Neuro-cognitive and psychological linguistics present important area of multidisciplinary research. In this paper we have described some possible applications of mathematical methods to neuro-cognitive linguistics. In neuro-cognitive study of language, neural architecture and neuropsychological mechanism of verbal cognition are basis of a vector–based modeling. A comparison of human mental space to a vector space is an effective way of analyzing of human semantic vocabulary, mental representations and rules of clustering and mapping in typologically different languages. Euclidean and non-Euclidean spaces can be applied for a description of human semantic vocabulary and high order structures reflecting internal and external features of object and action (event). Vector analysis of word meaning and basic syntax structures offers new methodological opportunities to interpret effect of semantic and pragmatic forces at morphology and syntax levels. Non-linear and metaphoric transformations present specific complex phenomenon to be described in 3D and other N-dimensional spaces in the framework of quantum semantics. Keywords: Mental mapping, human mental lexicon, embodied and symbolic cognition, verbal cognition, semantic space, scalar, vector space, mental transformation, semantic gravity.

1. 1
Verbal cognition: vector
space analysis
Chuluundorj. B
University of the Humanities, Mongolia
THE 11TH INTERNATIONAL
CONGRESS OF MONGOLISTS
ULAANBAATAR, 2016

2. Quantum brain – Quantum mind
Brain energy transmission – wave/particle duality
Human mental space – quantum semantic space
Deep structures – Mental structures
(Chomsky. N 2000. New horizons in the study
of language and mind. Cambridge)
2

3. Mental lexicon – semantic organization of vocabulary –
human semantic memory
Research question:
Universal principles of mental lexicon – embedding in neural
associative sets
3

4. 4

5. 5

6. qEEG and ERP
(quantitative electro-encephalo-graphy and event related potentials)
Assess: amount, time, frequency, localization of brain
activation and behavioral responses during verbal
thinking
Assumptions:
 Connection of different classes of words with different
regions of the brain
 Neural networks – different classes of words
N – static features
V – dynamic features
Open class of words
Closed class of words
6

7. 7
Brain electric waves involved in verbal thinking:
P300 – word and object recognition, working memory,
semantic congruity, decision making, novelty processing,
lie detection
P600 – word and semantic memory, syntactic congruity
N100 – cognitive flexibility, stimuli matching, expectancy
N200 - word and object recognition, semantic congruity,
cognitive inhibition
N400 – semantic congruity, semantic memory, word
decision, comprehension
P200 – working memory, verbal memory

8. 8Some examples from our study:
Raw qEEG data

9. 9
Word recognition
“Алим” (correct word)
“Лийр” (close meaning)
“Aяга” (distant meaning)

10. 10
Correct word Close meaning Distant meaning
Some results from our study:
P300 wave in brain mapping
Broca’s
expressive
area
Wernicke’s
perceptive
area
Broca’s
area
Wernicke’s
area
Broca’s
area
Wernicke’s
area

11. 11
Correct word Close meaning Distant meaning
Conclusion:
P300 wave in brain mapping
Word processing & expression - active in distant word recognition
Broca’s
expressive
area
Wernicke’s
perceptive
area
Broca’s
area
Wernicke’s
area
Broca’s
area
Wernicke’s
area

12. 12
Correct word Close meaning Distant meaning
Some results from our study:
N400 wave in brain mapping
Broca’s
expressive
area
Wernicke’s
perceptive
area
Broca’s
area
Wernicke’s
area
Broca’s
area
Wernicke’s
area

13. 13
Correct word Close meaning Distant meaning
Some results from our study:
N400 wave in brain mapping

14. 14
Correct word Close meaning Distant meaning
Conclusion:
N400 wave in brain mapping
Confusion by word’s close meaning activates frontal area
Broca’s
expressive
area
Wernicke’s
perceptive
area
Broca’s
area
Wernicke’s
area
Broca’s
area
Wernicke’s
area

15. 15Some results from our study:
Response time (behavioral data)

16.  Correct and distant noun meanings activated Broca’s area,
 Close noun activated frontal lobe (confusing noun)
16Some results from our study:
NOUN: max power (μV)
“Шил” correct meaning “Толь” close meaning “Арал” distant meaning
Broca’s
expressive
area
Wernicke’s
perceptive
area
Broca’s
area
Wernicke’s
area
Broca’s
area
Wernicke’s
area

17.  Correct noun - processed fast in most areas,
 Close noun – fast in left temporal area,
 Distant noun – slow in most areas
17Some results from our study:
NOUN: Reaction Time (sec)
“Шил” correct meaning “Толь” close meaning “Арал” distant meaning
Broca’s
expressive
area
Wernicke’s
perceptive
area
Broca’s
area
Wernicke’s
area
Broca’s
area
Wernicke’s
area

18.  Correct verb meaning activated frontal,
 Close verb – right occipital,
 Distant verb – frontal, left parietal areas
18Some results from our study:
VERB: max power (μV)
“Дуулах” correct “Хѳгжимдѳх” close “Унтах” distant
Broca’s
expressive
area
Wernicke’s
perceptive
area
Broca’s
area
Wernicke’s
area
Broca’s
area
Wernicke’s
area

19.  Correct verb meaning – fastest in left parietal,
 Close verb – slow in most,
 Distant verb – fast in most, slow in temporal & frontal areas
19Some results from our study:
VERB: Reaction Time (sec)
“Дуулах” correct “Хѳгжимдѳх” close “Унтах” distant
Broca’s
expressive
area
Wernicke’s
perceptive
area
Broca’s
area
Wernicke’s
area
Broca’s
area
Wernicke’s
area

20. 20Some results from our study:
Noun and verb: P300 power
“Шил”
“Толь”
“Дуулах”
“Унтах” “Хѳгжимдѳх”
“Арал”
Broca’s expressive area
Wernicke’s perceptive area

21. 21Some results from our study:
Noun and verb: Reaction time (sec)
“Шил”
“Толь”
“Дуулах”
“Унтах” “Хѳгжимдѳх”
“Арал”
Broca’s expressive area
Wernicke’s perceptive area

22. 22
Vector-based interpretation
Lexicon, morphology (word value/meaning)→ 2𝐷
Human mental space - semantic space – metric space –
similarity, distance between words

23. Object, action (event) tectonics and its characteristics -
Sequence regularities - Neural recurrent networks
Research question:
Mental syntax primitives - Universality in mental mechanism
of blending
23

24. Assumptions
 Semantic relationships between nouns, verbs and
adjectives are a reflection of knowledge sequence
represented in prefrontal association cortex.
 Phrase structure rules are a reflection of knowledge
sequence in perisylvian pattern-associator networks.
24

25. Vector based interpretation:
Syntax, discourse (semantic/pragmatic values/forces) →
scalar 2D and vector 3D
25

26. Word
Sentence
Number processing is similar to syntactic processing.
In numeral grammar, some words combine additively - forty-
three (40+3), whereas others combine multiplicatively:
seven hundred (7x100).
(David, L., Naoch, S., & Aleah, 2013.
Estimating large number C37).
Complex numbers - Complex nouns
“Хар бал” (additively),
“Хар шөнө” (multiplicatively),
“Хар санаа” (multiplicatively)
26
structure - mental blending 40+3
7x100

27. Similar features of object (noun reference) – scalar
multiplication
“Шар, улаан, ногоон бөмбөлөг”
Same direction, but different distances (magnitude)
Main reason → intrinsic and extrinsic features differ in
terms of strength of the association
27

28. “Төмөр хаалгатай модон хашаа”
Same direction, but different magnitude – vector addition
28
𝑅 𝑥=𝐴 𝑥+𝐵𝑥
𝑅 𝑦=𝐴 𝑦+𝐵𝑦
Magnitude of resultant:
𝑅 = 𝑅 𝑥
2
+ 𝑅 𝑦
2
Direction of resultant:
𝜃 𝑅= 𝑡𝑎𝑛−1
𝑅 𝑦
𝑅 𝑥

29. Complex scalar field – perceptual geometry.
High diving – прыжок в воду.
Complex scalar field – vector dot or cross product
29

30. Semantic + Pragmatic values – Complex effect
Mental blending (mental syntax):
“хар цамц (black shirt)” – vector dot product (scalar)
“хар шөл (meat soup)”
“хар санаа (bad, hostile idea)” – vector cross
product (vector)
30

31. Non-linear thinking - Non-linearity in mental syntax
Superposition and semantic transformation - metaphor
Complex effect of semantic pragmatic forces – vector dot
product
ном
авах оноо
санаа
хар
31

32. ном (book) – weak cohesion, linear association
санаа (idea) – strong cohesion, non-linear association
засах no semantic change, linear
semantically transformed
булаалдах no semantic change
semantically transformed (linear)
a ball (linear)
a disease (non-linear)
32
авах
ширээ
(table)
catch

33. Complex effect of semantic/pragmatic forces - Vector cross
product – torque
“ширээ булаалдах (ширээ – албан тушаал)”
“толгой угаах (толгой-бодол санаа)”
33

34. Typologically different languages –
Coordinates of verbal cognition (perceptual geometry) –
mental superposition in multi-dimensional tensor space
“од харвах”
“звезда упала”
“а star is falling”
Mental superposition – a phenomenon related to human
verbal cognition and object of analysis in quantum
semantics
34

35. Conclusions
 Vector analysis method in combination with
experimental study is a powerful tool for modeling of
localization of different classes of words in semantic
memory, and of connections of these classes with
different regions of the brain.
 Interpretation of word sequences in vector space is an
effective way for analysis of basic rules which regulate
these sequences in typologically different languages.
35

36. References:
1. Chuluundorj, B. 2013. Mathematical Approaches to
Cognitive Linguistics. International Journal of Applied
Linguistics & English literature. Vol. 2 No.4. Australian
International Academic Centre. Australia
2. Chuluundorj, B. 2014. Vector-Based Approach to Verbal
Cognition. Global Journal of Human-Social Science: Arts &
Humanities – Psychology. Vol.14, Issue 3/1.0 Global
Journals Inc. USA.
3. Chuluundorj, B. 2016. Vector Field Analysis of Verbal
Structures. British Journal of Applied Science &
Technology 12(3): 1-7. Science Domain International. UK.
36

37. Thank you!
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