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

Yukio Gunji, Hisato Sadaoka, Keisuke Ito

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 languageEnglish
Pages (from-to)43-97
Number of pages55
JournalApplied Mathematics and Computation
Volume79
Issue number1
Publication statusPublished - 1996
Externally publishedYes

Fingerprint

Boolean algebra
Bootstrapping
Inconsistent
Algebra
Cellular automata
Biological systems
Logic
Observer
Interaction
Artificial Life
Cellular Automaton Model
Deduction
Hierarchical Structure
Biological Systems
Deduce
Estimate

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

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

In: Applied Mathematics and Computation, Vol. 79, No. 1, 1996, p. 43-97.

Research output: Contribution to journalArticle

@article{400cbbce006e4ab3bfb790e7ba2499d4,
title = "Bootstrapping system defined by inconsistent relation between boolean and non-boolean algebra",
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.",
author = "Yukio Gunji and Hisato Sadaoka and Keisuke Ito",
year = "1996",
language = "English",
volume = "79",
pages = "43--97",
journal = "Applied Mathematics and Computation",
issn = "0096-3003",
publisher = "Elsevier Inc.",
number = "1",

}

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.

UR - http://www.scopus.com/inward/record.url?scp=23644453453&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23644453453&partnerID=8YFLogxK

M3 - Article

VL - 79

SP - 43

EP - 97

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 1

ER -