Real-Valued Logics for Typological Universals: Framework and Application (2020)

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.

## framework 1.language-property matrix universals are modelled as logical formulae which consist of variables and logical connectives. the variables are organized in an |l| × |p | matrix v , where l is the set of investigated languages and p is the set of typological properties/features. the variable at v ℓ p represents the value for the property p of the language ℓ. in our framework, these values are truth values in the range [ 0, 1 ]. in the simplest case, they are binary truth values as in the example matrix below. formulae can be constructed from the language-property matrix by logical connectives, such as the conjunction in (2). foot_0 ## implementation the framework allows implementing individual definitions for the variable matrix v , the valuation v and the weight function w. we experimented with various implementations for all of those @xcite ; this section explains the set-up used for the experiments in section 3. the ud treebanks v2.5 @xcite consist of dependency treebanks for 90 languages from 20 families and 39 subfamilies. the treebanks have a uniform annotation which allows defining properties based on dependency constructions and extracting statistics for various languages of the world. this data can be used to investigate syntactic universals. ## experiments the goal of our experiments is to demonstrate the usefulness of the proposed framework for empirical exploration of the language-typological space beyond simple implications and boolean variables. the framework is to serve as a methodological tool and should ultimately be complemented with a theoretically motivated agenda for exploring systematic correlations among underexplored properties of grammatical systems. to establish how the framework can be used we proceed in three steps: first, we re-evaluate some famous universals of @xcite and discuss the interpretations of varying truth values and standard deviations (sec. 3.1). in the second step, we demonstrate a scenario for testing unexplored candidates for typological universals (which can consist of arbitrary formulae from propositional logic) against the full spectrum of treebanks, taking into variability with respect to each property in the real-valued logic. we work with a simple procedure of generating candidate formulae: taking over the shape of potentially relevant logical combinations from established universals and replacing the properties they include with new ones. a framework is useful for empirical exploration if its diagnostics are robust: a statement capturing a systematic relationship should generalize from one sufficiently large sample of languages to another. we test this by splitting the set of treebanks in an estimation set and a held-out set (sec. 3.2). finally, we enumerate implications of two variables from a selected set of single-link properties and discuss the top-scoring formulae, also in comparison to the findings from previous work on binary properties (sec. 3.3). ## conclusion this paper proposes a framework for the expression of typological statements which uses real-valued logics to capture the empirical truth value of a formula in a given collection of comparable treebanks. we demonstrate the application of the framework by evaluating established formulae as well as new formulae generated from a search algorithm. the components of the framework can be customized: users not working with the universal dependencies can simply exchange the data component; the weighting approach we provide can also be easily exchanged. if a user wants to empirically check their own linguistic features, it is straightforward to obtain the relative frequencies from the treebank collection, complementing existing curated databases such as wals. very little manual work is needed. both approaches have their pros and cons: typological knowledge bases could be subjective or incomplete, while data from the treebanks are subject to problems such as annotation inconsistencies, genre differences etc. this paper discussed some experiments which have the purpose of providing an illustration of the expressiveness of the framework, focusing here on word-order variables. however, other variables could be expressed as well, and the framework also supports inclusion and combination of variables from completely different sources (e.g. phonological properties of a language), as long as the values range between 0 (false) and 1 (true). this especially allows using variables from corpora and from typological knowledge bases together.