Wilson 2003, 2006; Heinz & Lai 2013) has been regarded as pathological – both Use it or Lose it and Sour Grapes harmony patterns are non-myopic (Wilson 2003, 2006). Wilson argues that unbounded spreading patterns are universally myopic, and as such, no theory should predict that the realization of some element in spreading – trigger or target – depends on downstream information. However, recent research has shown that some patterns in natural languages are, in fact, non-myopic, indicating that the predictions of Agree are not as problematic as previously thought. This paper argues that the best analysis of Komo relies on the activity of [Atr] and both regressive [+Atr] spreading and [+Atr] trigger effacement are repairs to a single marked structure in the language, *VC0[Hi, Atr]

Decomposing phonological transformations in serial derivations

While most phonological transformations have been shown to be subsequential, there are tonal processes that do not belong to any subregular class, thereby making it difficult to identify a tighter bound on the complexity of phonological processes than the regular languages. This paper argues that a tighter bound obtains from examining the way transformations are computed: when derived in serial, phonological processes can be decomposed into iterated subsequential maps

Vowel Harmony Viewed as Error-Correcting Code

Robustness reduces the risk of information loss. At present the notion of error-correcting codes (ECCs) is used to achieve robustness in technical fields only. Viewing fault-tolerant natural systems as systems equipped with error-correcting codes permits a formal comparison of natural and technical robustness. Instancing natural language (NL), we show differences in technical and natural error-correcting approaches. By picking a specific grammar phenomenon which some NLs exhibit – vowel harmony (VH) – we show that (1) VH can be formalized as an ECC as well as (2) VH adds to the robustness of its NL. We provide empirical as well as formal evidence on this fact. (3) Consequently, the example of VH shows that the notion of an ECC serves as a suitable formal model not only for technical but also for natural robustness

A Computational Account of Tone Sandhi Interaction

This paper presents a computational account of three tone sandhi rules in Tianjin Chinese that have received a lot of attention in the literature due to the seemingly complex way in which they interact. Two of the rules apply right-to-left while the third applies left-to-right, making it difficult for both rule- and constraint-based formalisms to account for the interaction in a unified way. In the computational framework advocated for in this paper, the apparent difference in directionality of the three rules amounts to a subtle difference in computational classification: the left-to-right rule has the property of input strict locality (ISL) while the right-to-left rules share the property of output strict locality (OSL). However, the fact that the direction of rules with the ISL property doesn't actually matter, a unified account becomes possible in that all three rules can be modeled as a single input-output strictly local function

Computing Vowel Harmony: The Generative Capacity of Search & Copy

Search & Copy (S&C) is a procedural model of vowel harmony in which underspecified vowels trigger searches for targets that provide them with features. In this paper, we seek to relate the S&C formalism with models of phonological locality proposed by recent work in the subregular program. Our goal is to provide a formal description, within the framework of mathematical linguistics, of the range of possible phonological transformations that admit an analysis within S&C. We show that used in its unidirectional mode, all transformations described by an S&C analysis can be modeled by tier-based input strictly local functions (TISL). This result improves the previous result of Gainor et al 2012, which showed that vowel harmony processes can be modeled by subsequential functions. However, non-TISL transformations can be given S&C descriptions in the following ways. Firstly, since TISL functions are not closed under composition, a non-TISL vowel harmony pattern may be obtained by applying two S&C rules sequentially. Secondly, when S&C is used in its bidirectional mode, it has the ability to describe transformations that cannot be modeled by finite-state functions

Foot structure enables strict locality in phonological processes

The metrical foot has a long pedigree as a theoretical device in generative phonology (Liberman & Prince, 1977; Halle & Vergnaud, 1978; Selkirk, 1980; Hammond, 1984; Halle & Vergnaud, 1987; Idsardi, 1992; Hayes, 1995). While the motivations for foot structure are typically studied in terms of stress, this paper provides evidence from the principles of formal language theory (Chomsky, 1956; Hopcroft & Ullman, 1979) for foot-based analyses of non-stress processes. Though use of foot structure in these analyses is not novel (see Gonzalez (2018) for an overview) this paper contributes a precise characterization of what is at stake in terms of the computation of these processes when foot structure is present versus when it is not. This formal computational analysis indicates that feet have measurable implications for the predicted typology of these patterns. Thus, support is provided for a specific substantive phonological proposal based on the well-defined measures of complexity that formal language theory offers.

Representation and the Computation of Long Distance Tone Processes

This paper shows how enhancing the representation, while fixing the logical power of computation, provides a better characterization of the computationally complex tone processes, the unbounded circumembient (UC) processes noted in Jardine (2016). Using Autosegmental Representations, we define tone-TBU associations as quantifier-free least fixed point transductions, which allow us to extend the notion of subsequentiality to the otherwise non subsequential UC processes.