1 Introduction

Computational Linguistics or Natural Language Processing (NLP) is a significant and rapidly developing research area on the crossroads of linguistics and computer science. It deals with any issue, which involves human-computer interaction in a human (natural) language: speech recognition, information retrieval, question answering, opinion, sentiment and polarity identification, knowledge extraction, machine translation, among others.

The NLP fundamental challenges are ambiguity of language items and lexicon diversity. To combat these problems, various formal semantic concepts and models have been developed. In this article, we discuss one of these: the concept of lexical function. This formal tool was created, has been developed and implemented in order to assist in solving both challenges mentioned above.

To explain it informally, lexical function captures lexical, semantic, and syntactic features common to sufficiently big groups of words and phrases. The different types of lexical functions form a taxonomy allowing representing and classifying in a consistent way the variety of words and word combinations in a natural language.

In this article, we speak of what a lexical function is, briefly consider several types of lexical functions, illustrate and exemplify the lexical function typology using verbal lexical functions, which are probably most richly represented in natural languages, and discuss application and detection of lexical functions in language systems.

2 Lexical Function

Lexical function is a formalism proposed by Mel’čuk and Žolkovskij [²³] and exposed in detail in [²¹] to represent various relations among words. Originally, the concept of lexical function was created with the purpose to generalize typical lexical relations; however, it is often interpreted as a categorization of lexical items according to their lexical, semantic, and syntactic features [⁸].

A lexical function takes a word as input and outputs a set of words related to the input in a certain way on the paradigmatic or syntagmatic level. It is a function in the mathematical sense defined as a mapping from a word w₀ called the lexical function argument to the lexical function value, which is a set of words {w₁, w₂, … w_n} where each word w_i, 1 ≤ i ≤ n, has a particular (and the same) lexical relation with the argument w0; so using mathematical notation, lexical function (LF) is represented as LF(w₀) = {w₁, w₂, … w_n}.

Wanner [³⁴] states that lexical function is a concept, which can be used to systematically describe “institutionalized” lexical relations clarifying that “a lexical relation is institutionalized if it holds between two lexical units L₁ and L₂ and has the following characteristics: if L₁ is chosen to express a particular meaning M, its choice is predetermined by the relation of M to L₂ to such an extent that in case M and L₂ is given, the choice of L₁ is a language-specific automatism.”

Institutionalized lexical relations can be of two types: paradigmatic and syntagmatic. Paradigmatic relations are observed between lexical units within a lexicon (examples of paradigmatic relations are synonymy, antonymy, hypernymy, hyponymy, etc.) and syntagmatic relations hold between lexical units that co-occur in texts (make a decision, friendly attitude, rain cats and dogs).

Let us give some examples of institutionalized lexical relations:

In examples (1-3), the institutionalized lexical relations are paradigmatic and in examples (4-7), they are syntagmatic. The is-a relation in example (1), also known as hypernymy-hyponymy relation, is represented by the lexical function denominated Gener (from Lat. genus, category). Gener takes a word with a more specific meaning as its argument and outputs the word with a more generic meaning, so using the functional notation we get Gener(chair) = furniture.

The words in example (2) are related by means of nominalization of the verb, and this phenomenon is captured by the lexical function S0 (S is from Substantival): S0(laugh) = laughter. In the denomination of this function, two elements are present: the letter S which reflects the semantic aspect of the relation between laugh and laughter, and the number zero.

Numbers are employed in lexical function nomenclature to represent positions within the valency structure of the word, which is the lexical function value. These positions are called actants in the language model developed by Lucien Tesnière, the founder of the dependency grammar, see an explanation of dependency grammar and dependency parsing in [²⁵]. Actants are sometimes called participants of a situation in semantics and cognitive sciences, e.g. [¹⁰], and the typical term for an actant in natural language processing is semantic or thematic role [³⁰].

In the example of S0 given above, zero represents the fact that laughter is the name of the situation, therefore, information of its actants is irrelevant in the relation between the action verb laugh and the corresponding action noun laughter.

Another lexical function called IncepOper1 (from Latin incipere, begin, and operari, do) outputs a set of one or more verbs with the meaning ‘do, carry out, perform, experience’, so if its argument is laughter, IncepOper1 generates as its value the set {burst into, explode into, break into}, i.e. IncepOper1(laughter) = {burst into, explode into, break into}; 1 reflects the fact that the first actant (agent) of the situation laughter has the syntactic function of subject in sentences and clauses where laugher is used in combination with its IncepOper1 verb, e.g. It looked so funny that we burst into laughter.

Therefore, IncepOper1 represents the semantic and syntactic pattern ‘Agent performs the action denoted by the noun’. In the next section, we discuss various types of lexical functions.

3 Types of Lexical Functions

In this section, we consider three typologies of lexical functions. The first one categorizes lexical functions depending on the vertical or horizontal orientation of relation among words; with respect to this feature, paradigmatic and syntagmatic lexical functions are distinguished as explained in Section 2.

The second typology classifies lexical functions depending on the complexity of their internal semantic structure: according to this criterion, lexical functions can be simple and complex.

The third typology distinguishes lexical functions considering if they are applicable to broad or narrow word classes: here lexical functions can be standard and non-standard.

Semantic relations between words can be observed on the vertical and horizontal axes. In Section 2 we described the relations informally, i.e., relations between words within the lexicon are paradigmatic (synonymy, antonymy, hypernymy, hyponymy, etc.), and relations between words in utterances are syntagmatic (dependency, constituency, syntactic functions, semantic roles, etc.).

Formally, Murphy [²⁴] defines paradigmatic relation as the relation between words, which form a paradigm. For example, a semantic paradigm is a set of words belonging to:

“the same grammatical category that share some semantic characteristics in common, but fail to share others.

So, for example, the set of basic color terms forms a paradigm whose members are adjectives (or nouns), each referring to a different section of the color spectrum.

Not all paradigms are semantically defined, of course. Inflectional paradigms, for instance, include the possible variations of a lexical item in some inflectional category, such as number.

So, a morphological paradigmatic relation exists between child and children. Paradigmatically related words are, to some degree, grammatically substitutable for each other.

For example, blue, black, and any other member of the color paradigm can sensibly and grammatically occur in the phrase a chair. In this way, paradigmatic relations stand in contrast to syntagmatic relations, which are relations between words that go together in a syntactic structure. For example, we can speak of a syntagmatic relation between eat and dinner.”

Concerning syntagmatic relation, it is:

“also termed combinational relation, which exists typically, though not necessarily, between expressions of different grammatical categories that can be put together in grammatically well-formed combinations or constructions…, say, between nouns and adjectives, verbs and nouns, or verbs and adverbs etc.” [⁴].

Paradigmatic lexical functions represent paradigmatic relations, and syntagmatic relations are formalized by syntagmatic lexical functions.

In the example in Section 2, S0 is a paradigmatic lexical function, and IncepOper1 is a syntagmatic lexical function.

Mel’čuk [²¹] defines 27 paradigmatic and 37 syntagmatic lexical functions.

We give examples of paradigmatic lexical functions in Table 1, and in Tables 2-6 we included syntagmatic lexical functions whose values are verbs and whose arguments are nouns. For explanations and examples in these tables, we used [², ⁶-⁸, ¹¹, ¹⁴, ¹⁷, ¹⁹, ²⁰-²², ²⁹, ³²].

It can be observed in Tables 2-6 that some lexical functions represent one simple meaning or a single semantic unit, such functions are called simple (Oper, Func, Labor).

There are lexical functions that formalize combinations of unitary meanings, they are called complex lexical functions (IncepOper, CausFunc). The two categories of simple and complex lexical functions constitute the second typology used to describe and classify lexical functions.

The third typology of lexical functions, as we mentioned in the beginning of this section, considers if lexical functions are applicable to broad or narrow word classes: here standard and non-standard lexical functions are distinguished.

Lexical functions in Tables 1-2 are standard; an example of a non-standard lexical function is black coffee, where black is used in the meaning ‘without dairy product’, and such meaning is applicable only to the narrow class of beverages [²¹].

4 Detection of Lexical Functions

Lexical functions represent common semantic and syntactic patterns of certain word classes and can aid in many tasks of natural language processing, lexical and syntactic disambiguation being the most fundamental one among them. In this section, we review some research works on automatic detection of lexical functions in texts.

Wanner [³⁴] suggested to regard the task of lexical function automatic detection as classifying collocations according to the lexical function typology and applied the nearest neighbor technique to resolve it. The experiments were made on two groups of Spanish verb-noun collocations: one with emotion nouns and the other with field-independent nouns. The lexical function learning was done using hypernym information from the Spanish part of EuroWordNet [³³]. The highest F-measure achieved for field-independent collocations in the experiments was 0.76 for CausFunc0. An average F-measure of about 0.70 was obtained over all experiments.

The same average result was shown on more data in [³⁵] over four learning methods: nearest neighbor, Naïve Bayes, tree-augmented network, and ID3-algorithm. In this work, the best F-measure on field-independent verb-noun collocations (0.76) was achieved by ID3-algorithm.

Archer [¹] experimented on extracting collocations of the adjectival/adverbial lexical function Magn (from Lat. magnus, big, great. Magn values are intensifiers, for example: Magn(rain) = heavy, Magn(temperature) = high, Magn(storm) = sever, Magn(to weep) = bitterly. The research was done on French material. The reported result is 83% of precision. However, the process of extracting Magn collocations was semi-automatic and included human intervention, which improved the results significantly.

Ramos et al. [²⁸] proposed an algorithm to retrieve collocations of the type ‘support verb + object’ from the semantically annotated FrameNet corpus of examples [³¹]. Their interest was to see whether the collocations they extracted were of Opern. (in this article we denominated this function as Operi).

The authors assumed that certain syntactic, semantic, and collocation annotations in the FrameNet corpus could signal that a particular collocation belonged to Opern. The proposed algorithm was tested on 208 instances and showed an accuracy of 76%.

In our previous research, for automatic detection of lexical functions, we used a dataset of Spanish verb-noun collocations [¹⁵] annotated manually with lexical functions and the Spanish WordNet version 2000611 ([³³], Spanish WordNet online^fn) senses.

The dataset was submitted to 66 supervised machine learning techniques implemented in Weka 3-6-12-x64^fn to classify each sample in the dataset set as belonging or not to a particular lexical function (binary yes-no classification) using 10-fold cross validation. Table 7 presents the best results for eight lexical functions in terms of F1-measure indicating what algorithm achieved this result.

5 Application of Lexical Functions

Lexical functions possess a number of important properties, which make them an effective tool for natural language processing:

Lexical functions can be used to resolve syntactic ambiguity. In such cases, syntactically identical phrases are characterized by different lexical functions, which serve as a tool for disambiguation. For example, consider two phrases: support of the parliament and support of the president. In the first phrase support is the object, but in the second phrase support functions syntactically as the subject and semantically as the agent.

The surface phrase structure in both cases is identical: support + of + noun; this fact causes syntactic ambiguity and due to it both phrases may have both meanings: ‘support given by the parliament (by the president)’, which syntactically is the subject interpretation with the agentive syntactic relation between support and the subordinated noun, and ‘support given to the parliament (to the president)’, which syntactically is the object interpretation with the first completive syntactic relation between support and the subordinated noun. This type of ambiguity is often extremely difficult to resolve, even within a broad context. Lexical function’s verbs can be successfully used to disambiguate such phrases because they impose strong limitations on the syntactic behavior of their arguments in texts. Now let us view the same phrases in a broader context.

The first example is The president spoke in support of the parliament, where the verb speak in is Oper1 of the noun support, i.e., Oper1(support) = speak in. Oper1 represents the pattern ‘Agent performs w₀’ (where w₀ is the argument of Oper1), so the president is interpreted as the agent, and support as the object. Therefore, The president spoke in support of the parliament can only be interpreted as describing the support given to the parliament, with parliament having the syntactic function of the complement of support.

On the other hand, verbs of Oper2 participate in another pattern: ‘Patient undergoes w₀’. So Oper2 verb is by definition a verb whose grammatical subject represents the patient of w₀ and in the utterance The president enjoyed (Oper2) the support of the parliament, the phrase the support of the parliament implies the support given to the president by the parliament, with parliament having the syntactic function of the agentive dependent of the noun support.

Lexical ambiguity is another issue in natural language processing which lexical functions can help to resolve. For instance, the Russian expression provodit’ razlichie and its direct English equivalent to draw a distinction can be analyzed as composed of Oper1 + its argument. Taken in isolation, the Russian and the English verbs are extremely polysemous, and choosing the right sense for the given sentence becomes a formidable problem. Provodit’, for example, has half a dozen senses ranging from ‘spend’ via ‘perform’ to ‘see off’, while draw is a polysemous verb for which dictionaries list 50 or more senses.

However, in both expressions the mutual lexical attraction between the argument of the lexical function and its value is so strong that, once the fact of their co-occurrence is established by the parser, we can safely ignore all other meanings and keep for further processing only the one relevant here (Oper1).

Computer-assisted language learning is another area where lexical functions can be useful. It is a well-known fact in second language teaching practice that collocations are difficult to master by learners, so learner’s speech often sounds unnatural due to errors in restricted lexical co-occurrence. To deal with this issue, a lexical function dictionary can be used whose advantage is that it includes the linguistic material on word combinations which is absent in word dictionaries.

Due to semantic universality and cross-linguistic idiomaticity of lexical functions, they can be employed in machine translation. These characteristics make lexical functions an ideal tool for selecting idiomatic translations of set expressions in a machine translation system. They took a walk after lunch is translated into Spanish by Google Translate as Tomaron un paseo después del almuerzo. In English, Oper1(walk) = take, but in Spanish Oper1 of the argument paseo (English walk) is dar (English lit. give). So Oper1(paseo) = dar, however, the system translated the collocation take a walk literally as tomar paseo, since take is literally tomar in Spanish. Therefore, a module that annotates word combinations with lexical functions can be included in any machine translation system to improve the quality of translation of collocations and idiomatic expressions.

Probably, the area in which lexical functions are used the most is lexicography: in lexicons and dictionaries of collocations. Automatic semantic analysis of texts with high precision usually requires the use of semantically annotated lexical resources, since the approaches based on word counts in models of distributional semantics do not produce high quality and meaningful interpretation yet. Since lexical functions have the power to generalize and represent combinability of a lexical unit with other lexical units, a lexicon organized with respect to various lexical functions of each entry can serve as a valuable resource for any task of automatic language processing in which semantic procedures are performed on a shallow or deep level.

Syntagmatic lexical functions can serve as a typology of collocations organizing and structuring collocation dictionaries because lexical functions categorize diverse restricted word co-occurrences.

An example of such a collocation dictionary is DiCE, a Spanish collocation dictionary accessible online^fn. The DiCE includes lexical units, that is, word senses (not concepts or synsets as in WordNet^fn) in the domain of sentiment and emotion, and their collocations labeled with lexical functions, see an example entry of ilusión (illusion) in Fig. 1.

Fig. 1 Ilusión entry in DiCE 

Speaking of simple lexicons as sets of entries for every word (lexical unit), lexical functions can be associated with entries showing the types of phrases a given word can form with other words. Lareau et al. [¹⁶] give an example of the entry for the noun attention: the entry includes its argument structure and lexical functions (definitions of lexical functions given in this example and not explained in Section 3 can be consulted in [²¹]):

Attention [of X to Y]

A similar kind of a lexicon is presented in [⁹]. It was compiled manually for French and is called the French Lexical Network (fr-LN). In this resource, each entry represents one sense of a word, i.e., lexical unit, and the entries (vertices of the graph) are connected by arcs labeled with lexical functions. The corresponding English Lexical Network (en-LN) was generated from WordNet 3.0^fn [⁵].

There are four differences between WordNet and en-LN: first, WordNet is a graph of synsets, and en-LN is a graph of word senses (lexical units); second, the WordNet graph is partitioned based on four parts of speech (noun, verb, adjective, adverb) and the en-LN is not partitioned; third, the WordNet graph is organized hierarchically from top to bottom, and the en-LN has multidimensional organization; forth, WordNet is chiefly based on hypernym-hyponym relation between synsets and the en-LN is based on lexical function relations between lexical units.

Gader et al. [⁹] used 12 lexical functions to label lexical relations used in WordNet: seven lexical functions explained in Section 3 (Syn_∩, Anti_∩, Gener, Mult, Sing, A2, Caus), four lexical functions defined in [²⁶] as Cf, Hypo, Holo, Mero, and one non-standard lexical function (Unspecified derivative). Continuing the work in [⁹], Polguère [²⁷] presents an example of an entry in the French Lexical Network (Fig. 2).

Fig. 2 Hold up I entry in the French Lexical Network 

Applying the principles of the fr-LN, Ingrosso and Polguère [¹²] developed a lexical system of English chemical terms, see an example entry in Fig. 3. Jousse et al. [¹³] designed and compiled the DiCoInfo, Dictionnaire fondamental de l’informatique et de l’Internet, an online specialized database of collocations in the domain of computing and the Internet^fn. The dictionary allows for search of a collocate or collocates of a given word to convey a required meaning in the process of text generation. The dictionary is structured according to syntagmatic lexical functions used for representing collocations, see examples in Tables 2-6.

Fig. 3 Catalysis I.1 entry in a lexical system of English chemical terms 

The authors grouped the original lexical functions of [²¹] in several larger semantic classes such as ‘use’, ‘create’, ‘place somewhere’, among others. Table 8 gives examples of some entries in the DiCoInfo.

Another example of a lexicon based on lexical functions is DiCoEnviro, a lexicon of words related to the domain of environment described in [¹⁸]. Paradigmatic lexical functions of the word pollute in its different senses shown in Table 9 give a glimpse of this lexical resource.

Lexical functions are a convenient tool to apply in interfaces between a lexicon and an ontology [³] as well as in semantic networks [⁸]. In semantic networks, words are nodes and lexical functions are labels attached to the arcs, see Figs 4, 5 with an example of semantic relations for the nouns analysis and habit.

Fig. 4 Semantic network for the noun analysis 

Fig. 5 Semantic network for the noun habit 

Lexical functions can be applied in text generation using semantic and syntactic patterns corresponding to them creating relevant, grammatically correct and naturally sounded word combinations, see examples Table 7. The lexical function patterns can be employed also in other natural language processing tasks: parsing, semantic role tagging, text analysis, etc.

6 Conclusions

In this article, we discussed lexical functions [²¹], their identification in texts and usage in natural language processing. Lexical function is a formal representation of lexical relations on both paradigmatic and syntagmatic levels.

Paradigmatic lexical functions capture in a systematic way the fundamental relations between word senses (lexical units) such as synonymy and antonymy of various types, hypernymy, hyponymy, derivational relations, among others.

Syntagmatic lexical functions deal with a linguistic phenomenon, which has been an issue in natural language processing for many years, namely, restricted lexical co-occurrence or collocation. These lexical functions categorize collocations into classes depending on their semantic and syntactic features as well as predicate-argument structure, which allows for generalizations in such a diverse part of lexicon as collocations.

Therefore, the most common use of lexical functions is lexicography where words are arranged in semantic networks with lexical functions are relations among them. However, lexical functions serve as an effective instrument in resolving other issues: lexical and syntactic ambiguity, machine translation, second language acquisition, periphrasis. In future, we believe that lexical functions will find application on many other language tasks related to parsing, semantic role labelling, text analysis, generation and classification, among many others.