Real-Valued Logics for Typological Universals: Framework and Application

Proceedings of the 28th International Conference on Computational Linguistics, pages 3990–4003 Barcelona, Spain (Online), December 8-13, 2020 3990 Real-Valued Logics for Typological Universals: Framework and Application Tillmann D¨onicke G¨ottingen Centre for Digital Humanities University of G¨ottingen∗ tillmann.doenicke@ uni-goettingen.de Xiang Yu Institute for Natural Language Processing University of Stuttgart xiangyu@ims. uni-stuttgart.de Jonas Kuhn Institute for Natural Language Processing University of Stuttgart jonas.kuhn@ims. uni-stuttgart.de Abstract This paper proposes a framework for the expression of typological statements which uses real- valued logics to capture the empirical truth value (truth degree) of a formula on a given data source, e.g. a collection of multilingual treebanks with comparable annotation. The formulae can be arbitrarily complex expressions of propositional logic. To illustrate the usefulness of such a framework, we present experiments on the Universal Dependencies treebanks for two use cases: (i) empirical (re-)evaluation of established formulae against the spectrum of available treebanks and (ii) evaluating new formulae (i.e. potential candidates for universals) generated by a search algorithm. The availability of comparable treebanks – syntactically annotated corpora – for a growing number of typologically distinct languages (most prominently in the collaborative Universal Dependencies project (Nivre et al., 2016)) has led to a recent surge of interest in computational work aiming to detect systematic patterns in the grammatical systems of natural languages and/or to test hypotheses from theoretical work in language typology against empirical evidence. The treebank-based approach (Liu, 2010; Lochbihler, 2017; Gerdes et al., 2019; Bjerva et al., 2019c; Hahn et al., 2020) adds a more data-driven perspective to a strand of research in computational typology (Daum´e and Campbell, 2007; Malaviya et al., 2017; On- cevay et al., 2019; Bjerva et al., 2019a; Bjerva et al., 2019b) that is based on carefully curated typological databases such as WALS1 (Dryer and Haspelmath, 2013) or URIEL2 (Littell et al., 2017). The research strand in computational typology which relies on databases essentially builds on the language features that the long tradition of typological research has identified as most relevant for iden- tifying language universals. Examples of such features are the relative order of verbs and their objects, and the order of nouns and their dependents such as adjectives, numerals and genitives. In the computa- tional research relying on typological knowledge bases, the features are typically assumed to be Boolean and universals are formulated as propositional formulae. A major focus has been on (a) detecting uni- versals that have the form of an implication between two typological variables, and (b) predicting the value of unknown features in typological databases based on systematic patterns in attested grammatical systems. Graphical models have been widely used to calculate the strength of an implication (Daum´e and Campbell, 2007; Lu, 2013; Bjerva et al., 2019b; Bjerva et al., 2019a). While this approach is suitable if one wants to marginalize out the influence of confounding variables, it also constrains the investigated universals to have the form of an implication consisting of one implicand and usually one (but possibly multiple) implicant(s). In principle, comparable treebanks can provide the …

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