Extended Abstract

(De)constructing Paradigmaticity in Syntax: An Information-Theoretic Approach

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Abstract

The notions of paradigmatic and syntagmatic relations are central to linguistics. Traditionally, two linguistic forms are paradigmatically related if they fall in the same grammatical slot and can substitute for each other, and syntagmatically related if they occur next to each other. For example, in mainstream American English, modals may and can have a paradigmatic relationship since they share a syntactic position, but the modal may and perfect auxiliary have have a syntagmatic relationship as they co-occur in distinct syntactic positions, e.g. They may have eaten. Paradigmatically related forms may form a closed set, or paradigm. Paradigms are well-studied in morphology, e.g., English adjective inflections -er (comparative), -est (superlative), and -∅ (no suffix, positive) form a clear paradigm, but they are often less clear-cut in syntax (cf. Lehmann 2015). This study proposes a new approach for examining this issue which re-casts the conventionally categorical contrast between paradigmatic and syntagmatic relationships as a gradient information-theoretic notion, pointwise mutual information. The more strongly negative the PMI between two forms appearing in the same constructional environment, the more paradigmatic the relationship, and if PMI ≥ 0, it is not paradigmatic at all. Paradigmaticity between forms in this approach is thus the degree of mutual exclusivity between them. This proposal is motivated by cases in syntax where some forms belonging to similar functional domains may co-occur only occasionally, and thus appear marginally paradigmatic. Examples include the negative and affirmative potential modality markers 唔 m4 and 得 dak1 in Cantonese resultatives, and the focus marker も mo and case marker を o in Japanese. The PMI measure can describe both relations as strongly but not categorically paradigmatic. This study then extends this gradient measure to evaluate the degree to which paradigmatically related forms constitute a paradigm. This is done by taking the distribution of PMIs between any pair of members in the paradigm, then taking a summary statistic like the mean, median or maximum. This complements notions of gradient paradigmaticity from previous work (e.g. Lehmann 2015, Diewald & Smirnova 2010), which focus on factors like semantic dependence, by extending the notion to formal co-occurrence probability. Before the analysis, one must first identify a set of k forms from similar semantic domains that occur in the same constructional context, e.g. Japanese postnominal particles. Each instance of the construction examined containing the forms under investigation is then extracted from a corpus and modelled as a k-dimensional Bernoulli random vector, which is 0 when a form is absent and 1 when present (ignoring ordering information). To estimate PMI, the forms’ (co-)occurrence probabilities can be estimated in multiple ways. With the maximum likelihood estimator (MLE), the probability of (co-)occurrence is just the empirical proportion of times in which form(s) (co-)occur in the corpus. Yet since zero empirical co-occurrence probabilities are common in this type of situation, MLEs can be undefined, making it hard to compare across undefined values (which can be due to small n or truly high paradigmaticity), and usual Wald tests and confidence intervals based on asymptotic normality fail. An alternative is additive smoothing, from which one can get Dirichlet-based posterior intervals. Rather than smoothing word counts directly, I treat the Bernoulli random vectors as categorical random variables with 2^k categories (one for each combination of forms), so smoothing can be applied to each of these co-occurrence categories. With a sizeable form inventory, most co-occurrences will be extremely infrequent, so smoothing would be excessive using standard hyperparameter choices like alpha =1. I thus cap the maximum number of forms appearing at the maximum attested number M, and use the reciprocal of the number of resulting categories to concentrate density near zero. The study describes two applications to Japanese, revealing some patterns not statable in categorical approaches. The study adds to existing computational research (Salle & Villavicencio 2019) suggesting negative PMI encodes syntactic information, and adds a quantitative, formal dimension to paradigmaticity, a notion mostly explored in qualitative, semantic ways (Lehmann 2015, Diewald & Smirnova 2010).

Keywords: paradigmaticity, syntax, paradigms, paradigmatic relationships, grammaticalisation, information theory, pointwise mutual information, co-occurrence, distributional method

How to Cite:

Lai, R., (2023) “(De)constructing Paradigmaticity in Syntax: An Information-Theoretic Approach”, Society for Computation in Linguistics 6(1), 1-5. doi: https://doi.org/10.7275/z7fc-6970