pith. sign in

arxiv: 2606.08552 · v1 · pith:Y62SMCIXnew · submitted 2026-06-07 · 💻 cs.AI · cs.MA· cs.NE· physics.data-an

Quantitative Promise Theory: Intentionality and Inference in Autonomous Agents

Mark Burgess This is my paper

Pith reviewed 2026-06-27 18:51 UTC · model grok-4.3

classification 💻 cs.AI cs.MAcs.NEphysics.data-an
keywords Promise Theoryautonomous agentsBayesian probabilityactive inferenceinformation theoryagent alignmentboundary conditions
0
0 comments X

The pith

Boundary conditions act as promises that define scalable intent and let autonomous agents form information-minimizing swarms.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out a quantitative version of Promise Theory that incorporates Bayesian probability and information-theoretic optimization, including Active Inference. It shows how promises avoid the non-local coordination, calibration, and normalization problems that arise in pure probabilistic models of agents. Boundary conditions function as promises that constrain allowed states and set decision thresholds, while alignment between agents supplies a scalable definition of intent. Agents can therefore congeal into larger structures with superagent properties by each minimizing its own information even while uncertainty tends to increase it.

Core claim

Supplementing promise semantics with Bayesian probability and information optimization preserves local coordination. Boundary conditions serve as promises that constrain states and select thresholds. Agent alignment thereby supplies a scalable definition of intent. Autonomous agents may then congeal into swarms with superagent characteristics by minimizing information despite uncertainty that works to maximize it.

What carries the argument

Promise semantics augmented by Bayesian probability and information-theoretic optimization, in which boundary conditions function as promises that constrain states and define intent through alignment.

Load-bearing premise

Promise Theory semantics can be preserved and supplemented with Bayesian probability without reintroducing non-local coordination or normalization.

What would settle it

A concrete comparison of agent simulations that either include or omit promise-defined boundary conditions, checking whether information minimization produces observable swarm behavior only in the promise case.

Figures

Figures reproduced from arXiv: 2606.08552 by Mark Burgess.

Figure 1
Figure 1. Figure 1: Notation for promise graphs and semantics is fundamentally graphical and (despite a few overlapping concepts) is not equivalent to that for Bayesian networks. B. Promise parameterization Promise bodies affect only the agent making the promise, but may refer to its intentions towards other agents, e.g. • A scalar promise refers to no other agents, e.g. I promise to brush my teeth +b. • A vector promise refe… view at source ↗
Figure 2
Figure 2. Figure 2: The ‘data pipeline’ in a promised causal influence. An agent promises its own behaviour, i.e. a subset of possible outcomes of its own behaviour. This constrains events associated with the promised behaviour. Another agent, accepting this promise may observe the outcomes, measure and count them, assess whether they keep the promise or not. only promise its own behaviour, not that of other agents, thus the … view at source ↗
Figure 3
Figure 3. Figure 3: Probability trials and ensembles. In a frequentist interpreta￾tion, trial ensembles are effectively space-like separated snapshots (transverse variation), whereas a Bayesian samples are ordered by a conditional precedence relation and thus represent time-like snapshots (longitudinal variation). The logic of a Bayesian probabilistic reasoning quickly becomes maddeningly complicated when trying to adjust fai… view at source ↗
Figure 4
Figure 4. Figure 4: Two sets formed from collections of events A = {ea} and B = {eb}, and their overlap region A∩B. We note that the overlap region double counts coincident events. where ¬ea means NOT ea, ea ∩ eb means ea AND eb (conjunction), and ea ∪ eb means ea OR eb (disjunction). From these, we note that counting all elements in both sets must be corrected from double-counting the overlap region: P(ea ∪ eb||ec) = P(ea||e… view at source ↗
Figure 5
Figure 5. Figure 5: Quantitative descriptions of promises may refer to interior dynamics, involved in keeping promises, or exterior dynamics involved in propagation of influence between agents. If a dynamic variable cannot be predicted causally, one may still ask: can its probable or average value at least be made approximately causal? This is where statistics and probability help to give a formally precise algorithm for desc… view at source ↗
Figure 6
Figure 6. Figure 6: Semantically, the corrective pipeline in a Bayesian learning process is a bit like copy editing a lookup-table or information directory. One starts with a “first edition” or training set of data, then one enters into a copy editing phase of updating the text observation by observation. The schema of attributes associated with each value(key) is approximately constant, but the values w are random events. Wh… view at source ↗
Figure 7
Figure 7. Figure 7: Over a number of independent agents, there are potentially many independent parameters to capture behaviour. One must not assume coherence of sources without promises that enable coherence to form, and we should be aware of how values are normalized autonomously. data and calculate statistical results. Each source must promise access to its variables: πi(Si) : Si +xi −−→ R, (62) similarly, R must promise t… view at source ↗
Figure 8
Figure 8. Figure 8: In a promise based system, the sample space is formally enlarged to accommodate promise events that live alongside the pure states of the agent’s dynamical activity. More accurately, for each agent independently, Bayes scaling formula (47) can now be written in the form: P(π || ea) = P(ea || π)P(π) P(ea) , (69) where π is a promise, which is now used as a classifying conditional, and ea is an event generat… view at source ↗
Figure 9
Figure 9. Figure 9: Example of Bayesian network, from Duda et al. This also acts as a basic model for deconstructing semantics from a scenario: from context, to key states of nature, to attributes associated with them. The nodes of the graph are variables whose values play different roles in an inference. [29]. promises. Whether in terms of promises or straightforward probabilities for events, the pathways develop the initial… view at source ↗
Figure 10
Figure 10. Figure 10: The agents and promises in a Predictive Coding sensory inference pipeline, sketched roughly. Each circle is an agent. The stippled super agents clusters act as modules for partial memory centres where running averages are kept. An approximate ‘maximum likelihood’ estimate of the dynamical variable’s feature ϕ is computed within a few sampling iterations. We assume that each agent is working to sample inpu… view at source ↗
Figure 11
Figure 11. Figure 11: Curve fit of data using the formula in equation 115 with a data from around 200,000 agents on Wikipedia from [53]. It’s quite rare to be in a position to compare theory with data in such a scenario, but here we are fortunate [53]. Here, we have a model of the most probable size of a social group in a seeded collaboration of agents with human characteristics. Trust obviously has some semantics associated w… view at source ↗
Figure 12
Figure 12. Figure 12: From a parallel sensor array, through a pipeline of influence, to a memory representation. First, independent signals must be collated and classified, then stored in some interior representation, so first there is aggregation and then sparse representation. The final size is likely much larger than the original sensory image, so one must be economical in storage representation. If we want to make a quanti… view at source ↗
Figure 13
Figure 13. Figure 13: Representing bounded capabilities. In quantum mechanics, the boundary of a geometry and potential function of a spacetime arrangement (e.g. a square well or isolated hydrogen atom) forms a constraint on an energy distribution process, leading to a set of supportable eigenstates. Observables representing differential physical processes each have a set of supportable eigenstates that give observed value of … view at source ↗
Figure 14
Figure 14. Figure 14: Motion along a channel from coarse-grained superagent to superagent provides the most general scaled picture of transitions. This view leads naturally to a density matrix formulation due to the separation of interior and exterior process variables. The scale at which we describe this process now matters. If the circles represent a scale S, then the arrows are shown at scale S − 1. be the interior states o… view at source ↗
read the original abstract

I discuss some quantitative representations of Promise Theory for processes involving autonomous agents. Agent models are common in software systems, machine learning, and biology, for example, but may also apply to physics and other forms of engineering. I describe how Bayesian probability and information theoretic optimization, including Active Inference, may be incorporated with promise semantics -- as well as how Promise Theory supplements solutions, helping to avoid probability's pitfalls, which include non-local coordination, calibrating, and normalizing probabilistic computations. The role of boundary conditions in constraining allowed states and selecting decision thresholds is a form of promise, and agent alignment provides a scalable definition of intent. Autonomous agents may congeal into swarms with superagent characteristics by trying to minimize their information, despite uncertainty that works to maximize it. The use of Promise Theory involves some research challenges as well as stylistic preferences.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript offers a conceptual discussion of quantitative representations of Promise Theory applied to autonomous agents. It proposes incorporating Bayesian probability and information-theoretic optimization (including Active Inference) with promise semantics to model intentionality and inference, arguing that Promise Theory helps avoid pitfalls such as non-local coordination and normalization in probabilistic methods. Boundary conditions are framed as promises that constrain states and thresholds, agent alignment is presented as a scalable definition of intent, and agents are suggested to form swarms with superagent properties by minimizing information despite uncertainty maximizing it. The work also notes research challenges and stylistic preferences in applying the theory.

Significance. If the suggested integration can be formalized, the framework could meaningfully bridge Promise Theory with contemporary approaches in multi-agent AI, active inference, and biological modeling by supplying local, semantics-preserving mechanisms for intent and coordination. This would be particularly valuable in domains where non-local probabilistic computations are undesirable, potentially enabling more scalable definitions of alignment and swarm behavior.

major comments (2)
  1. [Abstract] Abstract: The central proposal that Bayesian probability and information-theoretic methods 'may be incorporated with promise semantics' while avoiding non-local coordination and normalization pitfalls is stated without any derivation, formal mapping, or concrete example showing how the combination is achieved or verified.
  2. [Abstract] Abstract: The claim that 'autonomous agents may congeal into swarms with superagent characteristics by trying to minimize their information' is presented as a possible outcome but lacks any supporting model, optimization objective, or boundary-condition analysis that would make the statement quantitative or testable.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and for recognizing the potential value of integrating Promise Theory with Bayesian and information-theoretic approaches. The comments correctly identify that the manuscript is a conceptual discussion rather than a fully formalized framework. We address each point below and will revise the abstract and relevant sections to better reflect the exploratory scope and to frame certain statements more precisely as proposals for future investigation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central proposal that Bayesian probability and information-theoretic methods 'may be incorporated with promise semantics' while avoiding non-local coordination and normalization pitfalls is stated without any derivation, formal mapping, or concrete example showing how the combination is achieved or verified.

    Authors: The manuscript opens by describing itself as a discussion of quantitative representations and explicitly frames the integration as a possibility ('may be incorporated') rather than a completed formal result. The body text elaborates qualitative mappings, such as the use of promises to supply local boundary conditions and semantics that complement probabilistic methods, while noting pitfalls like non-local coordination. No derivation or concrete example is supplied because the work is intended to outline a research direction, not to deliver a finished theory. We will revise the abstract to state the conceptual and suggestive character of the proposals more explicitly and will add a short illustrative scenario in the main text to clarify the intended complementarity. revision: yes

  2. Referee: [Abstract] Abstract: The claim that 'autonomous agents may congeal into swarms with superagent characteristics by trying to minimize their information' is presented as a possible outcome but lacks any supporting model, optimization objective, or boundary-condition analysis that would make the statement quantitative or testable.

    Authors: The statement is presented as a hypothesis that follows from the earlier discussion of information minimization under promise alignment and uncertainty maximization. The manuscript does not supply an optimization objective or quantitative model for swarm formation; a dedicated section already lists research challenges associated with making such ideas operational. We agree that the phrasing in the abstract could be read as stronger than intended. We will revise the abstract to present the swarm-formation idea explicitly as a suggested direction for future quantitative work rather than an established outcome, and we will cross-reference the existing challenges section. revision: yes

Circularity Check

0 steps flagged

No significant circularity; conceptual discussion only

full rationale

The manuscript is framed as a conceptual discussion of how Promise Theory semantics might be supplemented by Bayesian probability and information-theoretic methods (including Active Inference). No formal derivations, equations, quantitative predictions, or first-principles results are presented in the abstract or described in the full-text placeholder. The central claims concern possible incorporations and boundary-condition interpretations rather than any derivation chain that could reduce to its own inputs. Self-reference to the author's prior Promise Theory framework is normal for an originator and does not meet the criteria for load-bearing circularity because no unsubstantiated quantitative step relies on it. The paper is therefore self-contained as discussion and receives the default non-finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central discussion rests on the assumption that Promise Theory semantics remain intact under probabilistic augmentation and that boundary conditions function as promises; no free parameters or invented entities are stated in the abstract.

axioms (1)
  • domain assumption Promise Theory can be combined with Bayesian probability and active inference while preserving its core semantics and avoiding probability's coordination pitfalls.
    Invoked throughout the abstract as the basis for the proposed quantitative representations.

pith-pipeline@v0.9.1-grok · 5667 in / 1212 out tokens · 16022 ms · 2026-06-27T18:51:37.125648+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

65 extracted references · 2 canonical work pages

  1. [1]

    Bergstra and M

    J.A. Bergstra and M. Burgess.Promise Theory: Principles and Applications (second edition).χtAxisPress, 2014,2019

    2014

  2. [2]

    An approach to understanding policy based on autonomy and voluntary cooperation

    Mark Burgess. An approach to understanding policy based on autonomy and voluntary cooperation. InIFIP/IEEE 16th international workshop on distributed systems operations and management (DSOM), in LNCS 3775, pages 97–108, 2005

    2005

  3. [3]

    Wooldridge.An Introduction to MultiAgent Systems

    M. Wooldridge.An Introduction to MultiAgent Systems. Wiley, Chichester, 2002

    2002

  4. [4]

    Popper.Observation and Interpretation, chapter The Propensity Interpretation of the Calculus of Probability, and The Quantum Theory

    K. Popper.Observation and Interpretation, chapter The Propensity Interpretation of the Calculus of Probability, and The Quantum Theory. Butterworths, London, 1957

    1957

  5. [5]

    Englert, editor.Julian Schwinger, Quantum Mechanics: Symbolism of Atomic Measurement

    B.G. Englert, editor.Julian Schwinger, Quantum Mechanics: Symbolism of Atomic Measurement. Springer, 2001

    2001

  6. [6]

    Shannon and W

    C.E. Shannon and W. Weaver.The Mathematical Theory of Communica- tion. University of Illinois Press, Urbana, 1949

    1949

  7. [7]

    Cover and J.A

    T.M. Cover and J.A. Thomas.Elements of Information Theory. (J.Wiley & Sons., New York), 1991

    1991

  8. [8]

    Lewis and C

    H. Lewis and C. Papadimitriou.Elements of the Theory of Computation, Second edition. Prentice Hall, New York, 1997

    1997

  9. [9]

    M. Burgess. Spacetimes with semantics (i).arXiv:1411.5563, 2014

    Pith/arXiv arXiv 2014

  10. [10]

    M. Burgess. Spacetimes with semantics (ii).arXiv.org:1505.01716, 2015

    Pith/arXiv arXiv 2015

  11. [11]

    M. Burgess. Spacetimes with semantics (iii).arXiv:1608.02193, 2016

    Pith/arXiv arXiv 2016

  12. [12]

    M. Burgess. Motion of the third kind (i) notes on the causal structure of virtual processes for privileged observers. DOI: 10.13140/RG.2.2.30483.35361 (notes available on Researchgate), 2021

    work page doi:10.13140/rg.2.2.30483.35361 2021

  13. [13]

    M. Burgess. Motion of the third kind (ii) notes on kinematics, dynamics, and relativity. (notes available on Researchgate), 2022

    2022

  14. [14]

    M. Burgess. Motion of the third kind (iii): On the semantics of motion in discrete spacetimes and evolutionary selection. (notes available on Researchgate), 2024

    2024

  15. [15]

    M. Burgess. Two dimensional time-series for anomaly detection and regulation in adaptive systems.Lecture Notes in Computer Science, IFIP/IEEE 13th International Workshop on Distributed Systems: Opera- tions and Management (DSOM 2002), 2506:169, 2002

    2002

  16. [16]

    M. Burgess. Probabilistic anomaly detection in distributed computer networks.Science of Computer Programming, 60(1):1–26, 2006

    2006

  17. [17]

    Bjelland, M

    J. Bjelland, M. Burgess, G. Canright, and K. Engø-Monsen. Eigenvectors of directed graphs and importance scores: dominance, t-rank, and sink remedies.Data Mining and Knowledge Discovery, 20(1):98–151, 2010

    2010

  18. [18]

    Galam.Sociophysics

    S. Galam.Sociophysics. Springer, 2012

    2012

  19. [19]

    Ballentine.Quantum Mechanics: A Modern Development

    L.E. Ballentine.Quantum Mechanics: A Modern Development. World Scientific, 1998

    1998

  20. [20]

    Pearl.Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference

    J. Pearl.Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgen Kaufmann, San Francisco, 1988

    1988

  21. [21]

    Grimmett and D.R

    G.R. Grimmett and D.R. Stirzaker.Probability and random processes (3rd edition). Oxford scientific publications, Oxford, 2001

    2001

  22. [22]

    Testing the quantitative spacetime hypothesis using artificial narrative comprehension (i) : Bootstrapping meaning from episodic narrative viewed as a feature landscape, 2020

    Mark Burgess. Testing the quantitative spacetime hypothesis using artificial narrative comprehension (i) : Bootstrapping meaning from episodic narrative viewed as a feature landscape, 2020

    2020

  23. [23]

    Hebb.The Organization of Behavior

    D.O. Hebb.The Organization of Behavior. Wiley & Sons, 1949

    1949

  24. [24]

    Korb and A.E

    K.B. Korb and A.E. Nicholson.Bayesian Artificial Intelligence. Chapman and Hall, 2004

    2004

  25. [25]

    McInerney, R

    J. McInerney, R. Ranganath, and D.M. Blei. The population posterior and bayesian inference on streams, 2015

    2015

  26. [26]

    Reif.Fundamentals of statistical mechanics

    F. Reif.Fundamentals of statistical mechanics. McGraw-Hill, 1965

    1965

  27. [27]

    Wiener.Cybernetics or Control and Communication in the Animal and the Machine

    N. Wiener.Cybernetics or Control and Communication in the Animal and the Machine. MIT Press, 1948. 29

    1948

  28. [28]

    Continuous integration of data histories into consistent namespaces

    Mark Burgess and Andr´as Gerlits. Continuous integration of data histories into consistent namespaces. 2022

    2022

  29. [29]

    Duda, P.E

    R.O. Duda, P.E. Hart, and D.G. Stork.Pattern classification. Wiley Interscience, New York, 2001

    2001

  30. [30]

    M. Burgess. Describe the scene! the investment in context. Medium, April 2026

    2026

  31. [31]

    Rapoport.N-Person Game Theory: Concepts and Applications

    A. Rapoport.N-Person Game Theory: Concepts and Applications. Dover, New York, 1970

    1970

  32. [32]

    Myerson.Game theory: Analysis of Conflict

    R.B. Myerson.Game theory: Analysis of Conflict. (Harvard University Press, Cambridge, MA), 1991

    1991

  33. [33]

    Strassner.Handbook of Network and System Administration, chapter Knowledge Engineering Using Ontologies

    J. Strassner.Handbook of Network and System Administration, chapter Knowledge Engineering Using Ontologies. Elsevier Handbook, 2007

    2007

  34. [34]

    Fanizzi, C

    N. Fanizzi, C. d’Amato, and F. Esposito. Machine learning methods for ontology mining.Semantic Computing, pages 131–153, 07 2010

    2010

  35. [35]

    Dietz.Enterprise ontology

    J.L.G. Dietz.Enterprise ontology. Springer, 2006

    2006

  36. [36]

    Bishop and H

    C.M. Bishop and H. Bishop.Deep Learning. Springer, 2023

    2023

  37. [37]

    Burgess.A Treatise on Systems: Volume 1: Analytical description of human-information networks

    M. Burgess.A Treatise on Systems: Volume 1: Analytical description of human-information networks. in progress, 2004-

    2004

  38. [38]

    Burgess and S

    M. Burgess and S. Fagernes. Norms and swarms.Lecture Notes on Computer Science, 4543 (Proceedings of the first International Conference on Autonomous Infrastructure and Security (AIMS)):107–118, 2007

    2007

  39. [39]

    Rao and D.H

    R.P.N. Rao and D.H. Ballard. Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience, 2(1):79–87, 1999

    1999

  40. [40]

    Millidge, A.K

    B. Millidge, A.K. Seth, and C.L. Buckley. Predictive coding: a theoretical and experimental review.CoRR, abs/2107.12979, 2021

    arXiv 2021

  41. [41]

    K. Friston. A theory of cortical responses.Philosophical Transactions of the Royal Society B: Biological Sciences, 360(1456):815–836, 04 2005

    2005

  42. [42]

    K. Friston. The free-energy principle: a unified brain theory?Nature Reviews Neuroscience, 11:127–138, 2010

    2010

  43. [43]

    K. Friston. The free-energy principle: a rough guide to the brain?Trends in Cognitive Sciences, 13:293–301, 2009

    2009

  44. [44]

    T. Parr, G. Pezzulo, and K.J. Friston.Active Inference: the Free Energy Principle in Mind, Brain, and Behavior. MIT Press, 2022

    2022

  45. [45]

    R. Bogacz. A tutorial on the free-energy framework for modelling perception and learning.Journal of Mathematical Psychology, 76:198– 211, 2017. Model-based Cognitive Neuroscience

    2017

  46. [46]

    Feynman.Statistical Mechanics

    R.P. Feynman.Statistical Mechanics. Addison Wesley, 1972

    1972

  47. [47]

    M. Burgess. Configurable immunity model of evolving configuration management.Science of Computer Programming, 51:197, 2004

    2004

  48. [48]

    R. Cao. New labels for old ideas: Predictive processing and the interpretation of neural signals.Biology & Philosophy, 35(5):52, 2020

    2020

  49. [49]

    Applications of the free energy principle to machine learning and neuroscience (thesis), 2021

    Beren Millidge. Applications of the free energy principle to machine learning and neuroscience (thesis), 2021

    2021

  50. [50]

    Zemansky and R.H

    M.W. Zemansky and R.H. Dittman.Heat and Thermodynamics. McGraw- Hill, 1981

    1981

  51. [51]

    M. Burgess. Agent semantics, semantic spacetime, and graphical reasoning, arxiv cs.ai 2506.07756, 2025

    arXiv 2025

  52. [52]

    M. Burgess. Notes on trust as a causal basis for social science. SSRN Archive, available at http://dx.doi.org/10.2139/ssrn.4252501 (DOI: 10.2139/ssrn.4252501), August 2022

    work page doi:10.2139/ssrn.4252501 2022

  53. [53]

    Burgess and R.I.M

    M. Burgess and R.I.M. Dunbar. A promise theory perspective on the role of intent in group dynamics.arXiv:2402.00598 [cs.SI], 2023

    arXiv 2023

  54. [54]

    Dunbar.Grooming, Gossip and the Evolution of Language

    R. Dunbar.Grooming, Gossip and the Evolution of Language. Faber and Faber, London, 1996

    1996

  55. [55]

    W.X. Zhou, S. Sornette, R.A. Hill, and R.I.M. Dunbar. Discrete hierarchical organization of social group sizes.Proc. Royal Soc., 272:439– 444, 2004

    2004

  56. [56]

    Burgess and R.I.M

    M. Burgess and R.I.M. Dunbar. Group related phenomena in wikipedia edits.arXiv:2402.00595 [cs.SI], 2023

    arXiv 2023

  57. [57]

    M. Burgess. γ(3,4) ‘attention’ in cognitive agents: Ontology-free knowledge representations with promise theoretic semantics, 2026

    2026

  58. [58]

    The collapse of a quantum state as a joint probability construction.Journal of Physics A: Mathematical and Theoretical, 55(25):254006, June 2022

    Peter Morgan. The collapse of a quantum state as a joint probability construction.Journal of Physics A: Mathematical and Theoretical, 55(25):254006, June 2022

    2022

  59. [59]

    Wetterich

    C. Wetterich. Quantum formalism for classical statistics.Annals of Physics, 393:1–70, 2018

    2018

  60. [60]

    O.C. Granmo. The tsetlin machine - a game theoretic bandit driven approach to optimal pattern recognition with propositional logic.ArXiv, abs/1804.01508, 2018

    arXiv 2018

  61. [61]

    Bonabeau, M

    E. Bonabeau, M. Dorigo, and G. Theraulaz.Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press, Oxford, 1999

    1999

  62. [62]

    Kennedy and R.C

    J. Kennedy and R.C. Eberhart.Swarm Intelligence. Morgan Kaufmann (Academic Press), 2001

    2001

  63. [63]

    Arlotti, A

    L. Arlotti, A. Deutsch, and M. Lachowicz. On a discrete boltzmann type model of swarming.Math. Comp. Model, 41:1193–1201, 2005

    2005

  64. [64]

    PhD thesis, California Institute of Technology, 2000

    Kazadi S.Swarm Engineering. PhD thesis, California Institute of Technology, 2000

    2000

  65. [65]

    R.P. Feynman. There’s plenty of room at the bottom.Engineering and Science, 23(5):22–36, 1960. 30

    1960