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1.3. Morphological Models

There are many possible approaches to designing and implementing morphological models. Over time, computational linguistics has witnessed the development of a number of formalisms and frameworks, in particular grammars of different kinds and expressive power, with which to address whole classes of problems in processing natural as well as formal languages.

Various domain-specific programming languages have been created that allow us to implement the theoretical problem using hopefully intuitive and minimal programming effort. These special-purpose languages usually introduce idiosyncratic notations of programs and are interpreted using some restricted model of computation. The motivation for such approaches may partly lie in the fact that, historically, computational resources were too limited compared to the requirements and complexity of the tasks being solved. Other motivations are theoretical given that finding a simple but accurate and yet generalizing model is the point of scientific abstraction.

There are also many approaches that do not resort to domain-specific programming. They, however, have to take care of the runtime performance and efficiency of the computational model themselves. It is up to the choice of the programming methods and the design style whether such models turn out to be pure, intuitive, adequate, complete, reusable, elegant, or not.

Let us now look at the most prominent types of computational approaches to morphology. Needless to say, this typology is not strictly exclusive in the sense that comprehensive morphological models and their applications can combine various distinct implementational aspects, discussed next.

1.3.1. Dictionary Lookup

Morphological parsing is a process by which word forms of a language are associated with corresponding linguistic descriptions. Morphological systems that specify these associations by merely enumerating them case by case do not offer any generalization means. Likewise for systems in which analyzing a word form is reduced to looking it up verbatim in word lists, dictionaries, or databases, unless they are constructed by and kept in sync with more sophisticated models of the language.

In this context, a dictionary is understood as a data structure that directly enables obtaining some precomputed results, in our case word analyses. The data structure can be optimized for efficient lookup, and the results can be shared. Lookup operations are relatively simple and usually quick. Dictionaries can be implemented, for instance, as lists, binary search trees, tries, hash tables, and so on.

Because the set of associations between word forms and their desired descriptions is declared by plain enumeration, the coverage of the model is finite and the generative potential of the language is not exploited. Developing as well as verifying the association list is tedious, liable to errors, and likely inefficient and inaccurate unless the data are retrieved automatically from large and reliable linguistic resources.

Despite all that, an enumerative model is often sufficient for the given purpose, deals easily with exceptions, and can implement even complex morphology. For instance, dictionary-based approaches to Korean [35] depend on a large dictionary of all possible combinations of allomorphs and morphological alternations. These approaches do not allow development of reusable morphological rules, though [36].

The word list or dictionary-based approach has been used frequently in various ad hoc implementations for many languages. We could assume that with the availability of immense online data, extracting a high-coverage vocabulary of word forms is feasible these days [37]. The question remains how the associated annotations are constructed and how informative and accurate they are. References to the literature on the unsupervised learning and induction of morphology, which are methods resulting in structured and therefore nonenumerative models, are provided later in this chapter.

1.3.2. Finite-State Morphology

By finite-state morphological models, we mean those in which the specifications written by human programmers are directly compiled into finite-state transducers. The two most popular tools supporting this approach, which have been cited in literature and for which example implementations for multiple languages are available online, include XFST (Xerox Finite-State Tool) [9] and LexTools [11].5

Finite-state transducers are computational devices extending the power of finite-state automata. They consist of a finite set of nodes connected by directed edges labeled with pairs of input and output symbols. In such a network or graph, nodes are also called states, while edges are called arcs. Traversing the network from the set of initial states to the set of final states along the arcs is equivalent to reading the sequences of encountered input symbols and writing the sequences of corresponding output symbols.

The set of possible sequences accepted by the transducer defines the input language; the set of possible sequences emitted by the transducer defines the output language. For example, a finite-state transducer could translate the infinite regular language consisting of the words vnuk, pravnuk, prapravnuk, ... to the matching words in the infinite regular language defined by grandson, great-grandson, great-great-grandson, ...

The role of finite-state transducers is to capture and compute regular relations on sets [38, 9, 11].6 That is, transducers specify relations between the input and output languages. In fact, it is possible to invert the domain and the range of a relation, that is, exchange the input and the output. In finite-state computational morphology, it is common to refer to the input word forms as surface strings and to the output descriptions as lexical strings, if the transducer is used for morphological analysis, or vice versa, if it is used for morphological generation.

The linguistic descriptions we would like to give to the word forms and their components can be rather arbitrary and are obviously dependent on the language processed as well as on the morphological theory followed. In English, a finite-state transducer could analyze the surface string children into the lexical string child [+plural], for instance, or generate women from woman [+plural]. For other examples of possible input and output strings, consider Example 1–8 or Figure 1–1.

Relations on languages can also be viewed as functions. Let us have a relation R, and let us denote by [Σ] the set of all sequences over some set of symbols Σ, so that the domain and the range of R are subsets of [Σ]. We can then consider R as a function mapping an input string into a set of output strings, formally denoted by this type signature, where [Σ] equals String:

Finite-state transducers have been studied extensively for their formal algebraic properties and have proven to be suitable models for miscellaneous problems [9]. Their applications encoding the surface rather than lexical string associations as rewrite rules of phonology and morphology have been around since the two-level morphology model [39], further presented in Computational Approaches to Morphology and Syntax [11] and Morphology and Computation [40].

Morphological operations and processes in human languages can, in the overwhelming number of cases and to a sufficient degree, be expressed in finite-state terms. Beesley and Karttunen [9] stress concatenation of transducers as the method for factoring surface and lexical languages into simpler models and propose a somewhat unsystematic compilereplace transducer operation for handling nonconcatenative phenomena in morphology. Roark and Sproat [11], however, argue that building morphological models in general using transducer composition, which is pure, is a more universal approach.

A theoretical limitation of finite-state models of morphology is the problem of capturing reduplication of words or their elements (e.g., to express plurality) found in several human languages. A formal language that contains only words of the form λ1+k, where λ is some arbitrary sequence of symbols from an alphabet and k ε{1, 2,... } is an arbitrary natural number indicating how many times λ is repeated after itself, is not a regular language, not even a context-free language. General reduplication of strings of unbounded length is thus not a regular-language operation. Coping with this problem in the framework of finite-state transducers is discussed by Roark and Sproat [11].

Finite-state technology can be applied to the morphological modeling of isolating and agglutinative languages in a quite straightforward manner. Korean finite-state models are discussed by Kim et al. [41], Lee and Rim [42], and Han [43], to mention a few. For treatments of nonconcatenative morphology using finite-state frameworks, see especially Kay [44], Beesley [45], Kiraz [46], and Habash, Rambow, and Kiraz [47]. For comparison with finitestate models of the rich morphology of Czech, compare Skoumalová [48] and Sedláĉek and Smrž [49].

Implementing a refined finite-state morphological model requires careful fine-tuning of its lexicons, rewrite rules, and other components, while extending the code can lead to unexpected interactions in it, as noted by Oazer [50]. Convenient specification languages like those mentioned previously are needed because encoding the finite-state transducers directly would be extremely arduous, error prone, and unintelligible.

Finite-state tools are available in most general-purpose programming languages in the form of support for regular expression matching and substitution. While these may not be the ultimate choice for building full-fledged morphological analyzers or generators of a natural language, they are very suitable for developing tokenizers and morphological guessers capable of suggesting at least some structure for words that are formed correctly but cannot be identified with concrete lexemes during full morphological parsing [9].

1.3.3. Unification-Based Morphology

Unification-based approaches to morphology have been inspired by advances in various formal linguistic frameworks aiming at enabling complete grammatical descriptions of human languages, especially head-driven phrase structure grammar (HPSG) [51], and by development of languages for lexical knowledge representation, especially DATR [52]. The concepts and methods of these formalisms are often closely connected to those of logic programming. In the excellent thesis by Erjavec [53], the scientific context is discussed extensively and profoundly; refer also to the monographs by Carpenter [54] and Shieber [55].

In finite-state morphological models, both surface and lexical forms are by themselves unstructured strings of atomic symbols. In higher-level approaches, linguistic information is expressed by more appropriate data structures that can include complex values or can be recursively nested if needed. Morphological parsing P thus associates linear forms φ with alternatives of structured content ψ, cf. (1.1):

Erjavec [53] argues that for morphological modeling, word forms are best captured by regular expressions, while the linguistic content is best described through typed feature structures. Feature structures can be viewed as directed acyclic graphs. A node in a feature structure comprises a set of attributes whose values can be feature structures again. Nodes are associated with types, and atomic values are attributeless nodes distinguished by their type. Instead of unique instances of values everywhere, references can be used to establish value instance identity. Feature structures are usually displayed as attribute-value matrices or as nested symbolic expressions.

Unification is the key operation by which feature structures can be merged into a more informative feature structure. Unification of feature structures can also fail, which means that the information in them is mutually incompatible. Depending on the flavor of the processing logic, unification can be monotonic (i.e., information-preserving), or it can allow inheritance of default values and their overriding. In either case, information in a model can be efficiently shared and reused by means of inheritance hierarchies defined on the feature structure types.

Morphological models of this kind are typically formulated as logic programs, and unification is used to solve the system of constraints imposed by the model. Advantages of this approach include better abstraction possibilities for developing a morphological grammar as well as elimination of redundant information from it.

However, morphological models implemented in DATR can, under certain assumptions, be converted to finite-state machines and are thus formally equivalent to them in the range of morphological phenomena they can describe [11]. Interestingly, one-level phonology [56] formulating phonological constraints as logic expressions can be compiled into finite-state automata, which can then be intersected with morphological transducers to exclude any disturbing phonologically invalid surface strings [cf. 57, 53]

Unification-based models have been implemented for Russian [58], Czech [59], Slovene [53], Persian [60], Hebrew [61], Arabic [62, 63], and other languages. Some rely on DATR; some adopt, adapt, or develop other unification engines.

1.3.4. Functional Morphology

This group of morphological models includes not only the ones following the methodology of functional morphology [64], but even those related to it, such as morphological resource grammars of Grammatical Framework [65]. Functional morphology defines its models using principles of functional programming and type theory. It treats morphological operations and processes as pure mathematical functions and organizes the linguistic as well as abstract elements of a model into distinct types of values and type classes.

Though functional morphology is not limited to modeling particular types of morphologies in human languages, it is especially useful for fusional morphologies. Linguistic notions like paradigms, rules and exceptions, grammatical categories and parameters, lexemes, morphemes, and morphs can be represented intuitively and succinctly in this approach. Designing a morphological system in an accurate and elegant way is encouraged by the computational setting, which supports logical decoupling of subproblems and reinforces the semantic structure of a program by strong type checking.

Functional morphology implementations are intended to be reused as programming libraries capable of handling the complete morphology of a language and to be incorporated into various kinds of applications. Morphological parsing is just one usage of the system, the others being morphological generation, lexicon browsing, and so on. Next to parsing (1.2), we can describe inflection I, derivation D, and lookup L as functions of these generic types:

A functional morphology model can be compiled into finite-state transducers if needed, but can also be used interactively in an interpreted mode, for instance. Computation within a model may exploit lazy evaluation and employ alternative methods of efficient parsing, lookup, and so on [see 66, 12].

Many functional morphology implementations are embedded in a general-purpose programming language, which gives programmers more freedom with advanced programming techniques and allows them to develop full-featured, real-world applications for their models. The Zen toolkit for Sanskrit morphology [67, 68] is written in OCaml. It influenced the functional morphology framework [64] in Haskell, with which morphologies of Latin, Swedish, Spanish, Urdu [69], and other languages have been implemented.

In Haskell, in particular, developers can take advantage of its syntactic flexibility and design their own notation for the functional constructs that model the given problem. The notation then constitutes a so-called domain-specific embedded language, which makes programming even more fun. Figure 1–2 illustrates how the ElixirFM implementation of Arabic morphology [12, 17] captures the structure of words and defines the lexicon. Despite the entries being most informative, their format is simply similar to that found in printed dictionaries. Operators like >|, |<, |<< and labels like verb are just infix functions; patterns and affixes like FaCY, FCI, At are data constructors.

Figure 1-2

Figure 1-2. Excerpt from the ElixirFM lexicon and a layout generated from it. The source code of entries nested under the d r y root is shown in monospace font. Note the custom notation and the economy yet informativeness of the declaration

Even without the options provided by general-purpose programming languages, functional morphology models achieve high levels of abstraction. Morphological grammars in Grammatical Framework [65] can be extended with descriptions of the syntax and semantics of a language. Grammatical Framework itself supports multilinguality, and models of more than a dozen languages are available in it as open-source software [70, 71].

Grammars in the OpenCCG project [72] can be viewed as functional models, too. Their formalism discerns declarations of features, categories, and families that provide type- system-like means for representing structured values and inheritance hierarchies on them. The grammars leverage heavily the functionality to define parametrized macros to minimize redundancy in the model and make required generalizations. Expansion of macros in the source code has effects similar to inlining of functions. The original text of the grammar is reduced to associations between word forms and their morphosyntactic and lexical properties.

1.3.5. Morphology Induction

We have focused on finding the structure of words in diverse languages supposing we know what we are looking for. We have not considered the problem of discovering and inducing word structure without the human insight (i.e., in an unsupervised or semi-supervised manner). The motivation for such approaches lies in the fact that for many languages, linguistic expertise might be unavailable or limited, and implementations adequate to a purpose may not exist at all. Automated acquisition of morphological and lexical information, even if not perfect, can be reused for bootstrapping and improving the classical morphological models, too.

Let us skim over the directions of research in this domain. In the studies by Hammarström [73] and Goldsmith [74], the literature on unsupervised learning of morphology is reviewed in detail. Hammarström divides the numerous approaches into three main groups. Some works compare and cluster words based on their similarity according to miscellaneous metrics [75, 76, 77, 78]; others try to identify the prominent features of word forms distinguishing them from the unrelated ones. Most of the published approaches cast morphology induction as the problem of word boundary and morpheme boundary detection, sometimes acquiring also lexicons and paradigms [79, 80, 81, 82, 83].7

There are several challenging issues about deducing word structure just from the forms and their context. They are caused by ambiguity [76] and irregularity [75] in morphology, as well as by orthographic and phonological alternations [85] and nonlinear morphological processes [86, 87].

In order to improve the chances of statistical inference, parallel learning of morphologies for multiple languages is proposed by Snyder and Barzilay [88], resulting in discovery of abstract morphemes. The discriminative log-linear model of Poon, Cherry, and Toutanova [89] enhances its generalization options by employing overlapping contextual features when making segmentation decisions [cf. 90].

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