Rosen's modelling relations via categorical adjunctions

International Journal of General Systems 41 (5):439-474 (2012)
  Copy   BIBTEX

Abstract

Rosen's modelling relations constitute a conceptual schema for the understanding of the bidirectional process of correspondence between natural systems and formal symbolic systems. The notion of formal systems used in this study refers to information structures constructed as algebraic rings of observable attributes of natural systems, in which the notion of observable signifies a physical attribute that, in principle, can be measured. Due to the fact that modelling relations are bidirectional by construction, they admit a precise categorical formulation in terms of the category-theoretic syntactic language of adjoint functors, representing the inverse processes of information encoding/decoding via adjunctions. As an application, we construct a topological modelling schema of complex systems. The crucial distinguishing requirement between simple and complex systems in this schema is reflected with respect to their rings of observables by the property of global commutativity. The global information structure representing the behaviour of a complex system is modelled functorially in terms of its spectrum functor. An exact modelling relation is obtained by means of a complex encoding/decoding adjunction restricted to an equivalence between the category of complex information structures and the category of sheaves over a base category of partial or local information carriers equipped with an appropriate topology.

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 103,449

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Boolean information sieves: a local-to-global approach to quantum information.Elias Zafiris - 2010 - International Journal of General Systems 39 (8):873-895.
Category-theoretic analysis of the notion of complementarity for quantum systems.Elias Zafiris - 2006 - International Journal of General Systems 35 (1):69-89.
Interpreting observables in a quantum world from the categorial standpoint.Elias Zafiris - 2004 - International Journal of Theoretical Physics 43 (1):265-298.
Generalized topological covering systems on quantum events' structures.Elias Zafiris - 2006 - Journal of Physics A: Mathematics and Applications 39 (6):1485-1505.
Sheaf-theoretic representation of quantum measure algebras.Elias Zafiris - 2006 - Journal of Mathematical Physics 47 (9).

Analytics

Added to PP
2019-01-28

Downloads
37 (#640,129)

6 months
2 (#1,294,541)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

On Adjoint and Brain Functors.David Ellerman - 2016 - Axiomathes 26 (1):41-61.
Brain functors: A mathematical model for intentional perception and action.David Ellerman - 2016 - Brain: Broad Research in Artificial Intelligence and Neuroscience 7 (1):5-17.

Add more citations

References found in this work

No references found.

Add more references