mathematics

Lexical function

Lexical function is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Lexical function rather than just read about it. In short: A lexical function (LF) is a tool developed within Meaning-Text Theory for the description and systematization of semantic relationships, specifically collocations and lexical derivation, between particular lexical units (LUs) of a language. LFs are also used in the construction of technical lexica (Explanatory Combinatorial Dictionaries) and as abstract nodes in certain types of syntactic representation.

Key takeaways

Lexical function belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Lexical function to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Lexical function from memory before moving on to harder problems.

Reference excerpt

A lexical function (LF) is a tool developed within Meaning-Text Theory for the description and systematization of semantic relationships, specifically collocations and lexical derivation, between particular lexical units (LUs) of a language. LFs are also used in the construction of technical lexica (Explanatory Combinatorial Dictionaries) and as abstract nodes in certain types of syntactic representation. Basically, an LF is a function ƒ( ) representing a correspondence ƒ that associates a set ƒ(L) of lexical expressions with an LU L; in f(L), L is the keyword of ƒ, and ƒ(L) = {L´i} is ƒ’s value. Detailed discussions of Lexical Functions are found in Žolkovskij & Mel’čuk 1967, Mel’čuk 1974, 1996, 1998, 2003, 2007, and Wanner (ed.) 1996; analysis of the most frequent type of lexical functions—verb-noun collocations—can be found in Gelbukh & Kolesnikova 2013.

Standard Lexical Functions Standard LFs form a proper subset of normal LFs. A normal LF ƒ is called Standard if and only if it satisfies both following conditions: 1. Broadness of the domain of ƒ: ƒ is defined for a relatively large number of keywords; 2. Diversity of the range of ƒ: ƒ has a relatively large number of expressions as elements of its possible values and these expressions are more or less equitably distributed between different keywords. Normal LFs that do not satisfy both Conditions 1 and 2, on the one hand, and degenerate LFs, on the other, are called Non-Standard. An example of a Non-Standard LF is the meaning ‘without addition of dairy product’. It has two expressions in English, a phraseological one—BLACK (with COFFEE: black coffee), and a free one—WITHOUT MILK (tea without milk is not *black tea). This meaning fails Condition 1: it is too specific and applicable only to one beverage. It thus corresponds to a Non-Standard LF.

Simple Standard LFs 1. Syn [Lat. synonymum] = synonym.

Syn(helicopter) = copter, chopper Syn(telephoneV) = phoneV

2. Anti [Lat. antonymum] = antonym. 3. Convijk [Lat. conversivum] = conversive.

This LF returns for L an LU L´ with the same meaning as L but with its Deep Syntactic Actants (roughly, syntactic arguments) i, j and k permuted —for example, the DSyntAs k, i and j of L are permuted in L´ such that [i→k, j→i, and k→j]. Conv21(include) = belong Conv231⊃(opinion) = reputation Conv21(behind) = in front of Conv21(precede) = follow

4. Gener [Lat. genus] = the closest generic concept for L.

The value of this LF must appear in one of the following two constructions: 1) ‘Gener(L)−ATTR→DER(L)’ = ‘L’ [where DER is any DSynt-derivative, see 6–9 below]; or 2) L, X1, X2, ..., Xn and other (kinds of) Gener(L). Gener(republic) = state [republican state = republic] Gener(liquidN) = substance [liquidA substance = liquidN] Gener(arrestN) = reprisals [arrests and other (kinds of) reprisals]

5. Figur [Lat. figuraliter ‘figuratively’] = standard received metaphor for L.

Figur(fog) = wall [wall of fog ≈ fog] Figur(rain) = curtain [curtain of rain ≈ rain] Figur(remorse) = pangs [pangs of remorse ≈ remorse]

6. S0 = Substantival, output N having a congruent meaning to L (which can be of any part of speech except N):

S0(analyze) = analysis

7. A0 = Adjectival, output A having a congruent meaning to L (which can be of any part of speech except A):

A0(city) = urban

8. V0 = Verbal, output V having a congruent meaning to L (which can be of any part of speech except V):

V0(analysis) = analyze

9. Adv0 = Adverbial, output Adv having a congruent meaning to L (which can be of any part of speech except Adv):

Adv0(followV [N]) = after [N]

10. Si = standard name of the i-th (Deep-Syntactic) actant of L.

For the verb TEACH: ‘Person X1 teaches subject Y2 to people Z3’ S1(teach) = teacher S2(teach) = subject/matter [in high school] S3(teach) = pupil

For the noun LETTER: ‘Letter by person X to person Y about Z’ S1(letter) = author, sender [of the letter] S2(letter) = addressee [of the letter] S3(letter) = contents [of the letter]

11. Sinstr = standard name of the instrument used in the situation denoted by L.

Sinstr⊃(shoot) = firearm Sinstr(murderV,N) = murder weapon

12. Smed = standard name of the means used to bring about the situation denoted by L.

Smed⊃(shoot) = ammunition

13. Smod = standard name of the mode through which the situation denoted by L is realized.

Smod(consider [an issue]) = approach [I consider this issue ... ~ My approach to this issue ...]

14. Sloc = standard name of the location where the situation denoted by L is realized.

Sloc(fightV [two armies]) = battlefield Sloc(war) = theater (of war)

15. Sres = standard name of the result of the situation denoted by L.

Sres⊃(learn) = knowledge, skills Sres⊃(explosion) = shockwave Sres⊃(copyV) = copyN, reproduction

16. Ablei [Lat. habilis ‘able, manageable’] = determining property of the i-th potential DSyntA of L (‘such that it can L easily’/‘such that it can be L-ed easily’):

Able1(cryV) = tearful Able1(vary) = variable Able2(prove) = provable Able2(trustV) = trustworthy

17. Quali [Lat. qualitas] = determining property of the i-th probable DSynt-actant of L (‘such that it is predisposed to L’/‘such that it is predisposed to be L-ed’):

Qual1(cryV/N) = sad Qual1(laughV/N) = cheerful Qual2(doubtV/N) = implausible Qual2(laughV/N) = awkward, absurd

18. Ai = determining property of the i-th DSyntA of L from the viewpoint of its role in the situation ‘L’.

A1 is semantically roughly equivalent to an active participle (≈ ‘which is L-ing’), and A2 to a passive participle (≈ ‘which is being L-ed’): A1(anger) = in [anger] //angry A1(speed) = with [a speed of ...] A2(analyze) = //under analysis A2(conduct [an orchestra])= //under the baton [of N]

19. Advi = the determining property of the action by the i-th DSyntA of L from the viewpoint of the role of the DSyntAi of L in the situation denoted by L.

Adv1 is semantically roughly equivalent to an active verbal adverb (≈ ‘while L-ing’), and Adv2, to a passive verbal adverb (≈ ‘while being L-ed’): Adv1(anger) = with [~] //angrily Adv1(decreaseN,V) = //down [… a decrease of 2.7% = ... down 2.7%.] Adv2(applause) = to [the ~] Adv2(bombard) = //under bombardment [They came under heavy bombardment.]

20. Imper [Lat. imperāre ‘[to] command’] = imperative expression meaning ‘do L!’

Imper(shoot) = Fire! Imper(speak low) = Shhh! Imper(stop [to a horse]) = Whoa!

21. Result [Lat. resultāre ‘[to] result’] = ‘[to] be the expected result of L’:

Result(buyV) = ownV Result(lie down) = be lying Result(have learnt) = know [how], have the necessary skills

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Lexical function

Start with the simplest possible case. Write down what Lexical function claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Lexical function before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Lexical function ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Lexical function

In research: Lexical function appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Lexical function in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Lexical function is common in secondary-school and first-year university syllabi. It links to neighbouring topics Lexicography, Meaning–text theory, Semantics, so understanding it makes those chapters shorter.
In everyday life: Look for Lexical function outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Lexical function in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Lexical function means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Lexical function out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Lexical function in simple terms?

Why does Lexical function matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Lexical function?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Lexical function.