On dynamically non-trivial three-valued logics: Oscillatory and bifurcatory species

Chaos, Solitons and Fractals

Volumn 18, Issue 5, 2003, Pages 917-936

  Adamatzky, Andrew ^a  

^a UNIVERSITY OF THE WEST OF ENGLAND   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CHEMICAL REACTORS; COMBINATORIAL MATHEMATICS; COMPUTATIONAL COMPLEXITY; FORMAL LOGIC;

THREE-VALUED LOGICS;

CHAOS THEORY;

EID: 0038238296     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(03)00063-8     Document Type: Article

References (46)

1. Adamatzky A. Pathology of collective doxa. Automata models. Appl. Math. Comput. 122:2001;195-228.
2. Adamatzky A. Computing in nonlinear media and automata collectives. 2001;IoP Publishing.
3. Adamatzky A. Chemistry of belief - experiments with doxastic solutions. Kybernetes. 30:2001;1199-1208.
4. Adamatzky A. Collision-based computing. 2002;Springer-Verlag, London.
5. Adamatzky A. On patterns in affective media. International Journal of Modern Physics C (2003), in press.
6. Adamatzky A. Hot choosey sand: reflection of grain sensitivity on pattern morphology. Int. J. Mod. Phys. 11:2000;47-68.
7. Berry G., Boudol G. The chemical abstract machine. Theor. Comput. Sci. 96:1992;217-248.
8. Belnap N.D. How a computer should think. Ryle G. Contemporary aspects of philosophy. 1977;Oriel Press.
9. Bergstra J.A., Bethke I., Rodenburg P. A propositional logic with 4 values: true, false, divergent and meaningless. J. Appl. Non-Class. Logics. 5:1995;199-218.
10. Bochvar D.A. On a three-valued calculus and its application to analysis of paradoxes of functional calculus of classical reasoning. Matematicheskij Sbornik. 4:1939;287-308. (in Russian).
11. Bolc L., Borowik P. Many-valued logics. 1992;Springer-Verlag, Berlin.
12. Chemical Kinetics Simulator 1.01, IBM's Almaden Research Centre. Available: http://www.almaden.ibm.com/st/msim/ckspage.html.
13. Chopard B., Droz M. Cellular automata modeling of physical systems. 1999;Cambridge University Press.
14. Dennet D. Consciousness explained. 1991;Penguin, London.
15. Derrida B., Pomeau Y. Random networks of automata: a simple annealed approximation. Biophys. Lett. 1:1986;45-49.
16. Derrida B. Dynamical phase transition in nonsymmetric spin glasses. J. Phys. A. 20:1987;L721-L725.
17. Dittrich P., Ziegler J., Banzhaf W. Artificial chemistries - a review. Artif. Life. 7:2001;225-275.
18. Fontata W, Buss LW. The barrier of objects: from dynamical systems to bounded organizations, SFI Working Paper 96-05-035. Santa Fe Institute, 1996.
19. Goles E., Hernández G. Dynamical behavior of Kauffman networks with AND-OR gates. J. Biol. Cyber. 8:2000;151-175.
20. Hameroff S., Penrose R. Conscious events as orchestrated space-time selections. J. Conscious. Studies. 2:1996;36-53.
21. Hameroff S. Quantum computation in brain microtubules? The Penrose-Hameroff Orch or model of consciousness. Philos. Trans. Roy. Soc. Lond. A. 356:1998;1869-1896.
22. Hameroff S. Consciousness, the brain, and spacetime geometry. Ann. N.Y. Acad. Sci. 929:2001;74-104.
23. Hameroff S., Nip A., Porter M., Tuszynski J. Conduction pathways in microtubules, biological quantum computation, and consciousness. Biosystems. 64:2002;149-168.
24. Helbing D. A fluid-dynamic model for behaviour of pedestrians. Complex Syst. 6:1992;391-415.
25. Helbing D, Molnár P, Schweitzer F. Computer simulation of pedestrian dynamics and trail formation, 1998. Available: xxx.lanl.gov/cond-mat/9805074.
26. Helbing D., Farkas I.J., Vicsek T. Simulating dynamical features of escape panic. Nature. 407:2000;487-490.
27. Hodes H. Three-valued logics: an introduction, a comparison of various logical lexica, and some philosophical remarks. Ann. Pure Appl. Logic. 43:1989;99-145.
28. Kacperski K., Holyst J.A. Opinion formation model with strong leader and external impact: a mean field approach. Physica A. 269:1999;511-526.
29. Kauffman S.A. Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22:1969;437-467.
30. Kauffman S.A. The origins of order: self-organization and selection in evolution. 1993;Oxford University Press.
31. Kleene S.C. On a notation for ordinal numbers. J. Symb. Logic. 3:1938;150-155.
32. Langton C.G. Computation at the edge of chaos: phase transitions and emergent computation. Physica D. 42:1990;12-27.
33. Łukasiewicz J. On three-valued logic. Ruch Filosoficzny. 3:1920;169-171. (in Polish).
34. McCullock W.S., Pitts W.H. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5:1943;115-133.
35. McMullin B, Varela FJ. Rediscovering computational autopoiesis. SFI Working Paper 97-02-012, Santa Fe Institute, 1997.
36. Miyakawa M., Rosenberg I.G., Stojmenović I. Classification of three-valued logical functions preserving 0. Discrete Appl. Math. 28:1990;231-249.
37. Nota G., Orefice S., Pacini G., Ruggiero F., Tortora G. Legality concepts for three-valued logic programs. Theor. Comput. Sci. 120:1993;45-68.
38. Plewczyński D. Landau theory of social clustering. Physics A. 261:1998;608-617.
39. Rescher N. Many-valued logic. 1969;McGraw-Hill.
40. Sobociński B. Axiomatization of partial system of three-valued calculus of propositions. J. Comput. Syst. 11:1952;23-55.
41. Varela F.J., Maturana H.R., Uribe R. Autopoiesis: the organization of living systems, its characterization and a model. Biosystems. 5:1974;187-196.
42. Volker L.G., Conrad M. The role of weak interactions in biological systems: the dual dynamics model. J. Theor. Biol. 193:1998;287-306.
43. Wuensche A. The ghost in the machine: basins of attraction of random boolean networks. Langton C.G. Artificial life III, Santa Fe Institute studies in the sciences of complexity. 1994;Addison-Wesley, Reading, MA.
44. Wuensche A. The emergence of memory; categorisation far from equilibrium. Hameroff S.R., Kaszniak A.W., Scott A.C. Towards a science of consciousness: the first tuscon discussions and debates. 1996;MIT Press, Cambridge, MA.
45. Zak M. Dynamics of intelligent systems. Int. J. Theor. Phys. 39:2000;2107-2140.
46. Zak M., Zbilut J.P., Meyers R.E. From instability to intelligence: complexity and predictability in nonlinear dynamics. 1997;Springer-Verlag.