Formal Aspects of Computing

, Volume 24, Issue 1, pp 45–65 | Cite as

Emergence and refinement

Original Article

Abstract

Emergent behaviour—system behaviour not determined by the behaviours of system components when considered in isolation—is commonplace in multi-agent systems, particularly when agents adapt to environmental change. This article considers the manner in which Formal Methods may be used to authenticate the trustworthiness of such systems. Techniques are considered for capturing emergent behaviour in the system specification and then the incremental refinement method is applied to justify design decisions embodied in an implementation. To demonstrate the approach, one and two-dimensional cellular automata are studied. In particular an incremental refinement of the ‘glider’ in Conway’s Game of Life is given from its specification.

Keywords

Emergence Refinement Cellular automata Game of Life 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. And72.
    Anderson PW (1972) More is different. Science 177(4047): 393–396CrossRefGoogle Scholar
  2. BCF10.
    Backhouse R, Chen W, Ferreira JF (2010) The algorithmics of solitaire-like game. In: Bolduc C, Desharnais J, Ktari B (eds) Mathematics of Program Construction (MPC 2010) volume 6120 of LNCS. Springer-Verlag, Berlin, pp 1–18CrossRefGoogle Scholar
  3. BCG82.
    Berlekamp ER, Conway JH, Guy RK (1982) Winning ways for your mathematical plays vol 2. Academic Press, LondonMATHGoogle Scholar
  4. Bed97.
    Bedau MA (1997) Weak emergence. In: Tomberlin J (eds) Philosophical perspectives: mind, causation and world, vol 11. Blackwell Publishers, Oxford, pp 375–399Google Scholar
  5. Bed03.
    Bedau MA (2003) Downward causation and autonomy in weak emergence. Principia 6: 5–50Google Scholar
  6. BKS88.
    Back RJR, Kurki-Suonio R (1988) Distributed cooperation with action systems. ACM Trans Program Lang Syst 10(4): 513–555CrossRefMATHGoogle Scholar
  7. CNC07.
    Chen C-C, Nagl S, Clack C (2007) A calculus for multi-level emergent behaviours in component-based systems and simulations. In: Emergent properties in natural and artificial complex systems (EPNACS 2007), pp 35–51Google Scholar
  8. CS07a.
    Cucker F, Smale S (2007) Emergent behaviour in flocks. IEEE Trans Autom Control 52(5): 852–862CrossRefMathSciNetGoogle Scholar
  9. CS07b.
    Cucker F, Smale S (2007) On the mathematics of emergence. Jpn J Math 2: 197–227CrossRefMATHMathSciNetGoogle Scholar
  10. Dam00.
    Damper RI (2000) Emergence and levels of description. Int J Syst Sci 31(7): 811–818CrossRefMATHGoogle Scholar
  11. EB04.
    Edmonds B, Bryson J (2004) The insufficiency of formal design methods—the necessity of an experimental approach for the understanding and control of complex MAS. In: International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS’04). IEEE Computer Society, pp 938–945Google Scholar
  12. Fod74.
    Fodor JA (1974) Special sciences (or the disunity of science as a working hypothesis). Syntheses 28: 97–115CrossRefGoogle Scholar
  13. Fod97.
    Fodor JA (1997) Special sciences; still autonomous after all these years. In: Tomberlin J (ed) Philosophical perspectives: mind, causation and world, vol 11. Blackwell Publishers, Oxford, pp 149–163Google Scholar
  14. Fro06.
    Fromm J (2006) On engineering and emergence. arXiv preprint http://arxiv.org/abs/nlin.AO/0601002
  15. Gar70.
    Gardner M (1970) Mathematical games: The fantastic combinations of John Conway’s new solitaire game “life”. Scientific American, pp 120–123Google Scholar
  16. Gru09.
    Gruner S (2009) Mobile agent systems and cellular automata. Auton Agents Multi-Agent Syst 20(2): 198–233CrossRefGoogle Scholar
  17. HJJ03.
    Hayes IJ, Jackson M, Jones CB (2003) Determining the specification of a control system from that of its environment. In: Araki K, Gnesi S, and Mandrioli D (eds) Formal Methods Europe (FME 2003), volume 2805 of LNCS. Springer-Verlag, Berlin, pp 154–169Google Scholar
  18. HLRS08.
    Hu J, Liu Z, Reed GM, Sanders JW (2008) Ensemble engineering and emergence. In: Wirsing M, Banâtre J-P, Hölzl M, Rauschmayer A (eds) Software-intensive systems and new computing paradigms: challenges and visions, volume 5380 of LNCS. Springer-Verlag, Berlin, pp 162–178Google Scholar
  19. HW08.
    Hamann H, Wörn H (2008) A framework of space-time continuous models for algorithm design in swarm robotics. Swarm Intell 2: 209–239CrossRefGoogle Scholar
  20. JSW98.
    Jennings NR, Sycara K, Wooldridge MA (1998) Roadmap of agent research and development. Auton Agents Multi-Agent Syst 1(1): 7–23CrossRefGoogle Scholar
  21. Mor94.
    Morgan CC (1994) Programming from specifications, 2nd edn. Prentice-Hall InternationalGoogle Scholar
  22. NOS+09.
    Nafz F, Ortmeier F, Seebach H, Steghöfer J-P, Reif W (2009) A universal self-organisation mechanism for role-based Organic Computing systems. In: González Nieto J, Reif W, Wang G, Indulska J (eds) International Conference on Autonomic and Trusted Computing (ATC-09), volume 5586 of LNCS. Springer-Verlag, Berlin, pp 17–31Google Scholar
  23. Omi99.
    Omicini A (1999) On the semantics of tuple-based coordination models. In: 1999 ACM Symposium on Applied Computing. ACM Press, New York, pp. 175–182Google Scholar
  24. OOR04.
    Omicini A, Ossowski S, Ricci A (2004) Coordination infrastructures in the engineering of multiagent systems. In: Bergenti F, Gleizes M-P, Zambonelli F (eds) Methodologies and software engineering for agent systems. Kluwer, MAGoogle Scholar
  25. OW05.
    O’Connor T, Wong HY (2005) Emergent properties. In: Zalta EN (eds) The Stanford encyclopedia of philosophy. Stanford University, StanfordGoogle Scholar
  26. PS05.
    Polack F, Stepney S (2005) Emergent properties do not refine. In: Derrick J, Boiten E (eds) International Refinement Workshop (Refine’05), volume 137, Issue 2 of Electronic Notes in Theoretical Computer Science. Elsevier, pp 163–181Google Scholar
  27. SS08.
    Sanders JW, Smith G (2008) Formal ensemble engineering. In: Wirsing M, Banâtre J-P, Hölzl M, Rauschmayer A (eds) Software-Intensive Systems and New Computing Paradigms: Challenges and Visions, volume 5380 of LNCS. Springer-Verlag, Berlin, pp 132–138CrossRefGoogle Scholar
  28. SS09a.
    Sanders JW, Smith G (2009) Refining emergent properties. In: Boiten E, Derrick J, Reeves S (eds) International Refinement Workshop (Refine 2009), volume 259 of Electronic Notes in Theoretical Computer Science. Elsevier, pp 207–233Google Scholar
  29. SS09b.
    Smith G, Sanders JW (2009) Formal development of self-organising systems. In: González Nieto J, Reif W, Wang G, Indulska J (eds) International Conference on Autonomic and Trusted Computing (ATC-09) volume 5586 of LNCS. Springer-Verlag, Berlin, pp 90–104Google Scholar
  30. vdM08.
    von der Malsburg C (2008) The organic future of information technology. In: Würtz RP (eds) Organic computing: understanding complex systems. Springer-Verlag, Berlin, pp 7–24Google Scholar
  31. WBHR08.
    Wirsing, M, Banâtre, J-P, Hölzl, M, Rauschmayer, A (eds) (2008) Software-Intensive Systems and New Computing Paradigms: Challenges and Visions, volume 5380 of LNCS. Springer-Verlag, BerlinGoogle Scholar
  32. Weg97.
    Wegner P (1997) Why interaction is more powerful than algorithms. Commun ACM 40(5): 80–91CrossRefGoogle Scholar
  33. Wei95.
    Weinberg S (1995) Reductionism redux. The New York Review of BooksGoogle Scholar
  34. Wei01.
    Weinberg S (2001) Facing up. Harvard University Press, CambridgeMATHGoogle Scholar
  35. WH05.
    De Wolf T, Holvoet T (2005) Towards a methodology for engineering self-organising emergent systems. In: Czap H, Unland R, Branki C, Tianfield H (eds) Self-Organization and Autonomic Informatics (I), volume 135 of Frontiers in Artificial Intelligence and Applications. IOS Press, AmsterdamGoogle Scholar
  36. WLNM08.
    Winfield A, Liu W, Nembrini J, Martinol A (2008) Modelling a wireless connected swarm of mobile robots. Swarm Intell 2: 241–266CrossRefGoogle Scholar
  37. Wür08.
    Würtz, RP (eds) (2008) Organic computing: understanding complex systems. Springer-Verlag, BerlinGoogle Scholar
  38. Zhu05.
    Zhu H (2005) Formal reasoning about emergent behaviour in MAS. In: International Conference on Software Engineering and Knowledge Engineering (SEKE’05)Google Scholar
  39. ZO04.
    Zambonelli F, Omicini A (2004) Challenges and research directions in agent-oriented software engineering. Auton Agents Multi-Agent Syst 9(3): 253–283CrossRefGoogle Scholar
  40. ZW07.
    Zapf M, Weise T (2007) Offline emergence engineering for agent societies. In: European Workshop on Multi-Agent Systems (EUMAS’07)Google Scholar

Copyright information

© British Computer Society 2011

Authors and Affiliations

  1. 1.International Institute for Software TechnologyUnited Nations UniversityMacaoSAR China
  2. 2.School of Information Technology and Electrical EngineeringThe University of QueenslandBrisbaneAustralia

Personalised recommendations