SEMIOTICS, MODELS AND COMPUTING

Bertil Ekdahl

Department of Computer Science, Lund University

Ole Römers väg 3, SE-223 63 Lund, Sweden

Keywords: Computational semiotics, formal system, language, models, semiotics.

Abstract: Recently, semiotics has begun to be related to computing. Since semiotics is about the interpretation of

signs, of which language is a chief part, such an interest may seem quite reasonable. The semiotic approach

is supposed to bring semantics to the computer.

In this paper I discuss the realistic in this from the point of view of computers as linguistic systems, that is,

as interpreters of descriptions (programs). I maintain the holistic view of language in which the parts are a

whole and cannot be detached. This has the implication that computers cannot be semiotic systems since the

necessary interpretation part cannot be made part of the program. From outside, a computer program can

very well be considered semiotically since the equivalence between computers and formal system implies

that there is a well defined model (interpretation) that has to be communicated.

1 INTRODUCTION

Semiotics is a branch that recently has been of

interest for computer scientists in development of

information system. Shortly, semiotics can be

characterized as the “study of signs and their

meanings”. With sign is not only meant written signs

but also signs in artistic disciplines like music and

theatre. On the whole, semiotics is about the act of

interpretation. As is clear, language is a chief part of

it.

The interest in semiotics in computer science

stems from the idea of seeing computers as sign

systems. Andersen (Web, p.5) writes:

“A computer system can be seen as a complex

network of signs, and every level contains

aspects that can be treated semiotically.”

Andersen further believes that semiotics is a

global perspective on computer systems. He points

to the different views in which computers can be

treated; on the one hand one can focus on the

mechanical aspect, in which case “semiotics has

little to offer”, on the other hand on the

interpretational aspect, which latter is the semiotic

approach. Andersen seems here to consider a

computer system as a black box whose properties it

is the aim to reveal and it is in this process semiotics

comes in.

Another view of computational semiotics is the

idea that a computer in itself can be a semiotic

system involving its own understanding. This view

is put forth not at least by Gudwin [Web]:

“Computational Semiotics refers to the attempt

of emulating the semiosis cycle within a digital

computer. Among other things, this is done

aiming for the construction of autonomous

intelligent systems able to perform intelligent

behavior, what includes perception, world

modeling, value judgment and behavior

generation. […] Within Computational

Semiotics, we try to depict the basic elements

composing an intelligent system, in terms of its

semiotic understanding.”

As Andersen points out, thinking of computers as

physical machines does not relate computers to an

interpretative view but seeing a computer as an

interpreter of a program, (sentences) makes it a

linguistic system, qualitatively connected to our own

linguistic cerebral system, the foundational aspects

of which is logic.

A linguistic system has both a description

(sentences) and an interpretation of the description.

Were it possible for a computer to be a semiotic

system, as Gudwin assumes, it would, by itself, be

able to describe its own interpretation. However, this

is not possible due to a complementarity in

283

Ekdahl B. (2008).

SEMIOTICS, MODELS AND COMPUTING.

In Proceedings of the Tenth International Conference on Enterprise Information Systems - ISAS, pages 283-289

DOI: 10.5220/0001702602830289

 SciTePress

language. The domain of the validity of a description

is of a higher type than the description itself. In that

sense a computer will never be a semiotic system but

semiotics could be of value for studying computers

as linguistic systems. Such a study needs a

metalanguage for which purpose semiotics may

serve.

2 SEMIOTICS

Its origin can be traced back to the Swiss

philosopher Ferdinand de Saussure and the USA

philosopher Charles Saunders Peirce. Saussure

(1966) explained semiotics as “the science of the life

of signs within society”. (Saussure, 1983):

“It is... possible to conceive of a science which

studies the role of signs as part of social life. It

would form part of social psychology, and hence

of general psychology. We shall call it

semiology (from the Greek semeîon, 'sign'). It

would investigate the nature of signs and the

laws governing them. Since it does not yet exist,

one cannot say for certain that it will exist. But

it has a right to exist, a place ready for it in

advance. Linguistics is only one branch of this

general science. The laws which semiology will

discover will be laws applicable in linguistics,

and linguistics will thus be assigned to a clearly

defined place in the field of human knowledge.”

Peirce [1992] makes the following explanation of

what he called semiosis:

“[B]y ‘semiosis’ I mean […] an action, or

influence, which is, or involves, a cooperation of

three subjects, such as a sign, its object, and its

interpretatant, this tri-relative influence not

being in any way resolvable into actions

between pairs. “

From his understanding of Peirce, Morris

proposed that semiotics embraces syntax, the

morphology, semantics, what the words and signs

stand for, and pragmatism, the relation of signs to

the interpreter.

Syntax and semantics are well known parts while

the third part, pragmatism, is what Bar-Hillel (1970)

characterized as the “waste-basket”, i.e., a place to

put everything that is “difficult”. Sonesson (2002) is

concerned about the absence of explanatory power

of pragmatism:

“[…]’pragmatic’ approaches often leaves as a

complete mystery how meaning is conveyed”.

Computational semiotics is thought of as a way

“to synthesize artificial systems able to perform

some sort of semiosis” (Gomes et al., Web). They

further submit that according to Peirce, any

description of semiosis involves a relation of three

terms:

“A sign is anything which is related to a Second

thing, its Object, in respect to a Quality, in such

a way as to bring a Third thing, its Interpretant,

into relation to the same Object, and that in such

a way as to bring a Fourth into relation to that

Object in the same form, ad infinitum.”

In order to simulate, as they said, semiotic

systems, they try to devise a suitable formalism. As

will be shown, a new formalism is still a formalism

and will not make a system semiotic in itself.

Andersen, on his part, discusses three different

kinds of semiotic and linguistic theories: the

generative paradigm, the logical paradigm and the

European structuralist paradigm of which he reject

the two first. However, Andersen cannot reject the

logical paradigm since a computer, as a linguistic

system, is a logical system and cannot be differently

considered.

3 FORMAL SYSTEM

Formal system (logic) “is concerned with the

analysis of sentences or of propositions and of proof

with attention to the form in abstraction from the

matter.” (Church, 1956, p. 1)

This total abstraction from meaning is expressed

by Kleene (1952, p. 61) as follows:

“To Hilbert is due now, first, the emphasis that

strict formalization of a theory involves the total

abstraction from meaning, the result being

called a formal system […]”

Thus, the whole idea with a formal system is to

serve as a proof system; a system whose only aim is

to produce proofs. In accomplishing this, everything

except form must be rejected. It is like a play with

pieces that does not in itself have meaning. von

Neumann (1931) explicates the game idea in the

following sense:

“[C]lassical mathematics involves an internally

closed procedure which operates according to

fixed rules known to all mathematicians and

which consists basically in constructing

successively certain combinations of primitive

symbols which are considered “correct” or

“proved”. […] [W]e should investigate, not

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statements, but methods of proof. We must

regard classical mathematics as a combinatorial

game played with the primitive symbols.”

(italics, BE)

Hence, a formal system is constructed to be free of

semantics.

The first step in setting up a formal system

(logical system) is to list the formal symbols. Here,

any symbol will do; no one is preferable for the

system but possibly for the user of the system. For

example, in a formal system for arithmetic we can

choose the symbol Ŋ to stand for the number one.

However, it is normally better to use the symbol

because it immediately gives the user the intended

interpretation.

From the symbols the formal expressions are

derived. The next step is to introduce the formation

rules which can be considered as analogous to the

rules of syntax in grammar. The third step is to

define transformation rules. The transformation

rules, or inference rules, give the formal system the

structure of a deductive system or deductive theory.

What is stated above is the same for all formal

systems. What distinguish different formal systems

are the postulates (axioms) that turn a formal system

into a theory. For example, for number theory the

following are two postulates:

))(0(

)()(

xSx

yxySxS

=¬∃

=→=

where S is interpreted as the successor function, with

the meaning that S(x) is the next number coming

after the number symbolized by

x. The first sentence

is then interpreted as “if the successors of two

numbers are the same, the numbers are the same”.

The second axiom says that “zero is the least

number”. As will be seen, there are other possible

interpretations.

The relation of formal system to computers

clearly expressed by Gödel (1964) in a postscriptum,

prepared to Martin Davis:

“In consequence of later advances […] due to

A. M. Turing’s work, a precise and

unquestionably adequate definition of the

general concept of formal system can now be

given [,…] A formal system can simply be

defined to be any mechanical procedure for

producing formulas, called provable formulas.

For any formal system in this sense there exists

In this paper I will not distinguish between formal

system, computer and Turing machine.

one in the sense of page 41 above

that has the

same provable formulas (and likewise vice

versa), provided the term “finite procedure”

occurring on page 41 is understood to mean

“mechanical procedure”. This meaning,

however, is required by the concept of formal

system, whose essence it is that reasoning is

completely replaced by mechanical operations

on formulas.”

A formal system, used to develop formal

theories, is a system that utilizes processes, which

cannot themselves be completely described by some

theory in the system in question.

4 THE USE OF MODEL IN

NATURAL SCIENCES

There is no doubt that the term model is used in

many different ways, not only in everyday life but

also in science. Frequently the term is used in a

manner that makes its meaning diffuse, and also

there is a common tendency to confuse, or to

amalgamate, the terms model and theory. Even in

science those terms are often used interchangeably

as being synonymous.

Andersen (Web) argues that semiotics and

natural science are different in perspective. The

reason he states is that “natural science focuses on

the mechanical aspects of a system – those aspects

that can be treated as an automaton – semiotics

focuses of the interpretative aspects”. For Andersen

it seems as computer systems are sign systems

whose interpretations have to be wormed out.

However, there is a huge difference between a

computer system and a natural system. When

studying physics the system is unknown and starts

with observations with the aim to reveal a physical

structure. That is, we try to get an idea of the nature.

With computer systems it is the other way around.

Like all other artificial systems, the interpretation

(idea) is already known; it is the starting point. No

surprises are to be expected. For example, no one

constructs a gear box and then ask for its behavior.

We characterize the nature in such a way that it

can be grasped and, hopefully, visualized. This

visualization is a model like a model ship or model

plane. It is not the equations, the theory, that

constitutes a model. For example, in the 1920s and

1930s, the Friedman-Robertson-Walker

cosmological model was introduced as the simplest

Refers to p. 41 in Davis, 1965.

SEMIOTICS, MODELS AND COMPUTING

285

solution of the equations of Einstein’s general theory

of relativity. This cosmological model was a way of

thinking of the Universe in a way that satisfied our

understanding of the Universe while at the same

time keeping Einstein’s equations. This model was

non-rotating. However, Gödel was the first to

consider a model that was rotating. The curious

property of this model was that in it, it was possible

to travel into the past. The equations, that is, the

theory, were not altered but the interpretation was

quite new and much unexpected.

The interpretation aspect is everywhere present

in natural sciences. For example, Niels Bohr

struggled all his life with the question of the

interpretation of quantum theory and still today there

is no good interpretation of quantum phenomena.

Penrose has explained the difficulties as follows:

(Web)

“It must play its role when magnifying

something from a quantum level to a classical

level, which is what is involved in measurement.

The way to treat this, in standard quantum

theory, is to introduce randomness. Since

randomness comes in, quantum theory is called

a probabilistic theory. But randomness only

comes in when we go from the quantum to the

classical level. If we stay down at the quantum

level, there is no randomness. It is only when we

magnify something up, and make a

measurement. This consists of taking a small-

scale quantum effect and magnifying it out to a

level where we can see it. It is only in that

process of magnification that probabilities come

in.”

What Bohr wanted and Penrose wants is to find a

model of the quantum phenomena.

The confusing usage between model and theory

is harmless so long as we stay intradisciplinary but

when it comes to the explanation of systems that we

think of as having a cognitive ability, and

particularly systems which are furnished with

language, it is of importance to use the term model

in its linguistic sense otherwise it is easy to ascribe

properties to such systems that they never will

achieve.

5 MODELS IN LOGIC

Formal systems have “mathematical models” which

is a well defined concept. It is of no use to construct

a formal system without giving it a definite model,

i.e., giving the key of interpretation.

A model of a formal system is a (mathematical)

structure that consists of a non-empty set, called

domain, a set of functions, a set of relations and a set

of constants. In mathematical notation it is described

kmn

cccRRRfffA ,...,,,...,,,,...,,,

212121

where A is the domain, the fs are functions, the Rs

are relations and the cs are constants.

As an example we may consider a graph. A

graph is a set V (of vertices) and a set E (of edges),

where each edge is a set of two distinct vertices. An

edge {v,w} is said to join the two vertices v and w.

For example, a subway system constitutes a graph in

the sense above where the stations are the nodes and

the connections between the stations are the edges.

There is a natural way to make a graph V into a

structure G. The elements of G are the vertices.

There is one binary relation R. The ordered pair

wv, lies in R if and only if there is an edge

joining v to w.

Now, every natural structure, that can be

described in detail, can be turned into a

mathematical structure and if then a sentence is true

in the mathematical structure it is also true in the

natural structure and we may call the natural

structure a model of the sentence.

By way of example (fig. 5.1), we may consider a

sphere falling from a tower. This is the natural

(physical) model which can be turned into a function

which constitutes the mathematical model. The

program then is the theory of the model but does not

in itself say anything of what is computed.

Figure 5.1: The equation for a freely falling sphere.

A program can have many different models and

no one is pointed out by the program. For example,

the first sentence, in the postulates mentioned above

for arithmetic, can be given the interpretation that “if

two people have the same security number, then it is

one and the same person”. Another interpretation

could be the DNA-sequence of a person. Then the

axiom could state that “if a murder and a decent

ghv 2=

Program

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person have the same DNA, then the decent person

is the murder”. In this interpretation the second

axiom could be thought of as meaning that “there is

no person that not has a DNA”.

The things to consider are that the interpretation

is not part of the formal system and there is no way,

from the point of view of the system, to know the

meaning of the sentences.

6 THE CONCEPTION OF

LANGUAGE

In, for example, physics, language is not defined and

is considered as being outside the domain of the

discipline. Even in logic, language is considered

outside the domain of the discipline. Shoenfield

(1967, p.4) characterize language in the following

way:

“We consider a language to be completely

specified when its symbols and formulas are

specified. This makes a language a purely

syntactical object. Of course most of our

languages will have a meaning (or several

meanings); but the meaning is not considered to

be part of the language.”

This is a completely fragmentable view of

language in which the interpretation part and the

description part is outside the language. It is a

distorted approach which, however, has its origin in

the need of separating syntax from semantics in

order to make the concept of proof unambiguous.

For a proof it is of course important not to rely on

our beliefs. However, this view makes language

stunted and we may ask from where the

interpretation comes. The answer is that this process

is a non-fragmentable part of the language itself. A

full language, like a natural language, consists of

description, interpretation, an interpretation process

and a description process. In a full fledge language,

the parts are indivisible. In this holistic view,

language is a wholeness that can not be broken into

parts without being distorted. This is the holistic

view of language as formulated by Löfgren (1991):

“In no language, its interpretation process can be

completely described in the language itself.”

Unlike classical physics, language is impossible

to completely objectify in itself. Understanding of a

language is understanding of both form and meaning

in a complementary conception in which

fragmentation into parts does not succeed. When we

say that language is holistically considered or we say

that interpretations are non-linguistic entities or even

extra-linguistic entities, the result is the same,

namely that the interpretation of sentences does not

belong to the realm of sentences: a complete

epistemological description of a language L cannot

be given in the same language L, because the

concept of truth of sentences of L cannot be defined

in L.

The interpretation of a language makes the

concepts and the concepts we perceive give the

language. That is why we cannot objectify language

as is possible with objects in (classical) physics. We

cannot go outside the language but have to stay

within it; we are imprisoned in our own language.

As soon as we are trying to describe a language,

fragmentation is a necessity. Depending upon

whether an attempted fragmentation is thought of in

ontological and semantic terms or in epistemological

and descriptive terms, different complementarity

views results. According to Löfgren (1992), “the

fragmentation types are not independent, and an

autological closure onto language, in its ultimate

wholistic conception, will yield a general type of

complementarity, to which other can be reduces”.

7 COMPUTERS AS

INTERPRETERS

Two things are essential for a computer to be a

formal system. Firstly, every formula should be

possible to be coded in numbers. Secondly, the

mechanical procedure, referred to above, should be

recursive. Gödel (1951) explains it as follows:

“This concept [formal system] is equivalent to

the concept of “computable function of integers”

[…] The procedures to be considered do not

operate on integers but on formulas, but because

of the enumeration of the formulas in question,

they can always be reduced to procedures

operating on integers.”

By way of an example, let

),(

xxA be the

first two-place predicate symbol (in a list), then one

way of coding it is to the number

. (Mendelson, 1964, p. 191)

It is the mechanical characteristics of inference

rules that make a computer a formal system. With an

inference rule is attached an action (interpretation),

namely a new sentence that is produced from the old

sentences. As an action it cannot fully be described

in terms of axioms (sentences) alone. Without such a

SEMIOTICS, MODELS AND COMPUTING

287

complementary action, a theory

, with an infinite set

of theorems could not be finitely represented and

thus not communicated. This is in complete accord

with Gödel’s answer to a question of Burks

(Neumann, 1966, p. 55) “The complete description

of its [Turing machine, BE] behaviour is infinite

because, in view of the non-existence of a decision

procedure predicting its behavior, the complete

description could be given only by an enumeration

of all instances.”

8 CONCLUSIONS

The action of a computer is an act of interpretation

operating on numbers representing sentences. This

action cannot itself be reduced to sentences (axioms)

in the given logical language. There must always be

a production of new sentences from others. It is in

this sense that a computer is a linguistic system: a

behavior of a computer system is an interpretation of

its description.

Since the interpretation process is outside the

description (program), no computer will ever

simulate, in an acceptable way, a semiotic system.

This is prohibited by the complementarity view of

language, because if the linguistic complementarity

would be possible to invalidate, then the holistic

language phenomenon would not exist.

Interpretation should disappear and communication

would be completely syntactic. Uncomputability

would be a for ever unknown concept for such

beings.

Computer systems should be seen as the

linguistic systems they are with a well defined

model. It is the model, preceding the construction of

a program, that should be well communicated and

may very well benefit from semiotic methods.

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