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2019 | Buch

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Behaviourism in Studying Swarms: Logical Models of Sensing and Motoring

verfasst von: Andrew Schumann

Verlag: Springer International Publishing

Buchreihe : Emergence, Complexity and Computation

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book presents fundamental theoretical results for designing object-oriented programming languages for controlling swarms. It studies the logics of swarm behaviours. According to behaviourism, all behaviours can be controlled or even managed by stimuli in the environment: attractants (motivational reinforcement) and repellents (motivational punishment). At the same time, there are two main stages in reactions to stimuli: sensing (perceiving signals) and motoring (appropriate direct reactions to signals). This book examines the strict limits of behaviourism from the point of view of symbolic logic and algebraic mathematics: how far can animal behaviours be controlled by the topology of stimuli? On the one hand, we can try to design reversible logic gates in which the number of inputs is the same as the number of outputs. In this case, the behaviouristic stimuli are inputs in swarm computing and appropriate reactions at the motoring stage are its outputs. On the other hand, the problem is that even at the sensing stage each unicellular organism can be regarded as a logic gate in which the number of outputs (means of perceiving signals) greatly exceeds the number of inputs (signals).

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The notion of swarm intelligence was first introduced in to denote the collective behaviour of decentralized and self-organized systems. Now, this notion is used in robotics to design a population of robots interacting locally among themselves and reacting locally to their environment with an emergent effect when all the local reactions of them are being cumulated into the one collective reaction. There are many natural examples of swarm intelligence: ant colonies, bee colonies, fish schooling, bird flocking and horse herding, bacterial colonies with a kind of social behaviour, multinucleated giant amoebae Physarum polycephalum, etc. The main feature of all these systems is that their individual agents behave locally without any centralized control, but their interactions lead to the emergence of global behaviour of the whole group that cannot be reduced to subsystems additively. By placing attractants and repellents at different sites we can manage and program the swarm behaviour. This opportunity allows us to design a biological computer on swarms.

Andrew Schumann

Chapter 2. Actin Filament Networks

Abstract

The plasmodium of Physarum polycephalum is very sensitive to its environment and reacts to stimuli by its appropriate motions. The sensitive stage as well as the motor stage of these reactions are explained by hydrodynamic processes, based on fluid dynamics, with participating of actin filament networks. This chapter is devoted to actin filament networks as a computation medium. The point is that actin filaments with a participating of many other proteins like myosin are sensitive to outer cellular stimuli (attractants as well as repellents) and they appear and disappear at different places of the cell to change the cell structure, e.g. its shape. Due to assembling and disassembling actin filaments, some unicellular organisms like Amoeba proteus can move in responses to different stimuli.

Andrew Schumann

Chapter 3. Unconventional Computers Designed on Swarm Behaviours

Abstract

From the previous chapter we know that the opportunity of implementing decidable arithmetic functions on the amoeboid motions means that we can design an unconventional computer using amoeboid organisms. In this chapter, I am going to propose a kind of this computer designed on Physarum polycephalum. Designing computers on swarms (such as plasmodia or ant nests) would mean that behaviourism is valid indeed, that is, we can control the swarm behaviours by placing attractants and repellents. Nevertheless, this claim is only partly true, because we can implement undecidable arithmetic functions also.

Andrew Schumann

Chapter 4. Conventional and Unconventional Automata on Swarm Behaviours

Abstract

In this chapter, I try to formulate swarms as labelled transition systems with the same set of labels (events or actions): direction, splitting, fusion, repelling. Then I show that these labelled transition systems can implement Kolmogorov-Uspensky machines, but with a low accuracy because of emergent patterns which occur if we have many states of appropriate transition system. Then I propose a p-adic arithmetic and logic to formalize emergent patterns of swarms. To sum up, I offer a general logical approach to swarm intelligence.

Andrew Schumann

Chapter 5. Non-Archimedean Valued Fuzzy and Probability Logics

Abstract

In this chapter, I concern some basic logical aspects of non-Archimedean valued probabilities and non-Archimedean valued fuzziness involved in simulating swarm behaviours. So, this chapter contains general results concerning non-Archimedean probabilities and fuzziness, i.e. logical values which run over an uncountable infinite, non-well-ordered and non-well-founded set.

Andrew Schumann

Chapter 6. Individual-Collective Duality in Swarm Behaviours

Abstract

The main assumption of behaviourism is that any animal behaviour can be controlled by attractants and repellents. It is quite true just for bacteria, but evidently it is untrue for swarms. The matter is that any swarm with a coordination of its members can behave according to an individual-collective duality—it means, it can perform only one action or many concurrent actions simultaneously and there is a fundamental uncertainty which mode will by chosen by the swarm right now (to behave as a big individual or a collective of distributed members).

Andrew Schumann

Chapter 7. Syllogistic Systems of Swarm Propagation

Abstract

In the p-adic valued universe of stimuli for controlling the swarm behaviour (including swarm sensing and motoring), we can define syllogistic propositions with two quantifiers: ‘all neighbours of an attractant/repellent’ and ‘some neighbours of an attractant/repellent’. In this chapter, I examine Aristotelian and non-Aristotelian syllogistics for simulating the swarms. In the Aristotelian syllogistic the models verifying swarming are well-founded and in the non-Aristotelian syllogistic the models verifying swarming are non-well-founded (i.e. they have no logical atoms).

Andrew Schumann

Chapter 8. Context-Based Games of Swarms

Abstract

The behaviour of Schistosomatidae cannot realize the lateral inhibition. As a consequence, it cannot realize different pictures of reality depending on a context. The point is that the parasites try to be propagated in all possible directions, no matter what conditions are at the moment. Nevertheless, true swarms, such as the ant nests or plasmodia of Physarum polycephalum, react differently under different conditions. It means that they can produce different pictures of reality or even compete with their own kind. The latter situation of their competitions for the same food allows us to define their behaviour as a game.

Andrew Schumann

Chapter 9. Logics for Preference Relations in Swarm Behaviours

Abstract

Each action of swarm can have many possible modifications. It means that preference relations of swarm are being modified, too. As far as we know, there are at least the following two ways of modifications in sensing and motoring: (i) the lateral inhibition with increasing the proto-symbolic value of item and, as a result, with concentrating on the chosen item; and (ii) the lateral activation with decreasing the proto-symbolic value of concrete items which causes a consideration of many items simultaneously.

Andrew Schumann

Chapter 10. Non-Archimedean Probabilities and Reflexive Games

Abstract

Any swarm can change its preference relations in accordance with some conditions outside and inside the intercommunication of swarm members. These conditions can make the same stimuli more or less proto-symbolic (that is, laterally inhibited or laterally activated, respectively). So, some primitive forms of symbolic interactionism can be observed even at the level of swarming. Each player of swarms can change a decision during the game. This circumstance contradicts to the Aumann’s agreement theorem, according to that each rational player makes the same decision, basing on the same facts and appealing to Bayesian probabilities. Nevertheless, even a swarm does not follow this theorem. So what does that mean for human beings who interact first of all symbolically? The theorem becomes absurd.

Andrew Schumann

Chapter 11. Payoff Cellular Automata and Reflexive Games

Abstract

Reflexive games are just an abstract continuation of bio-inspired games. A high reflexivity of game is explained by a high level of modifications of involved actions and strategies at each game move. In this chapter, I will show that bio-inspired and reflexive games can be represented in the form of cellular automata. The more modified a cellular-automatic transition rule is at each step, the more reflexive our game is. For example, the Belousov-Zhabotinsky reaction can be described as a game, for which the transition rule does not change. It is a game of zero reflexion.

Andrew Schumann

Chapter 12. Foundations of Mathematics Within Lateral Inhibition and Lateral Activation

Abstract

In the previous chapters, I have shown that conventional logics can be suitable for modelling the swarm behaviour under the condition of lateral inhibition. In this chapter, I am going to demonstrate that mathematics is irreducible to conventional logics, too, since mathematical cognitions are grounded on both lateral inhibition and lateral activation. It shows that the lateral inhibition and lateral activation as basic forms of swarm sensing and motoring are fundamental for all cognitions, including the mathematical one.

Andrew Schumann

Chapter 13. Conclusion and Future Work

Abstract

In accordance with behaviourism, any animal behaviour based on unconditioned and conditioning reflexes can be controlled or even managed by stimuli in the environment: attractants (motivational reinforcement) and repellents (motivational punishment). In the meanwhile, there are the following two main stages in reactions to stimuli: sensing (perceiving signals) and motoring (appropriate direct reactions to signals). In this book, the strict limits of behaviourism have been studied from the point of view of symbolic logic and algebraic mathematics: How far can animal behaviours be controlled by the topology of stimuli? In other words, how far can we design unconventional computers on the basis of animal reactions to stimuli?

Andrew Schumann

Backmatter

Titel: Behaviourism in Studying Swarms: Logical Models of Sensing and Motoring
verfasst von: Andrew Schumann
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-91542-5
Print ISBN: 978-3-319-91541-8
DOI: https://doi.org/10.1007/978-3-319-91542-5