Intelligence among Humans The Case of Alcoholics

Andrew Schumann1 and Vadim Fris2 1Department of Cognitivistics, University of Technology and Management in Rzeszow, Sucharskiego 2, 35-225, Rzeszow, Poland 2Private Health Unitary Enterprise “Iscelenie”, Kazinca 120, 220000 Minsk, Belarus

Keywords: , Swarm Computing, Alcoholic, Illocutionary.

Abstract: There are many forms of , such as of , 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 , 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 mammals, too, e.g. among naked mole-rats (Heterocephalus glaber sp.). In one colony they Usually, a social behaviour is understood as a have only one queen and one to three males to synonymous to a animal behaviour. It is reproduce, while other members of the colony are claimed that there are many forms of this behaviour just workers (Jarvis, 1981). The same collective from and insects to mammals including behaviour is typical for Damaraland blesmols humans. So, bacteria and insects performing a (Fukomys damarensis sp.), another mammal species collective behaviour are called social. – they have one queen and many workers (Jacobs, et For example, a prokaryote, a one-cell organism al., 1991; Jarvis, Bennett, 1993). that lacks a membrane-bound nucleus (karyon), can All these patterns of ant-like collective behaviour build colonies in a way of growing slime. These (a brood care and a division of labour into colonies are called ‘biofilms’. Cells in biofilms are reproductive and non-reproductive groups) are organized in dynamic networks and can transmit evaluated as a form of , the so-called signals (the so-called ) (Costerton, highest level of organization of animal sociality Lewandowski, Caldwell, Korber, 1995). As a result, (Michener, 1969). Nevertheless, it is quite these bacteria are considered social. Social insects controversial if we can regard the ant-like collective may be presented by – insects of the family behaviour as a social behaviour, indeed. We can do Formicidae. Due to a division of labour, they it if and only if we concentrate, first, on outer stimuli construct a real society of their nest even with a controlling individuals and, second, on ‘social roles’ pattern to make slaves (D'Ettorre, J. Heinze, 2001). (‘worker’, ‘queen’, etc.) of individuals as functions Also, Synalpheus regalis sp., a species of snapping with some utilities for the group as such, i.e. if and that commonly live in the coral reefs, only if we follow, first, behaviourism which demonstrates a collective behaviour like ants. represents any collective behaviour as a complex Among of the same colony there is one system that is managed by stimulating individuals breeding female, as well, and a labour division of (in particular by their reinforcement and other members (Duffy, 2002). The ant-like punishment) (Skinner, 1976) and, second, if and organization of colony is observed among some only if we share the ideas of structural functionalism

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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

BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

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

18 Swarm Intelligence among Humans - The Case of Alcoholics

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

19 BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

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

20 Swarm Intelligence among Humans - The Case of Alcoholics

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

if A is a formula, then  ki is a formula, too. The atomic proposition ki(no S are P) means: “for agent i, alternative P is at least as bad as These  k are read as follows: “the k-th i alternative S by the k-th utterance”. In the model of utterance of preference relation uttered by agent i to alcohol-addicted swarms: “for the grouping of fulfil an illocutionary act”. The weaker modality k  i alcohol-dependent people i, alternative P is at least is defined thus: as bad as alternative S by the k-th utterance”. ki A ::=   ki A.  Semantic meaning of ki(no S are P): We assume that  k and k satisfy the i  i M = k (no S are P) ::= at the utterance k uttered necessity rule and distribution axiom as well. i by i, for all data points A M, AS is false or AP is Let us denote the new extension by Ki. false. Now let us define in Ki the four basic preference Semantic meaning of ki(no S are P) in alcohol- relations as atomic syllogistic propositions: ki(all S addicted swarms: for all groups of alcoholics i at are P), ki(some S are P), ki(no S are P), ki(some S are places A, A and S are not connected by exchanging not P). They are defined as follows. of some members of i or A and P are not connected by exchanging of some members of i. ki(all S are P) ::=  ki (S  P) (1)

21 BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

ki(some S are not P) ::=  ki (S  P) (4) ki(all S are P)  ki(some S are P);

The atomic proposition ki(some S are not P) ki(no S are P)  ki(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 (ki(all S are P)  ki(no S are P)); alcohol-addicted swarms: “for the grouping of k (some S are P)  k (some S are not P); alcoholics i, alternative P is not at least as good as i i alternative S by the k-th utterance”. ki(all S are P)  ki(some S are not P);

Semantic meaning of ki(some S are not P): (ki(all S are P)  ki(some S are not P));

M = ki(some S are not P) ::= at the utterance k ki(no S are P)  ki(some S are P); uttered by i, for any data points A  M, AS is false or there exists A  M such that AS  S and AP is (ki(no S are P)  ki(some S are P)). false. Proof. It follows from (1) – (4). Semantic meaning of ki(some S are not P) in alcohol-addicted swarms: for all groups of The fusion of two swarms i and j for universal alcoholics i at places A, A and S are not connected affirmative syllogistic propositions is defined in Ki by exchanging of some members of i or there exists in the way: place A such that A and S are connected by ki (all S1 are P); mj (all S2 are P) exchanging of some members of i and A and P are not connected by exchanging of some members of i. (km)ij (all (S1  S2) are P) We can distinguish different swarms according The splitting of one swarm ij is defined in Ki thus: to the acceptance of stronger or weaker modality: (km)ij (all S are (P1  P2)) Weak Agent: ki (all S are P1); mj (all S are P2)  agent i prefers  ki A instead of ki A Hence, the illocutionary logic Ki describes the iff  ki A   ki A. preference relations of alcoholics towards attractants Strong Agent: under the conditions of lateral inhibition. agent i prefers  k A instead of k A i  i 3.2 Agents in Case of Lateral iff  ki A   ki A. Activation An example of the weak agent: (s)he prefers not to like not-A instead of that to like A. An example of When the concentration of attractants (different the strong agent: (s)he prefers to desire A instead of places of grouping for common drinks) is high, the that to accept A. logic K for preference relations is unacceptable. Hence, in logic Ki we have the four kinds of Instead of K we will use its modification K' (with atomic syllogistic propositions: ki(all S are P), the same inference rules) (Schumann, 2013; ki(some S are P), ki(no S are P), ki(some S are not P) Schumann, Woleński, 2016): for different k, i, S, and P. All other propositions of Ki are derivable by Boolean combinations of atomic Necessitation Rule: propositions. Models for these combinations are If A is a theorem of K', then so is  A. defined conventionally: Distribution Weak Axiom: M = A iff A is false in M;  (A  B)  (  A   B). M = A  B iff M = A or M = B; Now let us construct K'i by adding countable one- place sentential connectives  ki and  ki to the M = A  B iff M = A and M = B; language of K' and then define the four basic preference relations k (all S are P)', k (some S are P)', M = A  B iff if M = A, then M = B. i i ki(no S are P)', ki(some S are not P)' in the following Proposition 1. Logic Ki is a conservative manner: extension of K.  ki(S, P)' ::=  ki (S  P) (5) Proposition 2. In Ki, the conventional square of The atomic proposition  ki(S, P)' means opposition holds, i.e. there are the following (Schumann, Woleński, 2016): “for agent i, tautologies: alternative P is at least as good as alternative S by

22 Swarm Intelligence among Humans - The Case of Alcoholics

the k-th utterance”. In the model of alcohol-addicted ki(some S are not P)' ::=  ki (S  P) (8) swarms: “for the group of alcoholics i, alternative P The atomic proposition ki(some S are not P)' is at least as good as alternative S by the k-th means (Schumann, Woleński, 2016): “for agent i, utterance”. alternative P is not at least as good as alternative S Let us define a model M'. by the k-th utterance”. In the model of alcohol- Semantic meaning of  ki(S, P)': addicted swarms: “for the group of alcoholics i, alternative P is not at least as good as alternative S M' =  ki(S, P)' ::= there exists a data point A M' such that AS  S and for any A M', AS  S and by the k-th utterance”. AP  S. Semantic meaning of ki(some S are not P)': Semantic meaning of  ki(S, P)' in alcohol- M' = ki(some S are not P)' ::= for any data addicted swarms: there is a string AS and for any point A M', AS is false or there exists a data point place A which is reachable for S and P by A  M' such that AS is false or AP is false. exchanging of members of i, there are strings AS and Semantic meaning of ki(some S are not P)' in AP. This means that we have an occupation of the alcohol-addicted swarms: for any place A which is whole region where the places S and P are located. reachable for S and P by exchanging of members of ki(some S are P)' ::=  ki (S  P) (6) i there is no string AS or there exists a place A which is reachable for S and P by exchanging of members The atomic proposition ki(some S are P)' means (Schumann, Woleński, 2016): “for agent i, of i such that there is no string AS or there is no alternative P is not at least as bad as alternative S by string AP. This means that the group of alcoholics i the k-th utterance”. In the model of alcohol-addicted does not occupy S or there is a place which is not swarms: “for the group of alcoholics i, alternative P connected to S or P by exchanging of members of i. is not at least as bad as alternative S by the k-th Models for the Boolean combinations of atomic utterance”. proposition of K'i are defined thus: M' = A iff A is false in M'; Semantic meaning of ki(some S are P)': M' = A  B iff M' = A or M' = B; M' = ki(some S are P)' ::= for any data point A M', both AS is false and AP is false. M' = A  B iff M' = A and M' = B; Semantic meaning of k (some S are P)' in i M' = A  B iff if M' = A, then M' = B. alcohol-addicted swarms: for any place A which is reachable for S and P by exchanging of members of Proposition 3. Logic K'i is a conservative i, there are no strings AS and AP. This means that the extension of K'. group of alcoholics cannot reach S from P or P from Proposition 2. In K'i, the unconventional square S immediately. of opposition holds, i.e. there are the following tautologies: ki(no S are P)' ::=  ki (S  P) (7) The atomic proposition ki(no S are P)' means ki(all S are P)'  ki(no S are P)';

(Schumann, Woleński, 2016): “for agent i, ki(some S are P)'  ki(some S are not P)'; alternative P is at least as bad as alternative S by the k-th utterance”. In the model of alcohol-addicted (ki(all S are P)'  ki(some S are P)'); swarms: “for the group of alcoholics i, alternative P ki(no S are P)'  ki(some S are not P)'; is at least as bad as alternative S by the k-th k (all S are P)'  k (some S are not P)'; utterance”. i i (ki(all S are P)'  ki(some S are not P)'); Semantic meaning of ki(no S are P)': ki(no S are P)'  ki(some S are P)'; M' = ki(no S are P)' ::= there exists a data point A  M' such that if AS is false, then AP  S. (ki(no S are P)'  ki(some S are P)'). Semantic meaning of ki(no S are P)' in alcohol- Proof. It follows from (5) – (8). addicted swarms: there exists a place A which is reachable for S and P by exchanging of members of Now, let us consider pairs  ki A and  mi A, i such that there is a string AS or there is a string AP. where different performative verbs  ki and  mi This means that the group of alcoholics i occupies S occur and these verbs belong to different groups of or P, but not the whole region where the places S illocutions in expressing a preference relation, i.e., and P are located. both cannot be simultaneously representatives, directives, declaratives, expressive, or comissives.

23 BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

For instance, ‘believing’ and ‘knowing’ are both parasite propagation for Schistosomatidae sp. representatives and ‘ordering’ and ‘insisting’ are (Schumann, Akimova, 2015) as well as the same both directives. Assume, ‘believing’ be denoted by axioms as the logic of slime mould expansion  ki and ‘advising’ by  mi. Notice that ‘assuming’ (Schumann, 2015, 2016). The difference is that is modally weaker than ‘believing’, and ‘advising’ is instead of syllogistics for Schistosomatidae sp. modally weaker than ‘insisting’. So, ‘assuming’ can (Schumann, Akimova, 2015) and for slime mould be denoted by  ki, and ‘advising’ can be denoted by (Schumann, 2016), where preference relations are  mi, such that  ki A   ki A and  mi A   mi simple and express only attractions by food, we A. The construction  ki A   mi A involve many performative actions (verbs), which express a desire to drink together, within modal (respectively,  mi A   ki A) fits the situation that a that A is ever stronger than some other logics Ki and K'i. The logic Ki is used to formalize illocutions (belonging to other illocution groups) lateral inhibition in distributing people to drink related to not-A. jointly and the logic K'i is used to formalize lateral Let us distinguish different swarms according to activation in distributing people to drink jointly. the acceptance of stronger or weaker modality: The main outcome of our research is to show that some forms of human group behaviour are not social Meditative Agent: in fact. A kind of unsocial group behaviours is (i) agent i prefers  mi A instead of  ki A iff designated by us as swarm behaviour. Many forms  ki A   mi A; and (ii) agent i prefers  ki A of human swarming have recently been studied – instead of  mi A iff  mi A   ki A. from crowds of people in escape panic (Helbing, Active Agent: Farkas, Vicsek, 2000) to aircraft boarding (John, Schadschneider, Chowdhury, Nishinari, 2008). (i) agent i prefers  ki A instead of  mi A iff However, some stable patterns of interconnected  ki A   mi A; (ii) and agent i prefers  A people have never been analyzed as a swarm. We have proposed to consider a network of instead of  ki A iff  mi A   ki A. coordinated alcoholics as human swarming. The An example of the meditative agent: (s)he reasons are as follows: (1) their behaviour is prefers to believe that not-A instead of that to order controlled by replacing stimuli: attractants (places that A. An example of the active agent: (s)he prefers where they can drink jointly and safely) and to insist that A instead of that to believe that not-A. repellents (some interruptions which can appear for The fusion of two swarms i and j universal drinking); this control is executed by the same affirmative syllogistic propositions is defined in K'i algorithms as for standard swarms from social as follows: bacteria to eusocial mammals; (2) the behaviour of ki (all S1 are P)'; mj (all S2 are P) ' alcoholics is collective and even cooperative, but it

(km)ij (all (S1  S2) are P) is subordinated to the only one uncontrolled intention, namely, how to drink; so, this motivation The splitting of one swarm ij is defined in K'i: bears no symbolic meanings in the terms of (km)ij (all S are (P1  P2)) symbolic interactionism (Blumer, 1969) and, then, it cannot be evaluated as social. ki (all S are P1); mj (all S are P2) Each alcoholic realizes a group and The illocutionary logic K'i is to express the belongs to a network of people with the same preference relations of alcoholics towards attractants addiction. This network allows its members to under the conditions of lateral activation. 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 4 CONCLUSIONS social behavior. One of the effective means to recover alcoholism We have shown that a habit of joint drinking of is a back replacement of ways of group optimization alcohol-addicted people in small groups can be how to drink by that how not to drink. It is possible considered a swarm behaviour controlled by outer within a network of the so-called Alcoholics stimuli (places to drink jointly). These swarms can Anonymous where alcoholics can help each other to be managed by localization of places for meeting to stay sober. drink. Generally, the logic of propagation of groups of alcoholics has the same axioms as the logic of

24 Swarm Intelligence among Humans - The Case of Alcoholics

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