Swarm Intelligence among Humans
The Case of Alcoholics
Andrew Schumann
1
and Vadim Fris
2
1
Department of Cognitivistics, University of Information Technology and Management in Rzeszow,
Sucharskiego 2, 35-225, Rzeszow, Poland
2
Private Health Unitary Enterprise “Iscelenie”, Kazinca 120, 220000 Minsk, Belarus
Keywords: Swarm Intelligence, Swarm Computing, Alcoholic, Illocutionary.
Abstract: There are many forms of swarm behaviour, such as swarming of insects, flocking of birds, herding of
quadrupeds, and schooling of fish. Sometimes people behave unconsciously and this behaviour of them has
the same patterns as behaviour of swarms. For instance, pedestrians behave as herding or flocking, aircraft
boarding passengers behave as ant colony, people in escape panic behave as flocking, etc. In this paper we
propose a swarm model of people with an addictive behaviour. In particular, we consider small groups of
alcohol-dependent people drinking together as swarms with a form of intelligence. In order to formalize this
intelligence, we appeal to modal logics K and its modification K'. The logic K is used to formalize
preference relation in the case of lateral inhibition in distributing people to drink jointly and the logic K' is
used to formalize preference relation in the case of lateral activation in distributing people to drink jointly.
1 INTRODUCTION
Usually, a social behaviour is understood as a
synonymous to a collective animal behaviour. It is
claimed that there are many forms of this behaviour
from bacteria and insects to mammals including
humans. So, bacteria and insects performing a
collective behaviour are called social.
For example, a prokaryote, a one-cell organism
that lacks a membrane-bound nucleus (karyon), can
build colonies in a way of growing slime. These
colonies are called ‘biofilms’. Cells in biofilms are
organized in dynamic networks and can transmit
signals (the so-called quorum sensing) (Costerton,
Lewandowski, Caldwell, Korber, 1995). As a result,
these bacteria are considered social. Social insects
may be presented by ants – insects of the family
Formicidae. Due to a division of labour, they
construct a real society of their nest even with a
pattern to make slaves (D'Ettorre, J. Heinze, 2001).
Also, Synalpheus regalis sp., a species of snapping
shrimp that commonly live in the coral reefs,
demonstrates a collective behaviour like ants.
Among shrimps of the same colony there is one
breeding female, as well, and a labour division of
other members (Duffy, 2002). The ant-like
organization of colony is observed among some
mammals, too, e.g. among naked mole-rats
(Heterocephalus glaber sp.). In one colony they
have only one queen and one to three males to
reproduce, while other members of the colony are
just workers (Jarvis, 1981). The same collective
behaviour is typical for Damaraland blesmols
(Fukomys damarensis sp.), another mammal species
– they have one queen and many workers (Jacobs, et
al., 1991; Jarvis, Bennett, 1993).
All these patterns of ant-like collective behaviour
(a brood care and a division of labour into
reproductive and non-reproductive groups) are
evaluated as a form of eusociality, the so-called
highest level of organization of animal sociality
(Michener, 1969). Nevertheless, it is quite
controversial if we can regard the ant-like collective
behaviour as a social behaviour, indeed. We can do
it if and only if we concentrate, first, on outer stimuli
controlling individuals and, second, on ‘social roles’
(‘worker’, ‘queen’, etc.) of individuals as functions
with some utilities for the group as such, i.e. if and
only if we follow, first, behaviourism which
represents any collective behaviour as a complex
system that is managed by stimulating individuals
(in particular by their reinforcement and
punishment) (Skinner, 1976) and, second, if and
only if we share the ideas of structural functionalism
Schumann A. and Fris V.
Swarm Intelligence among Humans - The Case of Alcoholics.
DOI: 10.5220/0006106300170025
In Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2017), pages 17-25
ISBN: 978-989-758-212-7
Copyright
c
 2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
17

which considers the whole society as a system of
functions (‘roles’) of its constituent elements
(Parsons, 1975). In case we accept both
behaviourism and structural functionalism, we can
state that a collective animal behaviour has the same
basic patterns from ‘social’ bacteria and ‘social’
insects to humans whose sociality is evident for
ourselves.
However, there are different approaches to
sociality. One of the approaches, alternative to
behaviourism and structural functionalism, is
represented by symbolic interactionism. In this
approach, a collective behaviour is social if in the
process of interaction it involves a thought with a
symbolic meaning that arises out of the interaction
of agents (Beni, Wang, 1969). In other words, social
behaviour is impossible without material culture,
e.g. without using some tools which always have
symbolic meanings. Obviously, in this sense the
collective behaviour of ants cannot be regarded as
social. There are no tools and no symbolic meanings
for the ants.
But not only humans perform social behaviour in
the meaning of symbolic interactionism. It is known
that wild bottlenose dolphins (Tursiops sp.)
“apparently use marine sponges as foraging tools”
(Krützen, Mann, Heithaus, Connor, Bejder, Sherwin,
2005) and this behaviour of them cannot be
explained genetically or ecologically. This means
that “sponging” is an example of an existing
material culture in a marine mammal species and
this culture is transmitted, presumably by mothers
teaching the skills to their sons and daughters
(Krützen, Mann, Heithaus, Connor, Bejder, Sherwin,
2005).
Also, chimpanzees involve tools in their
behaviours: large and small sticks as well as large
and small stones. In (Whiten, Goodall, McGrew,
Nishida, Reynolds, Sugiyama, Tutin, Wrangham,
Boesch, 1999), the authors discover 39 different
behaviour patterns of chimpanzees, including tool
usage, grooming and courtship behaviours. It is a
very interesting fact that some patterns of
chimpanzees are habitual in some communities but
are absent in others because of different traditions of
chimpanzee material cultures (Whiten, Goodall,
McGrew, Nishida, Reynolds, Sugiyama, Tutin,
Wrangham, Boesch, 1999). Hence, we see that the
collective behaviour of chimpanzees can be
evaluated as social, as well.
So, within symbolic interactionism we cannot
consider any complex collective behaviour, like the
ant nest, as a social behaviour. The rest of complex
behaviours can be called a swarm behaviour. Its
examples are as follows: swarming of insects,
flocking of birds, herding of quadrupeds, schooling
of fish. In swarms, animals behave collectively, e.g.
in schools or flocks each animal moves in the same
direction as its neighbour, it remains close to its
neighbours, it avoids collisions with its neighbours
(Viscido, Parrish, Grunbaum, 2004).
A group of people, such as pedestrians, can also
exhibit a swarm behaviour like a flocking or
schooling: humans prefer to avoid a person
conditionally designated by them as a possible
predator and if a substantial part of the group (not
less than 5%) changes the direction, then the rest
follows the new direction (Helbing, Keltsch, Molnar,
1997). An ant-based algorithm can explain aircraft
boarding behaviour (John, Schadschneider,
Chowdhury, Nishinari, 2008). Under the conditions
of escape panic the majority of people perform a
swarm behaviour, too (Helbing, Farkas, Vicsek,
2000). The point is that a risk of predation is the
main feature of swarming at all (Abrahams, Colgan,
1985; Olson, Hintze, Dyer, Knoester, Adami, 2013)
and under these risk conditions (like a terrorist act)
symbolic meanings for possible human interactions
are promptly reduced. As a consequence, the social
behaviour transforms into a swarm behaviour.
Thus, we distinguish the swarm behaviour from
the social one. The first is fulfilled without symbolic
interactions, but it is complex, as well, and has an
appearance from a collective decision making. In
this paper, we will show that an addictive behaviour
of humans can be considered a kind of swarm
behaviour, also. The risk of predation is a main
reason of reducing symbolic interactions in human
collective behaviours, but there are possible other
reasons like addiction. An addiction increases roles
of addictive stimuli (e.g., alcohol, morphine,
cocaine, sexual intercourse, gambling, etc.) by their
reinforcing and intrinsically rewarding.
It is known that any swarm can be controlled by
replacing stimuli: attractants and repellents
(Adamatzky, Erokhin, Grube, Schubert, Schumann,
2012), therefore we can design logic circuits based
on topology of stimuli (Schumann, 2016). For
swarms there are no symbolic meanings and the
behaviour is completely determined by outer stimuli.
In this paper, we will consider how the alcohol
dependence syndrome impacts on the human
behaviour.
We claim that alcohol-dependent humans
embody a version of swarm intelligence (Beni,
Wang, 1969; Schumann, 2016; Schumann,
Woleński, 2016) to optimize the alcohol-drinking
behaviour. Our research is based on statistic data
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18

which we have collected due to the questionnaire of
107 people who sought help for their alcohol
dependence at the Private Health Unitary Enterprise
“Iscelenie,” Minsk, Belarus.
In Section II we consider some basic features of
collective behaviour of alcohol-addicted people. In
Section III we formalize preference relations for
their swarm intelligence.
2 BASIC FEATURES OF SWARM
INTELLIGENCE OF
ALCOHOL-DEPENDENT
PEOPLE
According to our survey, all the respondents have
affirmed that they prefer to drink in small groups
from 3 to 7 people, but the same respondents can
join different small groups in due course. The
number of stable friends to drink commonly is from
2 to 5. The alcohol-addicted people distinguish their
groups from relatives or colleagues and 63% of the
respondents think that their family and job hinder
them to drink safely.
Thus, these small groups from 3 to 7 people can
be regarded as human swarms which help their
members to drink safely and to logistically optimize
the task to drink. 85% of the respondents have
responded that members of the group can pay for
drinks if the respondent does not have money and
91% of the respondents have claimed that they can
buy alcohol for somebody from the group who does
not have money. So, we deal with a form of
solidarity in helping to drink.
35% of the respondents drink in groups
consisting only of men and 65% drink in mixed-
gender groups. In the meanwhile, a sex/gender
behaviour is mainly reduced in these groups.
In the case of involving new members into
groups the main reasons are as follows: they are
neighbours or colleagues and they can treat/pay.
Entering new groups is possible if a
friend/acquainted has invited to join them because it
is more safe and interesting for the respondent to
join the new group. Without an invitation it is
impossible to enter the group.
Groups are very friendly and the only reason to
expel somebody from the group is that (s)he quarrels
(in particular, (s)he does not want to pay). 32% of
respondents have noticed that it would be better to
expel one member in their groups.
Only 28% of respondents have stated that in their
groups there are leaders. They are men or women
more than 40 years old. The leadership consists in a
support of the group to drink together.
We have discovered that alcoholics form a
network consisting of several small groups. And the
task of optimizing common drinks is solved not by a
small group, but by the whole network, i.e. by
several groups whose members are interconnected.
The point is that each small group of alcoholics
appears and disappears under different conditions,
but the network, these alcoholics belong to, is almost
the same. We have studied that small groups of
alcohol-addicted people are not stable and, by
exchanging their members, they can fuse or split in
the optimization of drinking. The same behavioural
patterns are observed in the slime mould
(Schumann, 2015, 2016): fusing and splitting in
front of attractants to optimize their occupation.
Outer stimuli (attractants) for the slime mould are
pieces of nutrients scattered before this organism.
Attractants for alcoholics are represented by places
where they can drink in small groups safely: flat or
outside. 38% of the respondents prefer to drink at
the same place and 62% at different places. The
arguments in choosing the places are as follows: the
short distance from the home, low price, quality of
drinks.
To sum up, the alcohol-dependent people
realizes a version of swarm intelligence to optimize
drinking in the way of fusing or splitting the groups
under different conditions. In case the groups are
rather splitting, we face a lateral activation effect;
and in case the groups are fusing, we deal with a
lateral inhibition effect of alcoholic networks.
Small groups of alcoholics are considered by us
as kind of human swarms. These swarms build a
network and within the same network alcoholics can
freely move from one swarm to another. As a
consequence, the swarms fuse or split.
3 PREFERENCE RELATIONS
FOR SWARM INTELLIGENCE
OF ALCOHOL-DEPENDENT
PEOPLE
So, the alcohol-addicted people prefer to drink in
small groups from 3 to 7 persons. These groups are
said to be agents of swarm intelligence (that is really
intelligence, because an appropriate network of
alcoholics solves always optimization tasks to drink
effectively). Each agent is virtual, namely with an
unconscious collective decision-making mechanism
that is decentralized and distributed among all
Swarm Intelligence among Humans - The Case of Alcoholics
19

members of the group. The same situation of
distribution of intelligence is observed in any
swarm. The agents are denoted by small letters i,
j,… As well as all swarms, these agents can fuse and
split to optimize a group occupation of attractants.
Usually, there are many agents who communicate
among themselves by exchanging people (their
members), e.g., someone can be a member of agent i
today and later became a member of agent j.
The places where agents i, j,… (appropriate
small groups of alcohol-dependent humans) can
drink safely are called attractants for swarm
intelligence. The attractants are denoted by S, P, ...
There are two different ways in occupying
attractants by swarm agents: (i) with high
concentration of people (lateral inhibition effect) at
places of meeting and (ii) with low concentration of
people (lateral activation effect) at places of meeting
(Jones, 2015; Schumann, 2016). In the first case
much less attractants are occupied. In the second
case much more attractants are occupied. For
instance, in snow winter there are less attractants
(places to drink jointly and safely) and this causes a
lateral inhibition effect in alcoholic swarming. In
sunny summer there are more attractants (places to
drink in a group) and this implies a lateral activation
effect in alcoholic networking.
Lateral inhibition and lateral activation can be
detected in any forms of swarm networking. For
example, this mechanism is observed also in the true
slime mould (plasmodium) of Physarum
polycephalum. The plasmodium has the two distinct
stages in responding to signals: (i) the sensory stage
(perceiving signals) and (ii) the motor stage (action
as responding). The effect of lateral activation in the
plasmodium is to decrease contrast between
attractants at the sensory stage and to split
protoplasmic tubes towards two or more attractants
at the motor stage (Fig. 1A). The effect of lateral
inhibition is to increase contrast between attractants
at the sensory stage and to fuse protoplasmic tubes
towards one attractant at the motor stage (Fig. 1B).
In human groups there are (i) the one sensory
stage consisting in perceiving signals (as well as for
the plasmodium) and the following two motor stages
consisting in actions as responding: (ii) illocutionary
stage and (iii) perlucotionary stage.
For the first time the well-known 20
th
-century
philosopher John L. Austin has investigated speech
acts as a way of coordination for human behaviour
by a verbal communication as well as by a non-
verbal communication (e.g. by gestures or mimics).
His main philosophical claim that was accepted then
by almost all later language philosophers has based
on the idea that we coordinate our joint behaviour by
Figure 1: The two plasmodia propagate protoplasmic tubes
towards three attractants denoted by black circles: A.
Lateral activation. The splitting of protoplasmic tubes of
each plasmodium. B. Lateral inhibition The fusion of two
plasmodia by the fusion of their protoplasmic tubes.
illocutionary acts – some utterances which express
our intentions and expectations to produce joint
symbolic meanings for symbolic interactions: “I
hereby declare,” “I sentence you to ten years'
imprisonment”, “I promise to pay you back,” “I pray
to God”, etc. These utterances can produce an effect
on the hearer that is called a perlocutionary act.
Hence, according to Austin, in order to commit a
group behaviour, the humans should start with
illocutionary acts (uttering illocutions) to coordinate
their common symbolic meanings. As a result, their
group behaviour appears as a kind of perlocutionary
act grounded on previous illocutionary utterances.
Thus, the motor stage for the plasmodium is just
a direct behaviour, while the motor stage for the
humans starts from illocutionary acts to produce
symbolic meanings for performing an interaction
and then this stage is continued in perlocutionary
acts (a direct coordinated behaviour of a human
group).
Attractants S, P, ... are detected by alcoholics at
the sensory stage. Then alcoholics perform
illocutionary acts to share preference relations on
detected attractants. Later they commit
perlocutionary acts to occupy some detected
attractants. A data point S is considered empty if and
only if an appropriate attractant (the place denoted
by S to drink within a group) is not occupied by the
group of alcohol-dependent people. Let us define
syllogistic strings of the form SP with the following
interpretation: ‘S and P are comparable positively’,
and with the following meaning: SP is true if and
only if S and P are reachable for each other by
members of the group i and both S and P are not
empty, otherwise SP is false. Let S be a set of all
true syllogistic strings.
Now we can construct an illocutionary logic of
alcohol-dependent people. In this logic we deal with
preference relations about detected attractants
from S.
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20

3.1 Agents in Case of Lateral
Inhibition
Let us construct an extension of modal logic K,
please see (Bull, Segerberg, 1984) about K, for
preference relations of agents in case of lateral
inhibition. Let ‘A’ and ‘B’ be metavariables ranging
over syllogistic letters S, P, ... or over standard
propositional compositions of syllogistic letters by
means of conjunctions, disjunction, implication,
negation. Let us introduce two modalities

and

with the following meaning:

A 

A,
i.e.,

A is modally stronger and

A is modally
weaker, e.g.,

A means ‘I like A’ (or ‘I desire A’)
and

A means ‘maybe A’ (or ‘it can be A’). So, the
performative verb of

is stronger and the
performative verb of

is weaker with the same type
of performativity (modality) to prefer A (Schumann,
Woleński, 2016).
In our logic K for preference relations we have
also only two axioms as in the standard K (the
inference rules are the same also):
Necessitation Rule:
If A is a theorem of K, then so is

A.
Distribution Axiom:

(A  B)  (

A 

B).
The operator

can be defined from

as follows:

A ::= 

A,
where

are any performative verbs for expressing a
preference relation with a strong modality: ‘like’,
‘want’, ‘desire’, etc.
Now let us add countable many new one-place
sentential connectives

k
i
to the language of K:
if A is a formula, then

k
i
is a formula, too.
These

k
i
are read as follows: “the k-th
utterance of preference relation uttered by agent i to
fulfil an illocutionary act”. The weaker modality

k
i
is defined thus:

k
i
A ::= 

k
i
A.
We assume that

k
i
and

k
i
satisfy the
necessity rule and distribution axiom as well.
Let us denote the new extension by Ki.
Now let us define in Ki the four basic preference
relations as atomic syllogistic propositions: k
i
(all S
are P), k
i
(some S are P), k
i
(no S are P), k
i
(some S are
not P). They are defined as follows.
k
i
(all S are P) ::=

k
i
(S  P)
(1)
The atomic proposition k
i
(all S are P) means: “for
agent i, alternative P is at least as good as alternative
S by the k-th utterance”. In the model of alcohol-
addicted swarms it means: “for the grouping of
alcohol-dependent people i, alternative P is at least
as good as alternative S at the k-th utterance”.
Let us define a model M.
Semantic meaning of k
i
(all S are P):
M = k
i
(all S are P) ::= at the utterance k uttered
by i, there exists a data point A  M such that AS 
S and for any A  M, if AS  S, then AP  S.
Semantic meaning of k
i
(all S are P) in alcohol-
addicted swarms: there is a group of alcoholics i at a
place A such that places A and S are connected by
exchanging of some members of i and for any place
A, if A and S are connected by exchanging of some
members of i, then A and P are connected by
exchanging of some members of i.
k
i
(some S are P) ::=

k
i
(S  P)
(2)
The atomic proposition k
i
(some S are P) means:
“for agent i, alternative P is not at least as bad as
alternative S by the k-th utterance”. In the model of
alcohol-addicted swarms it means: “for the grouping
of alcohol-dependent people i, alternative P is not at
least as bad as alternative S at the k-th utterance”.
Semantic meaning of k
i
(some S are P):
M = k
i
(some S are P) ::= at the utterance k
uttered by i, there exists a data point A  M such
that both AS  S and AP  S.
Semantic meaning of k
i
(some S are P) in alcohol-
addicted swarms: there exists a group of alcoholics i
at A such that A and S are connected by exchanging
of some members of i and A and P are connected by
exchanging of some members of i.
k
i
(no S are P) ::=

k
i
(S  P)
(3)
The atomic proposition k
i
(no S are P) means:
“for agent i, alternative P is at least as bad as
alternative S by the k-th utterance”. In the model of
alcohol-addicted swarms: “for the grouping of
alcohol-dependent people i, alternative P is at least
as bad as alternative S by the k-th utterance”.
Semantic meaning of k
i
(no S are P):
M = k
i
(no S are P) ::= at the utterance k uttered
by i, for all data points A M, AS is false or AP is
false.
Semantic meaning of k
i
(no S are P) in alcohol-
addicted swarms: for all groups of alcoholics i at
places A, A and S are not connected by exchanging
of some members of i or A and P are not connected
by exchanging of some members of i.
Swarm Intelligence among Humans - The Case of Alcoholics
21

k
i
(some S are not P) ::=

k
i
(S  P)
(4)
The atomic proposition k
i
(some S are not P)
means: “for agent i, alternative P is not at least as
good as alternative S by the k-th utterance”. In the
alcohol-addicted swarms: “for the grouping of
alcoholics i, alternative P is not at least as good as
alternative S by the k-th utterance”.
Semantic meaning of k
i
(some S are not P):
M = k
i
(some S are not P) ::= at the utterance k
uttered by i, for any data points A  M, AS is false
or there exists A  M such that AS  S and AP is
false.
Semantic meaning of k
i
(some S are not P) in
alcohol-addicted swarms: for all groups of
alcoholics i at places A, A and S are not connected
by exchanging of some members of i or there exists
place A such that A and S are connected by
exchanging of some members of i and A and P are
not connected by exchanging of some members of i.
We can distinguish different swarms according
to the acceptance of stronger or weaker modality:
Weak Agent:
agent i prefers

k
i
A instead of

k
i
A
iff

k
i
A 

k
i
A.
Strong Agent:
agent i prefers

k
i
A instead of

k
i
A
iff

k
i
A 

k
i
A.
An example of the weak agent: (s)he prefers not
to like not-A instead of that to like A. An example of
the strong agent: (s)he prefers to desire A instead of
that to accept A.
Hence, in logic Ki we have the four kinds of
atomic syllogistic propositions: k
i
(all S are P),
k
i
(some S are P), k
i
(no S are P), k
i
(some S are not P)
for different k, i, S, and P. All other propositions of
Ki are derivable by Boolean combinations of atomic
propositions. Models for these combinations are
defined conventionally:
M = A iff A is false in M;
M = A  B iff M = A or M = B;
M = A  B iff M = A and M = B;
M = A  B iff if M = A, then M = B.
Proposition 1. Logic Ki is a conservative
extension of K.
Proposition 2. In Ki, the conventional square of
opposition holds, i.e. there are the following
tautologies:
k
i
(all S are P)  k
i
(some S are P);
k
i
(no S are P)  k
i
(some S are not P);
(k
i
(all S are P)  k
i
(no S are P));
k
i
(some S are P)  k
i
(some S are not P);
k
i
(all S are P)  k
i
(some S are not P);
(k
i
(all S are P)  k
i
(some S are not P));
k
i
(no S are P)  k
i
(some S are P);
(k
i
(no S are P)  k
i
(some S are P)).
Proof. It follows from (1) – (4).
The fusion of two swarms i and j for universal
affirmative syllogistic propositions is defined in Ki
in the way:
k
i
(all S
1
are P); m
j
(all S
2
are P)
(km)
i

j
(all (S
1
 S
2
) are P)
The splitting of one swarm ij is defined in Ki thus:
(km)
i

j
(all S are (P
1
 P
2
))
k
i
(all S are P
1
); m
j
(all S are P
2
)
Hence, the illocutionary logic Ki describes the
preference relations of alcoholics towards attractants
under the conditions of lateral inhibition.
3.2 Agents in Case of Lateral
Activation
When the concentration of attractants (different
places of grouping for common drinks) is high, the
logic K for preference relations is unacceptable.
Instead of K we will use its modification K' (with
the same inference rules) (Schumann, 2013;
Schumann, Woleński, 2016):
Necessitation Rule:
If A is a theorem of K', then so is

A.
Distribution Weak Axiom:

(A  B)  (

A 

B).
Now let us construct K'i by adding countable one-
place sentential connectives

k
i
and

k
i
to the
language of K' and then define the four basic
preference relations k
i
(all S are P)', k
i
(some S are P)',
k
i
(no S are P)', k
i
(some S are not P)' in the following
manner:

k
i
(S, P)' ::=

k
i
(S  P)
(5)
The atomic proposition

k
i
(S, P)' means
(Schumann, Woleński, 2016): “for agent i,
alternative P is at least as good as alternative S by
BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing
22

the k-th utterance”. In the model of alcohol-addicted
swarms: “for the group of alcoholics i, alternative P
is at least as good as alternative S by the k-th
utterance”.
Let us define a model M'.
Semantic meaning of

k
i
(S, P)':
M' =

k
i
(S, P)' ::= there exists a data point A
M' such that AS  S and for any A M', AS  S and
AP  S.
Semantic meaning of

k
i
(S, P)' in alcohol-
addicted swarms: there is a string AS and for any
place A which is reachable for S and P by
exchanging of members of i, there are strings AS and
AP. This means that we have an occupation of the
whole region where the places S and P are located.
k
i
(some S are P)' ::=

k
i
(S  P)
(6)
The atomic proposition k
i
(some S are P)' means
(Schumann, Woleński, 2016): “for agent i,
alternative P is not at least as bad as alternative S by
the k-th utterance”. In the model of alcohol-addicted
swarms: “for the group of alcoholics i, alternative P
is not at least as bad as alternative S by the k-th
utterance”.
Semantic meaning of k
i
(some S are P)':
M' = k
i
(some S are P)' ::= for any data point
A M', both AS is false and AP is false.
Semantic meaning of k
i
(some S are P)' in
alcohol-addicted swarms: for any place A which is
reachable for S and P by exchanging of members of
i, there are no strings AS and AP. This means that the
group of alcoholics cannot reach S from P or P from
S immediately.
k
i
(no S are P)' ::=

k
i
(S  P)
(7)
The atomic proposition k
i
(no S are P)' means
(Schumann, Woleński, 2016): “for agent i,
alternative P is at least as bad as alternative S by the
k-th utterance”. In the model of alcohol-addicted
swarms: “for the group of alcoholics i, alternative P
is at least as bad as alternative S by the k-th
utterance”.
Semantic meaning of k
i
(no S are P)':
M' = k
i
(no S are P)' ::= there exists a data
point A  M' such that if AS is false, then AP  S.
Semantic meaning of k
i
(no S are P)' in alcohol-
addicted swarms: there exists a place A which is
reachable for S and P by exchanging of members of
i such that there is a string AS or there is a string AP.
This means that the group of alcoholics i occupies S
or P, but not the whole region where the places S
and P are located.
k
i
(some S are not P)' ::=

k
i
(S  P)
(8)
The atomic proposition k
i
(some S are not P)'
means (Schumann, Woleński, 2016): “for agent i,
alternative P is not at least as good as alternative S
by the k-th utterance”. In the model of alcohol-
addicted swarms: “for the group of alcoholics i,
alternative P is not at least as good as alternative S
by the k-th utterance”.
Semantic meaning of k
i
(some S are not P)':
M' = k
i
(some S are not P)' ::= for any data
point A M', AS is false or there exists a data point
A  M' such that AS is false or AP is false.
Semantic meaning of k
i
(some S are not P)' in
alcohol-addicted swarms: for any place A which is
reachable for S and P by exchanging of members of
i there is no string AS or there exists a place A which
is reachable for S and P by exchanging of members
of i such that there is no string AS or there is no
string AP. This means that the group of alcoholics i
does not occupy S or there is a place which is not
connected to S or P by exchanging of members of i.
Models for the Boolean combinations of atomic
proposition of K'i are defined thus:
M' = A iff A is false in M';
M' = A  B iff M' = A or M' = B;
M' = A  B iff M' = A and M' = B;
M' = A  B iff if M' = A, then M' = B.
Proposition 3. Logic K'i is a conservative
extension of K'.
Proposition 2. In K'i, the unconventional square
of opposition holds, i.e. there are the following
tautologies:
k
i
(all S are P)'  k
i
(no S are P)';
k
i
(some S are P)'  k
i
(some S are not P)';
(k
i
(all S are P)'  k
i
(some S are P)');
k
i
(no S are P)'  k
i
(some S are not P)';
k
i
(all S are P)'  k
i
(some S are not P)';
(k
i
(all S are P)'  k
i
(some S are not P)');
k
i
(no S are P)'  k
i
(some S are P)';
(k
i
(no S are P)'  k
i
(some S are P)').
Proof. It follows from (5) – (8).
Now, let us consider pairs

k
i
A and

m
i
A,
where different performative verbs

k
i
and

m
i
occur and these verbs belong to different groups of
illocutions in expressing a preference relation, i.e.,
both cannot be simultaneously representatives,
directives, declaratives, expressive, or comissives.
Swarm Intelligence among Humans - The Case of Alcoholics
23

For instance, ‘believing’ and ‘knowing’ are both
representatives and ‘ordering’ and ‘insisting’ are
both directives. Assume, ‘believing’ be denoted by

k
i
and ‘advising’ by

m
i
. Notice that ‘assuming’
is modally weaker than ‘believing’, and ‘advising’ is
modally weaker than ‘insisting’. So, ‘assuming’ can
be denoted by

k
i
, and ‘advising’ can be denoted by

m
i
, such that

k
i
A 

k
i
A and

m
i
A 

m
i
A. The construction

k
i
A 

m
i
A
(respectively,

m
i
A 

k
i
A) fits the situation
that a belief that A is ever stronger than some other
illocutions (belonging to other illocution groups)
related to not-A.
Let us distinguish different swarms according to
the acceptance of stronger or weaker modality:
Meditative Agent:
(i) agent i prefers

m
i
A instead of

k
i
A iff

k
i
A 

m
i
A; and (ii) agent i prefers

k
i
A
instead of

m
i
A iff

m
i
A 

k
i
A.
Active Agent:
(i) agent i prefers

k
i
A instead of

m
i
A iff

k
i
A 

m
i
A; (ii) and agent i prefers


A
instead of

k
i
A iff

m
i
A 

k
i
A.
An example of the meditative agent: (s)he
prefers to believe that not-A instead of that to order
that A. An example of the active agent: (s)he prefers
to insist that A instead of that to believe that not-A.
The fusion of two swarms i and j universal
affirmative syllogistic propositions is defined in K'i
as follows:
k
i
(all S
1
are P)'; m
j
(all S
2
are P) '
(km)
i

j
(all (S
1
 S
2
) are P)
The splitting of one swarm ij is defined in K'i:
(km)
i

j
(all S are (P
1
 P
2
))
k
i
(all S are P
1
); m
j
(all S are P
2
)
The illocutionary logic K'i is to express the
preference relations of alcoholics towards attractants
under the conditions of lateral activation.
4 CONCLUSIONS
We have shown that a habit of joint drinking of
alcohol-addicted people in small groups can be
considered a swarm behaviour controlled by outer
stimuli (places to drink jointly). These swarms can
be managed by localization of places for meeting to
drink. Generally, the logic of propagation of groups
of alcoholics has the same axioms as the logic of
parasite propagation for Schistosomatidae sp.
(Schumann, Akimova, 2015) as well as the same
axioms as the logic of slime mould expansion
(Schumann, 2015, 2016). The difference is that
instead of syllogistics for Schistosomatidae sp.
(Schumann, Akimova, 2015) and for slime mould
(Schumann, 2016), where preference relations are
simple and express only attractions by food, we
involve many performative actions (verbs), which
express a desire to drink together, within modal
logics Ki and K'i. The logic Ki is used to formalize
lateral inhibition in distributing people to drink
jointly and the logic K'i is used to formalize lateral
activation in distributing people to drink jointly.
The main outcome of our research is to show that
some forms of human group behaviour are not social
in fact. A kind of unsocial group behaviours is
designated by us as swarm behaviour. Many forms
of human swarming have recently been studied –
from crowds of people in escape panic (Helbing,
Farkas, Vicsek, 2000) to aircraft boarding (John,
Schadschneider, Chowdhury, Nishinari, 2008).
However, some stable patterns of interconnected
people have never been analyzed as a swarm.
We have proposed to consider a network of
coordinated alcoholics as human swarming. The
reasons are as follows: (1) their behaviour is
controlled by replacing stimuli: attractants (places
where they can drink jointly and safely) and
repellents (some interruptions which can appear for
drinking); this control is executed by the same
algorithms as for standard swarms from social
bacteria to eusocial mammals; (2) the behaviour of
alcoholics is collective and even cooperative, but it
is subordinated to the only one uncontrolled
intention, namely, how to drink; so, this motivation
bears no symbolic meanings in the terms of
symbolic interactionism (Blumer, 1969) and, then, it
cannot be evaluated as social.
Each alcoholic realizes a group adaptation and
belongs to a network of people with the same
addiction. This network allows its members to
optimize the task to drink. Therefore, it is a
substitute of social groups (from family to other
institutions) and it is a displacement of standard
social behavior.
One of the effective means to recover alcoholism
is a back replacement of ways of group optimization
how to drink by that how not to drink. It is possible
within a network of the so-called Alcoholics
Anonymous where alcoholics can help each other to
stay sober.
BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing
24

ACKNOWLEDGEMENTS
The project was supported by FP7-ICT-2011-8.
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