## Data Structures in Natural Computing: Databases as Weak or Strong Anticipatory Systems

Citations: | 2 - 2 self |

### BibTeX

@MISC{Rossiter_datastructures,

author = {B. N. Rossiter and M. A. Heather},

title = {Data Structures in Natural Computing: Databases as Weak or Strong Anticipatory Systems},

year = {}

}

### OpenURL

### Abstract

Abstract. Information systems anticipate the real world. Classical databases store, organise and search collections of data of that real world but only as weak anticipatory information systems. This is because of the reductionism and normalisation needed to map the structuralism of natural data on to idealised machines with von Neumann architectures consisting of fixed instructions. Category theory developed as a formalism to explore the theoretical concept of naturality shows that methods like sketches arising from graph theory as only non-natural models of naturality cannot capture real-world structures for strong anticipatory information systems. Databases need a schema of the natural world. Natural computing databases need the schema itself to be also natural. Natural computing methods including neural computers, evolutionary automata, molecular and nanocomputing and quantum computation have the potential to be strong. At present they are mainly at the stage of weak anticipatory systems.

### Citations

2256 |
The Unified Modeling Language User Guide
- Booch, Rumbaugh, et al.
- 1999
(Show Context)
Citation Context ...ject is included in another object to give a pointer-based approach. Relationships are often performed in a separate process such as earlier Entity-Relationship Modelling or current Unified Modelling =-=[9]-=-. Normalisation is needed to verify schema design, particularly to relate key and non-key attributes. The levels, mappings and relationships all have to be integrated in a consistent database design. ... |

968 |
Categories for the Working Mathematician
- Lane
- 1971
(Show Context)
Citation Context ...ic has been known for some time its possible great significance as the fundamental underlying logic of the world is only now just emerging 5 because it is the natural internal structure of a topos. 5 =-=[44]-=-; it is to be noted that Mac Lane’s Category Theory for the Working Mathematician does not deal with Heyting logic even in his second edition although it was referred to in [45] in 1991.s3 NATURAL SCH... |

892 | A fast quantum-mechanical algorithm for database search
- Grover
- 1996
(Show Context)
Citation Context ...r approach to naturality. Following the seminal work of Deutsch [15], Shor [58] was able to produce a quantum version of the fast Fourier transform requiring only n 2 rather than (2n) n steps. Grover =-=[28]-=- developed this idea of using quantum algorithms for faster searching of databases. Selinger [57] has produced a collection of operations at such a level that they could form the basis of a quantum pr... |

418 |
Category theory for computer science
- Barr, Wells
- 1999
(Show Context)
Citation Context ...6 show what happens when an arrow maps between two natural transformations. So an arrow from one natural transformation to another gives a composition of the natural transformations, not a new level (=-=[7]-=-, at p.85). This means that four levels are needed to give the natural closure [33]. Two squares, derived from Figure 4, are shown. Figure 5(a) commutes for each arrow f : cpt −→ cst if α is a natural... |

411 | Introduction to Evolutionary Computing
- Eiben, Smith
- 2003
(Show Context)
Citation Context ...umann’s self-reproducing cellular automata the assumption has to be made that the underlying rules are self-consistent [59]. Data applications have already begun using neural and evolutionary methods =-=[23]-=- for data classification with potential for data mining and network analysis or synthesis for use in schedules, timetables and financial and business models [40]. Molecular computing on the other hand... |

369 |
Three models for the description of language
- Chomsky
- 1956
(Show Context)
Citation Context ...normal forms and Skolem functions related to Horn clauses equivalent to a universal Turing machine [1]. In natural language processing formal grammars have been normalised in types 0,1,2,3 by Chomsky =-=[13]-=-. In Rosen’s terms data in the world is a reactive system anticipated by normalisation and within Dubois’ distribution of weak or strong [18], the normal form is a weak anticipatory system of the data... |

351 |
Rapid solution of problems by quantum computation
- Deutsch, Jozsa
- 1992
(Show Context)
Citation Context ...f the data will nevertheless still be in conventional form with the only advantage so far of an increase in speed rather than as a closer approach to naturality. Following the seminal work of Deutsch =-=[15]-=-, Shor [58] was able to produce a quantum version of the fast Fourier transform requiring only n 2 rather than (2n) n steps. Grover [28] developed this idea of using quantum algorithms for faster sear... |

210 | Fault-tolerant quantum computation
- Shor
- 1996
(Show Context)
Citation Context ...will nevertheless still be in conventional form with the only advantage so far of an increase in speed rather than as a closer approach to naturality. Following the seminal work of Deutsch [15], Shor =-=[58]-=- was able to produce a quantum version of the fast Fourier transform requiring only n 2 rather than (2n) n steps. Grover [28] developed this idea of using quantum algorithms for faster searching of da... |

102 |
Life Itself: a Comprehensive Inquiry into the Nature , Origin and Fabrication of Life
- Rosen
- 1991
(Show Context)
Citation Context ...entanglement. There is the further constructive (Brown [11] Chapter 8) characteristic of natural world parallelism that it is selfconsistent. For instance cellular automata are in Rosen’s terminology =-=[54]-=- reactive systems but with a much simplified version of the laws of physics operating between cells. In von Neumann’s self-reproducing cellular automata the assumption has to be made that the underlyi... |

71 |
Evolution of parallel cellular machines: The cellular programming approach
- Sipper
- 2004
(Show Context)
Citation Context ...much simplified version of the laws of physics operating between cells. In von Neumann’s self-reproducing cellular automata the assumption has to be made that the underlying rules are self-consistent =-=[59]-=-. Data applications have already begun using neural and evolutionary methods [23] for data classification with potential for data mining and network analysis or synthesis for use in schedules, timetab... |

68 |
Accessible Categories: the Foundations of Categorical Model Theory
- Makkai, Parè
- 1989
(Show Context)
Citation Context ...epresentation of Plato’s ideals but thought that this could be achieved by relaxing some categorical requirements. The first two senses above follow Ehresmann’s general approach [21]. The third sense =-=[49]-=- develops small, complete accessible categories as a mapping from sketches to a 2-cell categorial model. It is the first two that have been employed in work on database theory. In the database area sk... |

63 |
Theorie des faisceaux
- Godement
(Show Context)
Citation Context ... from P to P ′ ). Following the constructive principles of category theory, the composition of these arrows is natural. This consequently gives rise to a natural calculus first expounded by Godement (=-=[27]-=-; [7], pp 94-97) in the form of rules governing composition. The composition of functors and natural transformations is associative so that for instance: (I ′ O ′ )α = I ′ (O ′ α); γ(OP) = (γO)P Natur... |

62 |
Abelian Categories, an Introduction to the Theory of Functors
- Freyd
- 1964
(Show Context)
Citation Context ...provide ultimate systemic closure in unique strong anticipation. Between the four levels are three layers of adjoint 3 It was for this reason that the early categorists referred to abelian categories =-=[25]-=- where statements were identically true up to natural isomorphism if they held in the dual category obtained by reversing the arrows. 4 There is a typographical error in the diagram on p.247 of Johnst... |

36 | Computational capacity of the universe
- Lloyd
(Show Context)
Citation Context ... of the reactive system of the environment. 1 See Pagels [50] where however the Universe is treated more as a classical computer and thus a weak anticipatory system. As such by now according to Lloyd =-=[42]-=- the Universe could have factored a million bit number using classical methods or a 10 60 bit number using Shor’s quantum algorithm mentioned below.s1.2 Classical Data Structures Classical information... |

34 | Algebraic graph-based approach to management of multibase systems, I: Schema integration via sketches and equations
- Cadish, Diskin
- 1995
(Show Context)
Citation Context ... constraints, R is a finite set of discrete cones in E giving the relationships and S a finite set of discrete cocones in E specifying the attributes. Sketches have also been employed by Diskin et al =-=[16]-=- for modelling information systems, in particular again the ER model. His use of sketches follows the method identified by Johnstone as type (b) i.e. finitary product sketches in which S is empty and ... |

31 |
An elementary theory of the category of sets
- Lawvere
- 1964
(Show Context)
Citation Context ...topos. However, because of the importance of natural numbers for the modelling of properties of weak anticipatory systems, categorists introduce the natural number object from a suggestion by Lawvere =-=[41]-=- as categorical formulation of the axiom of infinity ([38] p.108). The natural number object in a category C is defined by the following commuting diagram in Figure 8. The terminal object 1 identifies... |

30 |
Zermelo’s Axiom of Choice
- Moore
- 1982
(Show Context)
Citation Context ...the whole of formal axiomatic set theory seems to rest on the ultimate basis that it works in practice. This stance is confirmed by Feferman [24] who highlights the role of the axiom of choice (Moore =-=[48]-=-). It is exercise of the choice that reduces strong anticipation to weak anticipation [31, 32].sThe mathematics within the sights of Maddy and Feferman is concerned mostly with collections and operati... |

24 |
Review of incursive, hyperincursive and anticipatory systemsFoundations of anticipation in electromagnetism. Computing Anticipatory Systems
- Dubois
- 2000
(Show Context)
Citation Context ...atory system is a local or small subcategory [32]. A classical computer is a weak anticipatory system where its output by means of software interprets the states of its hardware operating as a strong =-=[53, 17, 18]-=- anticipatory system. Weak anticipation can be very accurate even for non-linear phenomena like weather forecasting where the data capture and data processing can be on a large enough scale to contain... |

19 |
Foundation for future database systems: the third manifesto
- Date, Darwen
- 2000
(Show Context)
Citation Context ... andsreal-world performance and pragmatics. Triggers are an example of an attempt to patch the weakness of the system by providing some local strong anticipation using Event- Conditions-Actions (ECA) =-=[14]-=-. Concepts Policy ⊣ MetaMeta ✻ MetaMeta ✻ Policy ❄ Constructs Org ⊣ Meta Sys Platform Meta ✻ Org ❄ Schema ❄ Instance ⊣ Classi f y Classify ✻ Instance ❄ Data mission management enterprise information e... |

19 |
The Continuum: A Critical Examination of the Foundation of Analysis
- Weyl
- 1987
(Show Context)
Citation Context ...s f ,g as: A � ❅ � ❅ �f � ��✠ B g ❅ g f ❅❅❘ ✲ A ❅ ❅❅❅❅❘ f g � f � � � ��✠ B FIGURE 3. Composition of Identity Triangles 2 “daßjenes Haus zu einem wesentlichen Teil auf Sand gebaut est”, Das Kontinuum =-=[64]-=-, Vorwort p.ivsf : A −→ B g : B −→ A then there is an isomorphism between A and B when f ,g are mutually inverse. This may be written as A = B and B = A. The proof diagram for this is Figure 3 which d... |

18 | On constructing a molecular computer, DNA Based Computers, in - Adleman - 1996 |

18 |
Introduction to Computing Anticipatory Systems
- Dubois
- 1988
(Show Context)
Citation Context ...atory system is a local or small subcategory [32]. A classical computer is a weak anticipatory system where its output by means of software interprets the states of its hardware operating as a strong =-=[53, 17, 18]-=- anticipatory system. Weak anticipation can be very accurate even for non-linear phenomena like weather forecasting where the data capture and data processing can be on a large enough scale to contain... |

17 |
Introduction to the theory of structured categories
- Ehresmann
- 1966
(Show Context)
Citation Context ...mal sketches as an adaption of graph theory. Data processing in natural computers provides a good theoretical testing ground for the approach. The sketch was originally presented by Charles Ehresmann =-=[21]-=- as a culmination of work on structured categories, in particular the notion of an internal category in any category under the name of catégorie structurée généralisée [19]. Wells [62] claimed that th... |

16 |
The Cosmic Code: Quantum Physics as the Language of Nature
- Pagels
- 1982
(Show Context)
Citation Context ...ental work in biology. Processes in vivo are naturally strong, those in vitro are naturally weak because they are locally constrained as a part of the reactive system of the environment. 1 See Pagels =-=[50]-=- where however the Universe is treated more as a classical computer and thus a weak anticipatory system. As such by now according to Lloyd [42] the Universe could have factored a million bit number us... |

15 |
Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures
- Brown
- 1999
(Show Context)
Citation Context ...processes in chemistry to compute the viable from all possible physical configurations. 4. Quantum computation exploits the parallel property of entanglement. There is the further constructive (Brown =-=[11]-=- Chapter 8) characteristic of natural world parallelism that it is selfconsistent. For instance cellular automata are in Rosen’s terminology [54] reactive systems but with a much simplified version of... |

14 |
Quantum computation — a review
- Aharonov
- 1998
(Show Context)
Citation Context ...omputing listed above may be modelled on traditional computers which may be illuminating but can have no predictive power beyond the weak anticipatory system. As pointed out in the review by Aharonov =-=[4]-=- the Grover iteration can be understood as a product of two reflections. In this way Bhattacharya et al [8] have implemented a quantum search algorithm showing that classical waves can search a N-item... |

14 |
Rapid sampling through quantum computing
- Grover
- 2000
(Show Context)
Citation Context ... in the data. Shor’s algorithm is a look up of a natural number type. For this same reason an ordinary computer can be programmed to model the operation of a quantum computer with Grover’s algorithms =-=[29]-=- but only as a weak classical model of quantum processing and therefore very inefficiently. It will also be true to say that any of the four types of natural computing listed above may be modelled on ... |

14 |
Sketches of an Elephant: A Topos Theory
- Johnstone
- 2002
(Show Context)
Citation Context ...ors (conventionally F,G). Furthermore if in Figure 3 A,B are functors and f ,g are natural transformations (conventionally φ,γ) f g = g f are the identity natural transformations (1 φ ,1γ) (Johnstone =-=[38]-=- p.247-248 A1.1.7-1.1.8) 4 . The result is no different if ordinary A,B represent natural transformations. This is natural isomorphism which operates as a natural closure. 2.2 Natural Closure CST ✲SCH... |

7 |
Massively Parallel Computing with the DAP
- Parkinson, Litt
- 1990
(Show Context)
Citation Context ...l von Neumann architecture. Nevertheless interest in alternative approaches continued through the latter part of the century particularly in the use of parallelism. Attempts in the 1980s like the DAP =-=[51]-=- to produce parallel machines based on digital hardware of the time failed to compete with the power of the serial machines because of the complexity issues inherent in parallel methods 8 . The natura... |

6 |
Weak or Strong Anticipation and Quantum Computing I
- Heather, Rossiter, et al.
- 2002
(Show Context)
Citation Context ... in practice. This stance is confirmed by Feferman [24] who highlights the role of the axiom of choice (Moore [48]). It is exercise of the choice that reduces strong anticipation to weak anticipation =-=[31, 32]-=-.sThe mathematics within the sights of Maddy and Feferman is concerned mostly with collections and operations that exist only in the mind. These can be very fruitful in so far as they have an existenc... |

5 |
2002]: `Implementation of Quantum Search Algorithm using Classical Fourier Optics
- Battacharya, Heuvell, et al.
- 2002
(Show Context)
Citation Context ...edictive power beyond the weak anticipatory system. As pointed out in the review by Aharonov [4] the Grover iteration can be understood as a product of two reflections. In this way Bhattacharya et al =-=[8]-=- have implemented a quantum search algorithm showing that classical waves can search a N-item database just as efficiently. It is claimed that although the lack of quantum entanglement limits the data... |

5 | Database techniques for text modelling: the document architecture of British statutes, Computing Laboratory - Heather, Rossiter - 1987 |

5 |
The Computing Universe
- Zuse
- 1982
(Show Context)
Citation Context ...ms. Keywords: Naturality, Sketches, Natural Computing, Database Schema, Quantum Data Computation 1 INTRODUCTION 1.1 Computation as an Anticipatory System The Universe as a natural computer calculates =-=[65]-=- its new configuration at every instant of Planck space-time 1 . This computation operates as the ultimate anticipatory system: every other [53] is but its pale reflection. Formally a strong anticipat... |

4 | Emergence Processes up to Consciousness Using the Multiplicity - Ehresmann, Vanbremeersch - 2002 |

3 |
The Anticipatory and Systemic
- Heather, Rossiter
- 2002
(Show Context)
Citation Context ...sed ANSI/SPARC The classical ANSI/SPARC architecture of Figure 1 has the disadvantage that the levels are not independent of each other. This may be compared with the natural architecture of Figure 2 =-=[33]-=-. The four levels (top-down) are categories for concepts (real-world abstractions), constructs (facilities available for schema design), schema (definition of data types available in system) and data ... |

3 |
Towards a quantum programming language.” http://quasar.mathstat.uottawa.ca/ selinger/papers.html
- Selinger
- 2002
(Show Context)
Citation Context ...ce a quantum version of the fast Fourier transform requiring only n 2 rather than (2n) n steps. Grover [28] developed this idea of using quantum algorithms for faster searching of databases. Selinger =-=[57]-=- has produced a collection of operations at such a level that they could form the basis of a quantum programming language. Both offer potential for the development of quantum databases. In databases G... |

2 |
Sketches: Outline with References. http://www.cwru.edu/artsci/math/wells/pub/pdf/sketch.pdf
- Wells
- 1993
(Show Context)
Citation Context ... be defined for all composable pairs) plus specified cones and/or cocones (Ehresmann [22]). 2. a graph with specified cones and/or cocones plus some commutativity conditions on paths (Barr [7], Wells =-=[61]-=-). 3. a category with specified cones and/or cocones. Apparently at the time Ehresmann had in mind the need for a formal representation of Plato’s ideals but thought that this could be achieved by rel... |

1 |
Clause Logic, Walla Walla
- Aaby, Horn
- 1999
(Show Context)
Citation Context ...be interaction. For instance programming languages are often described in BNF 7 . In logic there are normal forms and Skolem functions related to Horn clauses equivalent to a universal Turing machine =-=[1]-=-. In natural language processing formal grammars have been normalised in types 0,1,2,3 by Chomsky [13]. In Rosen’s terms data in the world is a reactive system anticipated by normalisation and within ... |

1 |
A Programming Environment for DNA
- Carroll
- 2002
(Show Context)
Citation Context ...ine where the first and last pairs respectively complement each other) in some sequence can be treated as a bit-stream memory complex. The processing of these can be halved by using the Sticker model =-=[12]-=- which treats subsequences of the bases as a bit value 1 or its complementary subsequence (a sticker) as a bit value 0. Subsequences are unique and it is therefore possible to construct a programming ... |

1 |
On differentiable categories
- Ehresmann
- 2002
(Show Context)
Citation Context ...sented by Charles Ehresmann [21] as a culmination of work on structured categories, in particular the notion of an internal category in any category under the name of catégorie structurée généralisée =-=[19]-=-. Wells [62] claimed that the word sketch is used with at least three meanings: 1. a structure which is a weakening of the concept of category (the composite may not be defined for all composable pair... |

1 |
Oeuvres complètes et commentées Parts I to IV
- Ehresmann
- 1980
(Show Context)
Citation Context ...with at least three meanings: 1. a structure which is a weakening of the concept of category (the composite may not be defined for all composable pairs) plus specified cones and/or cocones (Ehresmann =-=[22]-=-). 2. a graph with specified cones and/or cocones plus some commutativity conditions on paths (Barr [7], Wells [61]). 3. a category with specified cones and/or cocones. Apparently at the time Ehresman... |

1 |
Database Searching
- Heather, Rossiter
- 2002
(Show Context)
Citation Context ...es use of the ’oracle’, treated as a black box and used for collapsing the wave function, that is to determine when a solution has been derived. However, this form of the oracle may lack non-locality =-=[34]-=-. The present position in data processing by natural computing may be summed up in the table below in Figure 11 by classifying each of the four subclasses in respect of their power as weak or strong a... |

1 |
Classical to Quantum Databases with Applied Pullbacks
- Rossiter, From
- 2003
(Show Context)
Citation Context ...apping between one functor and another. It needs to be emphasised that none of these categories are discrete: all have an internal arrow-based structure so the natural transformations are non-trivial =-=[55]-=-. The functors need to be of the same variance for a meaningful natural transformation to exist between them and this is the case for α, β and γ. An arrow comparing natural transformations is itself a... |

1 | Four-level Architecture for Closure
- Rossiter, Heather
(Show Context)
Citation Context ...s indicated by the op superscript. The earlier natural transformations were comparing the downward functorial mapping (towards data) while the current ones compare the upward mapping (away from data) =-=[56]-=-. alternative fundamental levels O ′ (g) category theory levels four levels of Figure 4 1. data values objects (identity arrows) id dat 2. named values category DAT 3. classified values functor C : DA... |

1 |
On sketches, Archive, Categories List ftp://tac.mta.ca/pub/categories
- Wells
- 2001
(Show Context)
Citation Context ...arles Ehresmann [21] as a culmination of work on structured categories, in particular the notion of an internal category in any category under the name of catégorie structurée généralisée [19]. Wells =-=[62]-=- claimed that the word sketch is used with at least three meanings: 1. a structure which is a weakening of the concept of category (the composite may not be defined for all composable pairs) plus spec... |