=Paper=
{{Paper
|id=Vol-1283/paper44
|storemode=property
|title=
Convention and Innovation in Social Networks
|pdfUrl=https://ceur-ws.org/Vol-1283/paper_44.pdf
|volume=Vol-1283
|dblpUrl=https://dblp.org/rec/conf/ecsi/Muhlenbernd14
}}
==
Convention and Innovation in Social Networks==
https://ceur-ws.org/Vol-1283/paper_44.pdf
Convention and Innovation in Social Networks
Roland Mühlenbernd
Eberhard Karls Universität Tübingen
Abstract. To depict the mechanisms that have enabled the emergence
of semantic meaning, philosophers and researchers particularly access a
game-theoretic model: the signaling game. In this article I will argue
that this model is also quite appropriate to analyze not only the emer-
gence of semantic meaning, but also semantic change. In other words,
signaling games might help to depict mechanisms of language change.
For that purpose the signaling game will be i) combined with innovative
reinforcement learning and ii) conducted repeatedly as simulation runs
in a multi-agent account, where agents are arranged in social network
structures: scale-free networks with small-world properties. The results
will give a deeper understanding of the role of environmental variables
that might promote semantic change or support solidity of semantic con-
ventions.
Keywords: signaling game, reinforcement learning, multi-agent account,
scale-free networks, small-world properties, mechanisms of language change
1 Introduction
“What are the mechanisms that can explain the emergence of semantic mean-
ing?” Philosophers have long been concerned with this question. Russell once
said: “[w]e can hardly suppose a parliament of hitherto speechless elders meet-
ing together and agreeing to call a cow a cow and a wolf a wolf.”[24]. With
this sentence Russell wanted to point to a particular paradox of the evolution of
human language: language (as a tool to make verbal agreements) is needed for
language (in form of semantic meaning) to emerge.
Lewis found a very elegant solution for this paradox: he showed that semantic
meaning can arise without previous agreements, but just by regularities in com-
municative behavior. He showed it with a game-theoretical model: the signaling
game [16]. This game basically models a communicative situation between a
speaker and a hearer, and just by playing this game repeatedly and using simple
update mechanisms to adjust subsequent behavior, both participants might fi-
nally agree on semantic conventions without making an overt verbal agreement
in advance [25]. In other words: semantic meaning can arise automatically and
“unconsciously” just by repeated communication and simple adaption mecha-
nisms;1 a signaling game is an elegant way to formalize these dynamics.
1
“Unconsciousness” of participants means here that they do not choose to use a
specific expression for an object, but rather learn it by optimizing behavior.
2 Roland Mühlenbernd
Apparently, quite similar mechanism can be assumed for language change,
or to be more precise: for semantic innovation, semantic shift and semantic loss.
Like we cannot assume that speechless elders made agreements to call a wolf
a “wolf”, we furthermore cannot assume that the people in the 1970s made a
public announcement to use the word “groovy” when they wanted to express that
something is really nice, and another announcement in the 1980s, that people
should not use this word anymore. Just as semantic meaning can emerge in an
unconscious and automatic way, in the same way, expressions arise, change their
meaning, or get lost. It seems to be plausible that a signaling game might also
be an appropriate model to explain general mechanisms of semantic change.
A number of studies came up to analyze how semantic meaning arises in
realistic population structures, by conducting multi-agent simulations: applying
repeated signaling games between connected agents placed in social network
structures, c.f. lattice structures [31, 18] and small-work networks [28, 20]. Next
to the signaling game, another line of research uses the so-called naming game
[26] to analyze the emergence of semantic conventions in realistic population
structures [27, 5]. It can be shown that both accounts imply similar mechanisms
and reveal similar resulting dynamics. However, as mentioned before, all these
studies analyze how semantic meaning ‘arises’, not how it ‘changes’.
Another line of research uses multi-agent simulations to analyze language
change in social network structures, but without applying signaling games or
similar models of communication [22, 14, 9]. In these studies agents i) do not
communicate, but just choose among (linguistic) variants they are aware of and
ii) make explicit decisions of what variant to use. Because of the first point
these studies somehow lack the quintessence of language change, namely that
it happens through repeated communication. Because of the second point these
studies let agents behave in a much too “conscious” way. Language change might
usually be the result of much more unconscious decisions and hidden dynamics.
In this study I use repeated signaling games in combination with an update
mechanism that depicts unconscious behavior of decision making. This mecha-
nism is called reinforcement learning [23]. Applying reinforcement learning on
repeated signaling games is not new, but in fact one of the most popular dy-
namics in this field [3, 4, 25]. What is new in this study is the fact that the
account is applied to analyze the change rather than the emergence of semantic
conventions. For that purpose signaling games and reinforcement learning will
be employed to conduct simulation experiments of communicating agents in so-
cial network structures with the goal to evaluate the environmental factors that
might or might not support semantic change or stability.
This article is divided in the following way: in Section 2 some basic notions of
repeated signaling games, reinforcement learning dynamics and network theory
will be introduced. Furthermore, I will discuss a noteworthy extension for rein-
forcement learning, called innovation [25, 1]. It can be shown that this additional
feature realizes an interesting interplay between stabilizing and renewing effects
[21]; and I will adopt it for my experiments, which are described and analyzed
in Section 3. A final conclusion will be presented in Section 4.
Convention and Innovation in Social Networks 3
2 Signaling Games, Learning and Networks
This section will give a coarse technical and theoretical background to under-
stand the important concepts of this article: the signaling game, reinforcement
learning with innovation, and some basic notions of network theory.
2.1 Signaling Games
A signaling game SG = h{S, R}, T, M, A, P r, U i is a game played between a
sender S and a receiver R. T is a set of information states, M is a set of messages
and A is a set of interpretation states (or actions). Pr(t) ∈ ∆(T )2 is a probability
distribution over T and describes the probability that an information state is
topic of communication. U : T × A → R is a utility function that basically
determines how well an interpretation state matches an information state.
Let us take a look at the simplest variant of the game where we have two
states, two messages and two actions: T = {t1 , t2 }, M = {m1 , m2 }, A = {a1 , a2 },
a flat probability distribution of P r(t) = 1/|T | ∀t ∈ T , and a simple utility func-
tion that gives a positive value if the interpretation state a matches the informa-
tion state t, marked by the same index: U (ti , aj ) = 1 iff i = j, else 0. Such a game
is played as follows: an information state t is chosen with prior probability P r3 ,
which the sender wants to communicate to the receiver by choosing a message m.
The receiver wants to decode this message by choosing an interpretation state a.
Communication is successful iff the information state matches the interpretation
state. In this study only a subset of all possible signaling games is considered,
which I call n × k-games, as defined in Definition 1.
Definition 1 (n × k-game). A n × k-game is a signaling game SG with:
1 if i = j
|T | = |A| = n, |M | = k, ∀t ∈ T : P r(t) = 1/|T | and U (ti , aj ) =
0 else
Note that messages are initially meaningless in this game, but meaningfulness
can arise from regularities in behavior. Behavior is here defined in terms of
strategies. A behavioral sender strategy is a function σ : T → ∆(M ), and a
behavioral receiver strategy is a function ρ : M → ∆(A). A behavioral strategy
can be interpreted as a single agent’s probabilistic choice.
Now, what circumstances can tell us that a message is attributed with a
meaning? The answer is: this can be indicated by the combination of sender
and receiver strategy, called strategy profile. A message has a meaning between
a sender and a receiver, if both use pure strategies that constitute a specific
isomorphic strategy profile. For the 2 × 2-game there are exactly 2 such strategy
profiles, as depicted in Figure 1. Here in profile L1 the message m1 has the
meaning of state t1 /a1 and message m2 has the meaning of state t2 /a2 . For
profile L2 it is exactly the other way around.
2
∆(X) : X → R denotes a probability distribution over random variable X.
3
Informally, the information state came to the sender’s mind. In game theory we say
that the state is chosen by an invisible participant, called nature N .
4 Roland Mühlenbernd
t1 m1 a1 t1 m1 a1
L1 : L2 :
t2 m2 a2 t2 m2 a2
Fig. 1. The two signaling systems of the 2 × 2-game.
Lewis called such strategy profiles signaling systems [16], which have in-
teresting properties. It can be shown that signaling systems i) ensure perfect
communication and maximal utility, ii) are Nash equilibria over expected util-
ities [7], and iii) are evolutionary stable states [29][12]. Furthermore, note that
the number of signaling systems increases strongly with the number of states
and/or messages: an n × k-game has k!/(k−n)! possible signaling systems.
At this point it is explained how semantic meaning can be expressed by
participants’ communicative behavior: a message has a meaning, if sender and
receiver communicate according to a signaling system. However, this does not
explain at all, how participants come to such a signaling system in the first place,
by expecting that messages are initially meaningless. To explore the paths that
might lead from a meaningless to a meaningful message, it is necessary to explore
the process that leads from participants’ arbitrary communicative behavior to a
behavior that constitutes a signaling system. Such a process can be simulated by
repeated signaling games, where the participants’ behavior is guided by update
dynamics. One popular dynamics is called reinforcement learning [3, 4, 25].
2.2 Reinforcement Learning and Innovation
Reinforcement learning can be captured by a simple model based on urns, also
known as Pólya urns [23]. An urn models a behavioral strategy, in the sense that
the probability of making a particular decision is proportional to the number of
balls in the urn that correspond to that choice. By adding or removing balls from
an urn after each access, an agent’s behavior is gradually adjusted. For signaling
games, the sender has an urn ft for each state t ∈ T , which contains balls for
different messages m ∈ M . The number of balls of type m in urn ft designated
with m(ft ), the overall number of balls in urn ft with |ft |. If the sender is faced
with a state t she draws a ball from urn ft and sends message m, if the ball
is of type m. The same holds in the same way for the receiver. The resulting
sender response rule σ and receiver response rule ρ is given in Equation 1 and
2, respectively.
m(ft ) a(fm )
σ(m|t) = (1) ρ(a|m) = (2)
|ft | |fm |
The learning dynamics is realized by changing the urn content dependent on the
communicative success. The standard account works as follows: if communication
via t, m and a is successful, the number of balls in urn ft is increased by α ∈ N
balls of type m. Similarly, for the receiver. In this way successful communicative
behavior is more probable to reappear in subsequent rounds.
Convention and Innovation in Social Networks 5
This mechanism can be intensified by lateral inhibition: if communication
via t, m and a is successful, not only will the number of ball type m in urn ft
be increased, but also will the number of all other ball types m0 ∈ M \ {m} be
decreased by γ ∈ N. Similarly, for the receiver. Franke and Jäger [10] introduced
the concept of lateral inhibition for reinforcement learning in signaling games
and showed that it leads the system more speedily towards pure strategies.
Furthermore, negative reinforcement can be used to punish unsuccessful be-
havior. It changes urn contents in the case of unsuccessful communication in
the following way: if communication via t, m and a is unsuccessful, the number
of balls in the sender’s urn ft is decreased by β ∈ N balls of type m; and the
number of balls in the receiver’s urn fm is decreased by β balls of type a.
Note that reinforcement learning might have the property to slow down the
learning effect: if the total number of balls in an urn increases over time, but
the rewarding value α is a fixed value, then the learning effect mitigates. A way
to prevent learning from slowing down is to keep the overall number of balls |f|
on a fixed value Ω by scaling the urn content appropriately after each round of
play. Such a setup is a variant of so-called Bush-Mosteller reinforcement [6].
All in all, a reinforcement learning setup for a signaling game can be captured
by RL = h(σ, ρ), α, β, γ, Ω, φi, where σ and ρ are the participants’ response rules,
α is the reward value, β the punishment value, γ the lateral inhibition value and
Ω the urn size. Finally, φ is a function that defines the initial urn settings.
With the goal to analyze issues of language change, a really interesting ad-
ditional feature for reinforcement learning is called innovation. The basic idea
stems from Skyrms [25] and works as follows: each sender urn contains, next to
the balls for each message, an additional ball type, which Skyrms calls black ball.
Whenever the sender draws a black ball from an urn, he sends a completely new
message that was never sent before. In other words, the sender invents a new
message. Further experiments with this setup were made for 2-players games [1]
as well as for multi-agent accounts [21].
The second study [21] used a reinforcement learning setup with negative re-
inforcement and lateral inhibition. In such a setup the black balls of the agents’
sender urns can increase and decrease in dependence of communicative success.
By naming the total number of an agent’s black balls her force of innovation,
the study revealed an interesting relationship between society-wide force of in-
novation and communicative success: increasing communicative success leads to
decreasing force of innovation, and vice versa.4 Note that this relationship be-
tween both values implies two things: i) once a population has learned one unique
signaling convention and reaches perfect communication, the force of innovation
has dropped to zero: the society has reached a stable state without any spirit of
innovation; ii) if the society contains multiple conventions and communication
is therefore not perfectly successful society-wide, the force of innovation has a
positive level and produces new strategies that might finally manifest as new
conventions; in other words: language change is possible to be realized.
4
It was shown for experiments with 3-agent populations that the force of innovation
and communicative success reveal a significant negative correlation.
6 Roland Mühlenbernd
2.3 Basic Notions of Network Theory
To ensure that a network structure resembles a realistic interaction structure
of human populations, it should have small-world properties; c.f. Jackson found
out that these properties show in the analysis of human friendship networks [13].
According to this line of studies, the essential two properties of small-world net-
works are i) a short characteristic path length, and ii) a high clustering coefficient
[30].5 Additionally, most often human networks display a third property, namely
to be scale-free: the frequency of agents with ever larger numbers of connections
roughly follows a power-law distribution. In this sense I consider a special kind
of a scale-free network, which is both scale-free and has small-world properties
[2]. This network type is constructed by a preferential attachment algorithm that
takes two parameters m that controls the network density, and p that controls
the clustering coefficient [11]. In my experiment I used a scale-free network with
500 nodes, m = 2 and p = .8, which ensures small-world properties.
A main goal of this work is to investigate the relationship between the change
of meaning and the structural properties of the network and its members. As
the experiments will show, there seems to be an explanatory value of network
properties that express an agent’s connectivity and embeddedness. In order to
capture these properties more adequately, suitable notions from social network
theory will be considered: degree centrality (DC) describes the local connectivity
of an agent, closeness centrality (CC) and betweenness centrality (BC) her global
centrality, and individual clustering (CL) her local embeddedness.5
As I will argue later, also the strength of ties between agents might play
an important role in language change. Easley and Kleinberg [8] showed that the
strength of a tie between two agents has basically a strong linear correlation with
the overlap of both agents’ neighborhoods. To keep things easy I will define the
strength of a tie by this neighborhood overlap. Furthermore, since my analysis
deals with agents rather than with ties between them, I calculate an agent’s ties
strength T S as the average strength value of all ties of this agent:
Definition 2 (Ties Strength). For a given network the ties strength of agent
n is defined as follows (where N (i) is the set of neighbors of agent i):
P N (n)∪N (m)
N (n)∩N (m)
m∈N (n)
T S(n) = (3)
|N (n)|
Note: the notions of DC, CC, BC, CL and T S describe static network properties
of an agent, since they do not change during a simulation run and are determined
by the network structure and the agent’s position inside it.
5
For the definition of these network properties I refer to Jackson’s Social and Eco-
nomic Networks [13], Chapter 2.
Convention and Innovation in Social Networks 7
Finally, as the experiments will show, agents in a social network agree on
signaling systems as groups, which constitute connected components 6 . Such a
group-wide signaling system is called a signaling convention (Definition 3).
Definition 3 (Signaling Convention). For a given network structure of agents
that play the repeated signaling game with their connected neighbors, a signaling
convention is a signaling system that is used by a group of agents that constitutes
a connected component of the network structure.
3 Simulating Language Change
A fascinating puzzle in the theory of language change is the threshold-problem[22]:
how can a new linguistic variant spread and reach a particular threshold of speak-
ers that enables to replace a concurrent old variant? To reach such a threshold
is rather improbable considering the facts that i) the new variant is expected to
be initially used by a minority and ii) the old variant is expected to be a society-
wide linguistic conventions that serves for perfect communication. Therefore,
sociolinguists expect that new variants mostly do not disseminate but remain
in small social groups, often with short durability [17]. Now, what enables new
variants in rare cases to spread and establish a new linguistic convention?
Some sociolinguists expect particular environmental patterns of the social
network structure to be source and engine for language change [17]. Their weak-
ties theory purports that new (innovative) variants i) emerge most often among
edges that constitute weak ties in the social network, and ii) disseminate via
central nodes. According to the theory, exactly the combination of weak ties and
central nodes supports new variants to overcome the threshold problem [17].
In my experiments agents in a social network communicate via signaling
games and update by innovative reinforcement learning. This leads to the effect
that i) multiple local conventions emerge (see c.f.[31, 18, 28, 20]), and ii) agents
invent new messages from time to time, since communication is not perfectly
successful in a society with multiple conventions and therefore the force of in-
novation stays on a positive level. As my experiments will show, while mostly
invented messages disappear as fast as they appear, from time to time new
variants can spread and realize new regional conventions. Therefore, I want to
analyze if particular structural features support emergence and spread of inno-
vation. Do the results support the weak-tie theory? Is it possible to detect other
network properties that support language change?
3.1 Experimental Settings
I conducted simulation runs of agents that are placed in a social network struc-
ture. Per simulation step the agents communicate by playing a signaling game
with each of their direct neighbors. They update their behavior by innovative
reinforcement learning. The concrete settings of the experiments were as follows:
6
A connected component of a network is a subgraph in which any two nodes are
connected to each other by at least one path.
8 Roland Mühlenbernd
– network structure: a scale-free network with 500 agents (Holme-Kim algo-
rithm [11] with m = 2 and p = .8)
– signaling game: a 3 × 9-game
– reinforcement learning: Bush-Mosteller reinforcement with negative rein-
forcement and lateral inhibition (α = 1, β = 1, γ = 1, Ω = 20)
– stop condition: reaching 100,000 simulation steps
– initiation condition: the network is initially divided in 8 connected compo-
nents, and agents communicate only with neighbors of the same component
with a given signaling system for the first 100 simulation steps
– number of simulation runs: 10
Since I am interested in the mechanisms that show how and why seman-
tic conventions change, not how they evolve from the scratch, the simulation
runs were started with the given initiation condition, which ensures that al-
ready established local signaling conventions are given from the beginning. In
the following the results of the simulation runs will be presented.
3.2 Global Values
To get a good impression of how the population behaves during a simulation
run, two global values were measured: i) the average communicative success: the
utility value of a played game averaged over all plays during a simulation step,
and ii) the global number of signaling conventions: the total number of signaling
conventions agents have learned7 at the given simulation step.
In all simulation runs similar results were observed: after around 1,000 sim-
ulation steps the average communicative success increased to a value of around
.85, and the number of signaling conventions to a value of around 25. Further-
more, while both values show no tendency to increase or decrease in the long-run,
they oscillate quite strongly: the communicative success oscillates between .8 and
.9 and the number of signaling conventions oscillates between 20 and 30. This
result reveals a global interaction dynamics that shows long-term stability and
short-term reactivity at the same time.
Especially the oscillation of the number of signaling conventions is an in-
dicator for local reactivity. To get a better understanding of what is actually
happening, Figure 2 shows a sequence of the first 10,000 simulation steps for
the number of learners for 6 different signaling conventions: here regions of new
conventions emerge, grow to a specific amount and possibly get extinct. This
pattern shows quite nicely how language change is realized: an innovation is
made at one point in time and place, and then it spreads and its number of
speakers increases to a specific amount and constitutes a region of a new signal-
ing convention. The next step is now to detect agents that tend to contribute to
innovation and spread, and to investigate if specific structural patterns support
such a behavior.
7
Since generally agents do not learn a totally pure strategy, an agent is attributed
to have learned a signaling convention, when her behavioral strategy profile and a
signaling system reveal a so-called Hellinger similarity of > .7. For a formal definition
see [19], Definition 2.11.
Convention and Innovation in Social Networks 9
number of learners
20
15
10
5
0
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
simulation steps
Fig. 2. Simulation run of a 3 × 39 -game in a population of 500 agents placed in a social
network: the number of learners for 6 specific different signaling conventions for the
first 10,000 simulation steps.
3.3 Agent Features
Considering the dynamic picture of language change in the simulation runs,
I was interested if it is possible to detect specific roles of agents that might
support language change or strengthen local conventions. Following the study of
Mühlenbernd and Franke [20], I was particularly interested in the way an agent’s
static structural features and dynamic behavioral features might correlate. Static
features are given by an agent’s network properties ties strength T S, degree
centrality DC, closeness centrality CC, betweenness centrality BC and clustering
coefficient CL, as introduced in Section 2.3.
Dynamic features of an agent can be measured through her behavior or
position during a simulation run. Since I was interested in the way agents were
involved in the spread of a new variant, I defined and measured the dynamic
features innovation skill and impact. To compare these values to a number of
further dynamic features, I also defined and measured loyalty, interiority and
mutual intelligibility. For an agent n these features are defined as follows:
– innovation skill IN V (n): the proportion of simulation steps at which agent
n switched to a new convention, which no neighbor has actually learned
– impact IM P (n): the proportion of simulation steps at which a neighbor of
agent n switched to agent n’s convention
– loyalty LOY (n): the proportion of simulation steps agent n played her fa-
vorite strategy (most often played strategy)
– interiority IN T (n): the proportion of simulation steps for which agent n has
exclusively neighbors with the same convention
– mutual intelligibility M I(n): the average M I 8 value of agent n to her neigh-
borhood at a given simulation step, averaged over all simulation steps
8
The mutual intelligibility value M I reproduces the expected utility for two different
strategy pairs. For the definition see [21], Definition 3.
10 Roland Mühlenbernd
LOY
IMP
INV
INT
DC
CC
BC
TS
CL
MI
1
TS ● ● ●
0.8
DC ● ● ● ● ●
0.6
CC ● ● ● ●
0.4
BC ● ● ● ● ● ●
0.2
CL ● ● ● ● ●
0
INV ● ● ●
● ●
●
−0.2
IMP ● ● ● ●
● ●
−0.4
LOY ● ● ● ● ●
●
−0.6
INT ● ● ● ● ●
−0.8
MI ● ● ● ●
−1
Fig. 3. The correlations for all different pairs of features: the static network properties
ties strength T S, degree centrality DC, closeness centrality CC, betweenness centrality
BC and clustering coefficient CL; and the dynamic behavioral features innovation skill
IN V , impact IM P , loyalty LOY , interiority IN T and mutual intelligibility M I.
In my analysis I measured the correlation of all 5000 data points9 and for
each possible combination of feature. The resulting plot is shown in Figure 3:
here correlations are depicted as circles, where the size represents the strength
of the correlation, and the brightness represents the direction of the relationship
(positive: light, negative, dark).
The results show first of all: the data support the weak-tie theory, since
i) IN V has a high negative correlation with T S, and ii) IM P reveals a high
positive correlation with all three centrality properties DC, CC and BC. Thus,
innovation mostly starts at weak ties and spreads via central nodes.
But there are further interesting correlations. IN V has a high negative corre-
lation with LOY , M I and IN T . This shows that innovative agents i) do hardly
stay with their favorite convention, ii) are not very intelligible to neighbors, and
iii) are rather positioned at the border of a convention region. Note: the point
that innovation is expected to emerge at the periphery of societies was also
supported by field studies and computational work [9, 17].
9
Data points are the agents’ features; for 10 simulation runs with 500 agents each.
Convention and Innovation in Social Networks 11
4 Conclusion
In this study I used the signaling game – a model that is generally used to deal
with issues of language evolution – to analyze the dynamics of language change.
At first this is an ambitious challenge by considering that signaling games are
designed in a way that players are generally attracted to convention and stabil-
ity. For all that, I was particularly interested in the way environmental variables
in terms of network structure might describe characteristics that promote or
mitigate semantic change. For that purpose I made experiments on social net-
work structures of agents that play the signaling game repeatedly with connected
neighbors and update their behavior by a simple dynamics: reinforcement learn-
ing. I extended this learning account by an additional feature – innovation –
that supports the changing nature of the population’s dynamics. In my analysis
I compared different features of agents – static network properties and dynamic
behavioral properties of agents – to extract the characteristics of different roles
that might be involved in language change. The results support the weak ties-
theory: innovation start at weak ties and spreads via central nodes [17].
Since this study gives only a first impression of where to look for forces of
language change, there are at least two steps necessary to reveal more insightful
results. First of all, the current data should be further analyzed by using re-
gression models to find out, if there are non-trivial interactions – e.g. non-linear
dependencies – between static network properties and the role of agents in lan-
guage change dynamics. Second, my current results indicate to analyze further
i) static properties, like information flow measures [13] or closeness vitality [15];
and ii) dynamic features like the individual force of innovation, the number of
known messages or the growth magnitudes of an agent’s newly innovated sig-
naling system. These two additional steps are currently investigated and can
hopefully enrich subsequent work by delivering deeper insights into the role of
innovation in dynamics of semantic change.
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