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Anticipation in constructing and interrogating Natural Information


									Information Systems and the
   Theory of Categories:

  Is Every Model an Anticipatory
• M. A. Heather, Sutherland Building,
  Northumbria University, NE1 8ST,
• B. Nick Rossiter, Informatics, Northumbria
  University, Newcastle upon Tyne, UK, NE1
        Exploring the Unknown
• Knowledge advances:
   – by using the known to understand the unknown.
• Information systems are sources of the known
   – but also contain the unknown by reason of yet
     unrealised connections between what is known
• Practical applications in Data Mining
   – looking for new rules not explicit in data schema
         Advance of Categories
• The philosophy of idealism and categories, the
  limits and colimits of knowledge, have developed
   – classical Platonic idealism
   – Aristotolean categories
   –  through modern Kantian judgments
   – categories of pure and applied reasoning (analytic and
   – on to a postmodern formalism of topos theory
• To deal with organisms as complex, not just
  simple mechanisms:
   – modern information systems have to cope with:
      • dynamic,
      • open and
      • non-local nature of knowledge beyond set theory.
• Current interest with sketches.
Behaviour of Reactive System




   Reactive System
          Behavioural Aspects
• The figure represents the possible unknown
  behaviour of a reactive system whether physical,
  biological or social.
• The change may not be fully understood but may
  be modelled in an information system by a
  corresponding behavioural change
         Strength of Anticipation
• In the upper limiting case:
   – the universe is a reactive system
   – the information system belongs to it as a subcategory.
• Any other existing reactive system is a subcategory of the
  universe as a topos.
• If the information system is predictive:
   – termed anticipatory.
• Where the anticipatory is a subcategory of the reactive
  system it is often referred to as strong anticipation.
• Otherwise it is weak.
• However the strength of an anticipatory system is not just
  Boolean because the internal topos logic is Heyting.
• There are quantitative () and qualitative () degrees of
• The monad gives:
   – idempotent isomorphism
• The split epimorphism provides:
   – extensional equivalence
• A freely constructed slice provides:
   – information through
      • a right adjoint retract to the extent of the equivalence of the
        slice category,
   – that is any model including the predictive anticipatory
Formalisation of Anticipatory
  System -- Adjointness 
Formalisation of Anticipatory
  System -- Adjointness 
Formalisation as 2-cell -- Upper
            Limit 
Formalisation as 2-cell -- Lower
            Limit 
                 The question
• To model is to interrogate an information system.
• Prediction is relative to the observer and
  consequent to use and the type of query.
• Whether every model is an anticipatory system is
  a relativistic question of subjective locality in time
  and space.
[1] Heather, M A, & Rossiter, B N, Locality, Weak or Strong
   Anticipation and Quantum Computing I. Non-locality in
   Quantum Theory, International Journal Computing
   Anticipatory Systems 13 307-326 (2002).
 [2] Heather, M A, & Rossiter, B N, Locality, Weak or Strong
   Anticipation and Quantum Computing. II. Constructivism
   with Category Theory, International Journal Computing
   Anticipatory Systems 13 327-339 (2002).
 [3] Johnstone, P T, Sketches of an Elephant, A Topos Theory
   Compendium, Oxford Logic Guides 43, Clarendon (2002).
 [4] Rosen, R, Life Itself, A Comprehensive Inquiry into the
   Nature, Origin, and Fabrication of Life, Columbia
   University Press, New York (1991).

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