fundamentals of
Information technology from cognitive
point of view
Algirdas
Budrevičius
Vilnius University, Saulėtekio 9, I, Vilnius. E-mail: algirdas.budrevicius@kf.vu.lt. WWW: www.kf.vu.lt/~albud
This
paper was presented at the
Conference
Information Technologies 2001,
held at
Kaunas University of Technology in
Kaunas, January 30-31,
2001. Printed version forthcoming in
the Proceedings of the Conference by the end of the
year 2001.
The conditions
required for a computational device to operate with the meaning of information
are analysed. Computation is treated as operations that are carried out over
representations. General theory of signs (Peircean semiotics) and the
measurement theory are used to describe a
representation. Definition of computation is proposed to be based on the
permissible operations carried out over representations. Five basic
levels of computation (according to basic types of signs, and levels, or
scales, of measurement) are obtained as a result. The levels correspond to the extent
of the meaning that is preserved in processing of information: from its absence
at the first level (or a "0-level"), until its full presence at the
highest level. The first two levels are viewed as the types of computation that
make a basis of a digital computer and of an artificial neural network,
accordingly. Three next levels are considered as a basis to develop the
advanced computing architectures. Their features are predicted. In this paper,
the meaning is considered as an irreducible phenomenon. Such was a conclusion
of the previous research in developing an intelligent software agent for
helping a user in formulating his query to a textual database.
Computation, defined
according to Turing [1], is not related to meaning of information. The meaning
was excluded from the consideration in the early stages of the development of
information processing devices. A reason was to simplify the processing of
information.
The challenge of
information society stresses the role of human as a part of the information
system. A human is capable to process information in a most complicated way,
including the treatment of its meaning. A relatively new direction in science,
the cognitive science (its history see, for example in [2]), considers information
processing in artificial and natural environment. It uses the similar, that is,
the computational models, in particular [3]. Cognitive science treats
information as a complex phenomenon as well. The aspect of meaning is also
taken into account.
In this paper, an attempt is made to define the conditions required for
a computational device to operate with the meaning of information. The main
premises of this paper are as follows: 1) The meaning should be considered as a
unique and irreducible phenomenon, 2) Operations with meaning should be put
into the elementary basis of a computational device.
The main idea of
this paper evolved from the development of a human-computer interaction system.
The system was designed to help a user in formulating his query to the textual
database. The system may be attributed to the intelligent software agents as
well. One of the tasks considered was a measurement of the meaning of
information contained in a query. The theory of measurements was used for this
purpose. The measurements of meaning were considered as a membership function
of a fuzzy set that described the query. The process of the query formulation
then was described by the formal operations with fuzzy sets [4]. One idea of
the used approach was of a special importance then and now, for this paper: the
logical structure of the model used to describe the query must be in accordance
with the logical structure of the empirical data. Therefore, it was necessary
for the considered fuzzy sets to have the measurements of the ordinal level at
least. This condition also meant, that certain (the ordinal) level of the
meaning was preserved operating with the fuzzy representations of the query.
The query meaning was measured, processed and presented without decomposing it
into units that are more elementary. That is, the meaning was considered as an
irreducible element. The research was described in a monograph [5].
From the point of
view of cognitive science, there are two basic ideas that are used to account
for the cognition and the functioning of a computer. These are the ideas of
computation and representation. Computation idea primarily belongs to computer
science, and representation idea to semiotics, philosophy, and some other
sciences. Representations exist both in artificial and natural cognition
processes. There are various types of representations: data structures in a
digital computer; patterns in an artificial neural network; images, ideas,
memories in a human brain. The functioning of a computer, and a process of
human cognition is viewed in cognitive science similarly, that is, as
operations performed over representations. The idea of computation
traditionally implies a syntactical processing of information where the meaning
is ignored. A proposal of this paper is to modify the traditional idea of
computation so, that the meaning is taken into account. Firstly, the idea of
representation is analysed.
The idea of representation, according to the Encyclopaedia of Cognitive
Science [3], has its roots in the general theory of signs (Peircean semiotics)
[6]. Representation is the basic idea for this theory: every sign is a
representation. A sign (and representation, thus) is defined by three
components: sign, interpretant (meaning) and object. Ogden and Richards [7]
proposed in 1923 a term "meaning triangle" (or "semiotic
triangle") for the same triadic definition of sign. Peirce has described
three basic types of signs [6]: "There are three kinds of signs. Firstly,
there are likenesses, or icons; which serve to convey ideas of the
things they represent simply by imitating them. Secondly, there are indications,
or indices; which show something about things, on account of their being
physically connected with them. (
). Thirdly, there are symbols, or
general signs, which have become associated with their meanings by usage".
Icons are further classified into three types: metaphors, diagrams, and
pictures (or icons, again). In total thus, according to Peirce, there are five
types of signs: symbols, indices, metaphors, diagrams and pictures (or icons).
Representation is
also the basic idea in the measurement theory [8]. A measurement M is defined
as a homomorphic representation (or homomorphism) of the empirical system E
(that is, of what is measured) into a numerical system C (it consist of numbers
to be considered as measurements). A homomorphism [9] is a mapping of a
mathematical set (here it is the empirical system E) into or onto another set
or itself (here into the numerical system C). The mapping must be performed in
such a way that the result obtained by applying the operations to elements of
the first set is mapped onto the result obtained by applying the corresponding
operations to their respective images in the second set. A measurement M is
presented formally as a triad:
{E, C, M:EàC}.
According to the
idea of homomorphism, the same relations must hold between the elements of E, C
and M. Relations are explored and described most extensively in the theory of
relations, where they are considered by defining their formal features.
An equivalence
relation, for example, is defined as a relation between
elements of a set that is symmetric, reflexive, and transitive and for any two
elements either holds or does not hold. The three listed elementary logical features for the elements e1,
e2 and e3 of the empirical system E, are defined as
follows (the sign à denotes an implication):
The reflexivity: e1=e1;
The symmetricalness:
e1=e2 à e2=e1;
The transitivity: e1=e2,
e2=e3 à e1=e3.
A more complex one
is a relation of the order. Further it will be denoted also using the notations
of > and <.
There are five basic
types (or levels, or scales) of measurements: 1) nominal, 2) ordinal, 3)
interval, 4) ratio, and 5) absolute. They are defined by certain sets of
relations. Thus, there are five types of the homomorphic representations as
well. It should be reminded, that the same number of basic types of
representations was mentioned earlier, when representation was considered from
the semiotic point of view.
The first two levels
of measurement, that is, the nominal and the ordinal measurements, are often
considered as qualitative measurements, because they are not numbers in their
usual sense; the nominal measurement is only a name (from the Latin nomen,
the name), the ordinal measurement is only a rank. The other three, that is,
the interval, ratio and absolute measurements are quantitative measurements,
and they are numbers. Such numbers, however, differ in their sense and formal
features.
According to the
measurement theory, certain restrictions are imposed upon operations with
measurements. An operation is permissible, if it is compatible with the logic
of the empirical system. A set of permissible operations is defined for each
level of measurement. For the nominal measurements, for example, only
operations that determine the equivalence of measurements are permissible. For
the ordinal measurements, an operation of ranking is permissible, but addition
operation still is not permissible. Further, for the interval measurements, operation
of addition is already permissible, but multiplication is still not allowed.
For the ratio level measurements, both operations, the addition and
multiplication, are already permissible. Finally, for the absolute level
measurements, all the algebraic operations are permissible. More about the
measurements see in [8].
By uniting the two
aspects, that is, the representation as sign and measurement, there may be
obtained important conclusions. First, the relation between the two aspects
should be stated more precisely. For this purpose, the ingredients of the
semiotic triangle that describes a model of the sign and the components of the
triad of the measurement are placed in a table (see Table 1).
Table 1.
Representation as sign and measurement: the ingredients.
|
1 |
2 |
3 |
|
Representation (as sign) |
Interpretant |
Object |
|
Representation (as measurement) |
Numerical system C |
Empirical system E |
For the main idea of
this paper, it is important to stress the role of permissible operations that
are applied to representations as measurements. Now, the idea of permissible
operations may be extended also for the signs that are considered as measurements.
Thus, for symbols (a symbol here is only one type of a sign), only the simplest
operations may be applied: the symbols can be compared to determine their
equivalence, and the only operation of denotation is permissible. For indices
(here it is a type of a sign) the permissible operations are as follows:
determining of the equivalence and ranking of the elements.
In case, when not
permissible operations are applied, a representation is distorted or destroyed,
because the relation between the object and sign is distorted or destroyed. The
meaning triangle is distorted or destroyed accordingly, and a representation
seizes to be a representation. So, the meaning is not preserved, when not
permissible operations over representations are used.
Digital computer operates upon symbolic representations. The 0 and 1 are
two elementary representations here. The complex representations (data
structures) are built out of these two representations. Formal logic is applied operating with
symbolic representations. Only equivalence relation among the elementary
symbols can be established. No other meaning than the conventional one there
can be attributed to symbolic representations. Thus, the elementary
representations in digital computer may be considered as being of the nominal
type. This statement, however, should be admitted as a hypothesis.
Artificial neural
network consist of formal neurons that are the elementary information
processing units. A formal neuron is a simplified model of a real neuron. The
neuron in certain state is an elementary representation for an artificial
neural network. The main feature of the formal neuron is its capability to accumulate
the input signal and to produce a signal at the output, when the accumulated
value exceeds a threshold value. The neuron, thus, implements a threshold
element. Consequently, the relation of order is determinant for description of
its functioning.
Artificial neural
networks are widely used in pattern recognition. For such task, namely, the
ranking operation is of special importance. This fact well fits with the above
statement, that the artificial neural networks may be viewed as the ordinal (or
indexical) type representations.
Thus,
representations in an artificial neural network may be viewed as being of the
ordinal (or indexical) type. Again, such statement, however, should be admitted
as a hypothesis.
Computation is often
described as manipulation with symbols according to given rules. Traditional
definition of computation is given by Searle [10]:
"A Turing
machine can carry out certain elementary operations: It can rewrite a 0 on its
tape as a 1, it can rewrite a 1 on its tape as a 0, it can shift the tape 1
square to the left, or it can shift the tape 1 square to the right. It is
controlled by a program of instruction and each instruction specifies a
condition and an action to be carried out if the condition is satisfied."
Turing himself gives
the full original definition in [1].
Digital computation as a nominal level
computation. In Turing's definition
of computation, there are two elementary representations: 0 and 1. There are
also elementary operations with 0 and 1. These operations can be described by
means of the Boolean algebra. It was concluded earlier, that representations
here are of the nominal type. The digital computation, thus, may be viewed as
operating with the nominal representations.
Neural computation as an ordinal type computation. The idea to carry out computations by means of
the neural networks dates back to the 1943, when McCulloch and Pitts [11]
proposed a "logical calculus of ideas". The definition of computation
given by Turing does not suit directly for neural networks. There are no
formalized rules here for processing of information. There are no symbols in
neural networks, and processing of information cannot be accounted for as
manipulation with symbols.
For the artificial
neural network patterns that were considered earlier as the ordinal level
representations, in particular, there may be considered operations that are
defined for fuzzy sets; see, for example the seminal paper by Zadeh [12].
Operations with fuzzy sets are described in terms of determining the maximums and minimums of the membership function.
Such operations are permissible for the ordinal representations. Thus, fuzzy
algebra may be (and, actually, it is) applied to describe the functioning of an
artificial neural network; similarly as Boolean algebra is applied for the
nominal level computation. The fuzzy models, however, are not the only possible
choice.
Thus, a hypothesis
may be proposed, that computation in an artificial neural network may be
accounted for as operations that are carried out over representations of the
ordinal level.
Etymology of the
term "computation".
The Websters dictionary explains the word "to compute" as follows:
"to determine, as amount, by reckoning". The word
"computation" has its roots in Latin: "computare" =
"cum + putare", and the latter means "with + to count, to
think". So, from the linguistic point of the view, the term computation
could be used to denote a broader idea, even including the meaning "to
think".
Approach to the
definition of the extended (advanced) computation. Following the approach of cognitive science, the
idea of computation here is considered in an unbreakable relation to the
representation. Representation then is considered from the semiotic point of
the view, that is, as consisting of a sign, an interpretant and an object.
Then, each level of representation, following the measurement theory approach,
is related to an appropriate set of permissible operations. Computation finally
is defined by a set of permissible operations.
The logical sequence
of definition may be presented as follows: Representation à {sign, interpretant, object} à {five basic levels of representation} à {permissible operations} à computation.
According to such
approach, there are five basic levels of computation also. The first two levels
form the fundamentals of conventional (digital) computers and of the artificial
neural networks, respectively.
As a factor that determines a level of
computation, the meaning of information that is preserved in computation may be
considered. The first level, that is, the nominal level of computation
corresponds to the conventional (free) meaning. No motivated relation there
exists between an object and a sign here. For this reason, the nominal level of
computation (and the level of meaning) should be denoted as a
0-level.
Definition and
features of the basic levels of
computation. A k-level (where k=0,1,
4) computation is defined by the
permissible operations that may be carried out over the corresponding k-level
representations. The features of the first two levels of computation were
described earlier. Here are some statements to outline the main features of the
2-, 3-, and 4-level that corresponds to an interval, ratio and absolute levels
of computation (see also Table 1.). Complete inventory and interpretation of
the features may be derived exploring the ingredients of the model of
computation (that is, analysing the features of the corresponding
representations and measurements). It should be noted, that each level includes
all the lower levels. Thus, each level inherits the features of all lower
levels. A set of permissible operations grows
respectively with the number of the level.
Main feature of the 2-level (or the interval level) of computation is
that there is addition among the permissible
operations. That is, representations here can be united by means of addition.
Starting from this level, representations may be a continuous media. Main
feature of the 3-level (or the ratio level) of computation is that there is a
multiplication among the permissible operations. There exist certain
measurement units also. Main feature of the 4-level (or the absolute level) of
computation is that a set of permissible operations here consists of all the
algebraic operations.
The existing basic
types of the architecture of computational devices now may be placed into the
framework of the extended idea of computation. The framework also allows
predicting the existence of the advanced types of architectures. The features
of the advanced architectures (see Table 2) may be derived by analysing the
earlier described semiotic and a measurement theory aspect of computation. The
data in the table should be considered only as a forecast, but not as a precise
and ultimate list of the features. It is meant to illustrate the general idea
of the considered architectures.
Table 2. Features of existing and
predicted advanced architectures
Note. A period mark
in a table cell means, that the issue was not considered still.
|
No. |
Level |
0 |
1 |
2 |
3 |
4 |
|
1. |
Existing name of the architecture |
Von
Neumann type architecture |
Non von
Neumann type architecture |
Does not exist |
Does not exist |
Does not exist |
|
2. |
Data/programs separation |
Yes |
No |
|
|
|
|
3. |
Name of the device |
Digital computer |
Artificial neural network; neurocomputer |
|
|
|
|
4. |
Proposed working name of the architecture |
Nominal |
Ordinal |
Interval |
Ratio |
Absolute |
|
5. |
Level of universality |
Universal |
Less universal |
|
|
Non-universal |
|
6. |
Level of measurement |
Nominal |
Ordinal |
Interval |
Ratio |
Absolute |
|
7. |
Algebra for description of computation |
Boolean |
Fuzzy, for example |
|
|
|
|
8. |
Permissible operations |
Boolean |
Max, min |
All previous and addition |
All previous and multiplication |
All algebraic operations |
|
9. |
Existence of measurement units |
No* |
No |
Yes |
Yes |
Yes |
|
10. |
Mode of information processing |
Discrete |
Discrete |
Continuous |
Continuous |
Continuous |
|
11. |
Level of representation (a type of a sign) |
Symbol |
Index |
Metaphor |
Diagram |
Icon |
|
12. |
Level of meaning |
Symbolic |
Indexical |
Metaphorical |
Diagrammatic |
Iconic |
* The units of measurement
are introduced, according to the measurement theory, starting only from the
interval level; the "bits" are not units for measuring the meaning of
information, therefore, it is marked, that there are no units at the 0-level.
Some words also should
be said about the possibility of implementation of the advanced levels of the
architectures. Development of the first two architectures lasts several
decades. This points out the possible time necessary for the development and
implementation of the new architectures: it may last several decades. Such type
of a forecast, however should be treated as "a first type naïve
forecast", according to the theory of forecasting [13]. So, the talk is
about a future technology. It should be noted also, that a part of the proposed
model, that is, the absolute level of computation, might be only a theoretical
explanation of the principles that cannot be implemented in an artificial
device.
Considering the ways
of implementation, a modelling approach should be taken into account. An
artificial neural network can be modelled on a digital computer. Similar
possibility should be explored for the architectures of the interval and the
ratio level. An alternative approach is to develop certain semantic media. A
possibility to "discover" the elements of the advanced architectures
in the already existing devices for processing of information should also be
taken into account.
In this paper, an
attempt to put the aspect of the meaning of information into the fundamental
level of information processing was considered. This led to a conclusion, that
there may be developed the different, advanced types of the architectures. A
definition of a multiple level computation was proposed. The two now existing
types of the architectures were considered as corresponding to the first two
levels of computation. A forecast was made, that there should exist three more,
advanced levels of architectures. Their features were predicted.
The meaning was
excluded from consideration trying to simplify the fundamentals of information
technology at the beginning of the computer era. Now it may be possible to
treat information in a more complicated way. It may be useful to come back, rethink
and to attempt to develop a new technology that is capable to operate with the
meaning of information.
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