### Abstract

We claim the using the formal biological system as a model evoking life must be much more unpredictable than Langton's guiding principle for artificial life, because any interaction is assumed to be computable in Langton's idea. In order to estimate nonlogical aspects of interactions which are not computable, we concentrate here on the relationship between a part and a whole. In other words, nonlogical aspects of interactions are articulated into the "prescription" described by a local observer and the " postscription" by a nonlocal observer. In this framework, we cannot deduce a prescribed local rule from a wholeness, and a local rule cannot be reduced from postscribed wholeness. We first show that such articulations with hierarchical structures result from descriptions involving measurements and/or observations. We propose a Bootstrapping system in which a local rule has two modes of descriptive manner: prescription, described in a logic a priori and a postscription, described in a logic a posteriori. We define cellular-automata fashioned model with a Bootstrapping system in adopting restricted Pseudo-Boolean algebra and Boolean algebra as a logic a priori and a posteriori, respectively, and show unpredictability underlying in the relation between a part and a whole, or deduction and reduction.

Original language | English |
---|---|

Pages (from-to) | 43-97 |

Number of pages | 55 |

Journal | Applied Mathematics and Computation |

Volume | 79 |

Issue number | 1 |

Publication status | Published - 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

### Cite this

*Applied Mathematics and Computation*,

*79*(1), 43-97.

**Bootstrapping system defined by inconsistent relation between boolean and non-boolean algebra.** / Gunji, Yukio; Sadaoka, Hisato; Ito, Keisuke.

Research output: Contribution to journal › Article

*Applied Mathematics and Computation*, vol. 79, no. 1, pp. 43-97.

}

TY - JOUR

T1 - Bootstrapping system defined by inconsistent relation between boolean and non-boolean algebra

AU - Gunji, Yukio

AU - Sadaoka, Hisato

AU - Ito, Keisuke

PY - 1996

Y1 - 1996

N2 - We claim the using the formal biological system as a model evoking life must be much more unpredictable than Langton's guiding principle for artificial life, because any interaction is assumed to be computable in Langton's idea. In order to estimate nonlogical aspects of interactions which are not computable, we concentrate here on the relationship between a part and a whole. In other words, nonlogical aspects of interactions are articulated into the "prescription" described by a local observer and the " postscription" by a nonlocal observer. In this framework, we cannot deduce a prescribed local rule from a wholeness, and a local rule cannot be reduced from postscribed wholeness. We first show that such articulations with hierarchical structures result from descriptions involving measurements and/or observations. We propose a Bootstrapping system in which a local rule has two modes of descriptive manner: prescription, described in a logic a priori and a postscription, described in a logic a posteriori. We define cellular-automata fashioned model with a Bootstrapping system in adopting restricted Pseudo-Boolean algebra and Boolean algebra as a logic a priori and a posteriori, respectively, and show unpredictability underlying in the relation between a part and a whole, or deduction and reduction.

AB - We claim the using the formal biological system as a model evoking life must be much more unpredictable than Langton's guiding principle for artificial life, because any interaction is assumed to be computable in Langton's idea. In order to estimate nonlogical aspects of interactions which are not computable, we concentrate here on the relationship between a part and a whole. In other words, nonlogical aspects of interactions are articulated into the "prescription" described by a local observer and the " postscription" by a nonlocal observer. In this framework, we cannot deduce a prescribed local rule from a wholeness, and a local rule cannot be reduced from postscribed wholeness. We first show that such articulations with hierarchical structures result from descriptions involving measurements and/or observations. We propose a Bootstrapping system in which a local rule has two modes of descriptive manner: prescription, described in a logic a priori and a postscription, described in a logic a posteriori. We define cellular-automata fashioned model with a Bootstrapping system in adopting restricted Pseudo-Boolean algebra and Boolean algebra as a logic a priori and a posteriori, respectively, and show unpredictability underlying in the relation between a part and a whole, or deduction and reduction.

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M3 - Article

VL - 79

SP - 43

EP - 97

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 1

ER -