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STUDIES IN LOGIC, GRAMMAR
AND RHETORIC 67 (80) 2022
DOI: 10.2478/slgr-2022-0010
This work is licensed under a Creative Commons Attribution BY 4.0 License
(http://creativecommons.org/licenses/by/4.0)
Andr´e Włodarczyk
Ch. De Gaulle University (Lille)
Sorbonne University (Paris)
(Centre for Theoretical and Applied Linguistics)
e-mail: wlodarczyk.andre@gmail.com
ORCID: 0000-0001-6706-8702
CONCEPTS AND CATEGORIES:
A DATA SCIENCE APPROACH
TO SEMIOTICS*
Abstract. Compared to existing classical approaches to semiotics which are
dyadic (signifier/signified, F. de Saussure) and triadic (symbol/concept/object,
Ch. S. Peirce), this theory can be characterized as tetradic ([sign/semion]//
[object/noema]) and is the result of either doubling the dyadic approach along
the semiotic/ordinary dimension or splitting the ‘concept’ of the triadic one into
two (semiotic/ordinary). Other important features of this approach are (a) the
distinction made between concepts (only functional pairs of extent and intent)
and categories (as representations of expressions) and (b) the indication of
the need for providing the mathematical passage from the duality between two
sets (where one is a singleton) within systems of sets to category-theoretical
monoids within systems of categories while waiting for the solution of this prob-
lem in the field of logic.
Last but not least, human language expressions are the most representative
physical instances of semiotic objects. Moreover, as computational experiments
which are possible with linguistic objects present a high degree of systematicity
(of oppositions), in general, it is relatively easy to elucidate their dependence
on the concepts underlying signs. This new semiotic theory or rather this new
research program emerged as the fruit of experimentation and reflection on the
application of data science tools elaborated within the frameworks of Rough Set
Theory (RST), Formal Context Analysis (FCA) and, though only theoretically,
Distributed Information Logic (DIL).
The semiotic objects (s-objects) of this theory can be described in tabu-
lar datasets. Nevertheless, at this stage of formalisation of the theory, lattices
(not trees) can be used as working representation structures for characterizing
the components of concept systems and graphs for categories of each layer.
Keywords: Sign theory, human language, data science, formal concept, monoid
category, theory of semiotics.
ISSN 0860-150X 169
Andr´e Włodarczyk
Since signs may also be regarded as objects, capable of being them-
selves represented in form of other signs, there is no need (at least
at first) to make a distinction between objects and signs.
Maria Nowakowska (1980)
...a modern tradition of psychological research has developed in
which concepts and categories are seen as central to theories of
knowledge representation and long-term memory.
J. A. Hampton and D. Dubois (1993)
1. Introduction
The reason why expressions of human languages are specifically partial
and ambiguous is, first of all, that they are built out of signs which have
a double functionality per se (semantics) and per alia (ontology). In addi-
tion, language expressions are context-dependent (they rely heavily on all
the cognitive sensory skills of human beings) which, in turn, roughly refer
to objects and situations “out there”. Noteworthily, the classic theories of
language either attributed the overall thinking capacities to language only
or refused any participation of language in the process of thinking. In this
essay, I adopt the hypothesis of mental code even though its existence is still
to be proven by neuroscientists. Although both mental code and language
and the relationship between them are basically culture-dependent, we can
nevertheless expect that the nature of the primary structures of the code,
language, and operations on them are universal to humans.
At this point, an important philosophical (but, as we will see, also
methodological) problem arises: is it possible to construct theoretically
a system of primitives (a priori) or can we only try to discover it ex-
perimentally (a posteriori)? To answer this question, it would be neces-
sary to evaluate more than a half-century of research on transformational
generative grammar, including all the attempts of its diverse technologi-
cal implementations on computers and the results achieved in all the other
frameworks of Natural Language Processing (NLP) technology as well. As
a matter of fact, the search for primitive elementary concepts (in philos-
ophy and language studies known as “universals”) has failed, at least as
of now, and, in the domain of computer science, investigations into the
deep “pivot language” for machine translation purposes have been discontin-
ued and rather rapidly replaced by the elaboration of “transfer techniques”
aimed at bypassing the “pivot language” representations during machine
translation processes. Still, this first step which consisted of the theoret-
ical construction of an overall ontology failed in implementation. Person-
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Concepts and Categories: A Data Science Approach to Semiotics
ally, I believe that the next step on this way will need to pass through
a period of rather long-lasting technological effort in research on human
languages (and especially, on languages belonging to as divergent fami-
lies as possible) using methods of data science (Knowledge Discovery in
Databases – KDD), as an example see the research project “Computer-aided
Acquisition of Semantic Knowledge – CASK (Włodarczyk 2007), includ-
ing machine learning (neural networks). Usually, objects when perceived
are considered to be denoted as cognitive objects. In the present theory,
families of ordinary concepts (o-concepts) in the mind, which contribute
to represent ordinary objects, are named noemata. Given that the vehi-
cles (support) of signs have also a physical nature, families of semiotic
concepts (s-concepts), which contribute to represent semiotic objects, are
named semions. In addition, the term “object” in this paper is used in two
different ways: (1) as the single (formal) object of one or more semiotic
concepts (s-concept) and (2) as the object of a semiotic monoid category
(s-category). In this theory, “traces” of signs are considered to have a dou-
ble functionality: (1) as objects per se (objects) and (2) as objects per alia
(para-objects).
Language signs, when used, are organised by degree of complexity
in 5 layers of semiotic categories: sounds,syllables,words,phrases and sen-
tences (utterances) which appear through emergence (synergetic interaction
between objects and features) in a strict dependence of context (data pro-
cessed by all the senses of humans and their knowledge). Therefore, signs
are represented by categories and concepts which underlie these categories.
In other words, semiotic categories appear in context-dependent emergence
from concepts (or rather their families, or even aggregations of their fam-
ilies). Rules are used only in cases of necessity to create new schemata
of signs (not yet in memory) but, even when schemata are ready to use,
there is also a need to use recombination rules in order to extend the base
utterances (or their schemata) into grounded language messages. In this
paper, I am going to argue that today the adoption of computer technol-
ogy will lead to further progress in order to create new frameworks for
a tetradic semiotic theory based on the alignment of semiotic objects with
ordinary objects, thus refining both the dyadic view of signs (issued from
the Saussurean tradition) and the triadic one (issued from the Peircean
tradition). In addition, this approach leads to the view of human lan-
guage semantics as (a) the activation (per se) and (b) alignment of semi-
otic code units with ordinary code units replacing the logical interpreta-
tion of form by its sense or the transformation of “surface structures” into
“deep structures”.
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Andr´e Włodarczyk
2. A short reminder of semiotic issues in linguistics and logics
Roughly speaking, there are two complementary classic theories of semi-
otic systems:
(1) a structural linguistic theory in which the sign is defined as a dyadic
relationship between form (‘signifier’) and sense (‘signified’) – Ferdi-
nand de Saussure [1857–1913],
(2) a logical semiotic theory in which the sign is an element of a triangular
relationship between representamen (symbol), interpretant (comprehen-
sion device) and referent (object) – Charles Sanders Peirce [1839–1914].
In structural linguistics, the traditional couple of form and sense, con-
sidered to be like a coin which has two “inseparable faces”, gave rise to
what is often qualified today as the dyadic semiotic theory by de Saussure
for whom form corresponds to the signifier (signifiant) and sense to the
signified (signifi´e) of signs which are located in the memory of humans. In
this traditional setting, language units are arranged hierarchically, units of
higher layers (words, phrases and utterances) are said to be ‘meaningful’
while those of the lower ones (sounds, syllables) are, as it were, ‘distinc-
tive’. Note however that distinctivity is an inseparable characteristic of any
structured collection of objects (cf. Lapis 2014). This dichotomy of notions
applied to the hierarchical character of signs is supposed to determine two
big layers of expression components and is known in structural linguistics as
‘duality of patterning’. Furthermore, as the semiotic units of all the layers
exhibit at the same time (a) sequential (syntagmatic, “actual”) and (2) par-
allel (paradigmatic, “virtual”) relationships, signs are considered to have
a twofold nature: they combine and commute. In addition to this, signs
form clusters following various opposition principles. Hence, the meaning of
each of them is relative to that of the others. The term semiosis is often
used to designate all the semantic changes that language signs undergo both
in synchrony and diachrony.
According to the classic semiotics by Peirce, without taking into ac-
count, besides the representamen (symbol) and referent (object), the third
component of semiosis, the interpretant (concept)1, the distinction between
form and sense is substantially inadequate. During its history, the Peircean
model of semiosis underwent a few important interpretations (cf. Richards
and Ogden 1923). The resulting model is widely known today under the
name of “semiotic triangle” containing a modernised version of the triad
of totally correlated notions: sign,concept and object. The notion of con-
cept in the original Peircean version of the model of semiotics renders well
the idea of conceptual representations of semantic situations. There is no
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Concepts and Categories: A Data Science Approach to Semiotics
doubt that, at its basis, the notion of interpretant introduced a pragmatic
element (the skill of the speech act participant, i.e. an agent endowed with
human language ability) into the definition of sign. Indeed, the general the-
ory of signs should account for the utilisation of signs by men (human beings
equipped with cognitive systems2) in order to elucidate the interpretation
(assignment function) of language expressions as transformation leading to
conceptual representations and vice-versa.
Consider now that classic logic symbols are a sort of artificial signs:
1. their support is formal, hence presumed to be transparent,
2. nevertheless, they can be spelled or listened to, imitating human lan-
guage signs,
3. their phonetic structure usually follows one of their host human lan-
guages,
4. to note variables and constants, logics needs to use names,
5. the only reason for using multi-character symbols for constants and
variables is that the alphabets of their host human languages contain
a limited number of letters (the theoretical “duality of patterning” of
logic symbols is hardly conceivable),
6. they obey the fundamental laws of ‘distinctiveness’ and ‘combinatorics
on words’, but these do not usually form any systematic opposition
system (they are just lists of symbols),
7. they combine following very few syntactic rules,
8. they can be interpreted with respect to one or more formally defined
closed (possible) worlds.
3. Data science tools for modelling linguistic signs
Due to the history of mankind and to the inevitable limitations of our
experience in the world, human cognition can only be consistent locally.
Human languages are highly complex systems with heterogeneous nature
of “parts of speech” which need sophisticated scientific tools for their explo-
ration. If language objects were homogeneous, the explanation of linguistic
expressions would undoubtedly have a rather easy and completely recursive
character to which rules of simple formal grammars could probably apply.3
Despite enormous efforts by many research teams, machine translation has
been declared a hard problem of Artificial Intelligence. As a matter of fact,
theoretical linguistic endeavours and human language processing techniques
are not yet well equipped neither with appropriate meta-theories nor with
advanced data scientific methods and tools.
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Andr´e Włodarczyk
Consequently, under no circumstances can we expect that representa-
tions using solely such simple structures as hierarchies (“trees”) suffice to
represent and process human language expressions. Instead, linguists should
revise their philosophical positions so that it becomes possible to apply
the notions and tools of distributed computing in order to create/develop
a truly scientific paradigm in the study of language. In other words, the in-
vestigations into language domain should be based on data validated with
the help of computational tools for processing interactively produced de-
scriptions, with data mining methods (using not just text-mining4). Bear-
ing in mind the diversity of operations needed for processing data, I pro-
pose to use the following computational techniques (jointly or separately)
among others:
1. Rough Set Theory (RST – Pawlak 1982) which provides discerning for
concept approximation
2. Formal Concept Analysis (FCA – Ganter and Wille 1999; Wille 1982,
2005) which provides calibration for concept scaling
3. Distributed Information Logic (DIL – Barwise and Seligman 1997) which
provides classification for concept integration
Tables with objects and features (datasets) are basic data structures
used in computer science. The research on their nature gave rise to what
has recently been launched as data science that tries to integrate not
only the investigations into the deep learning mechanisms using the neu-
romimetic intelligence technology but also the techniques of Knowledge
Discovery in Databases (KDD) using management techniques of seman-
tic/ontological databases. In computer science, there are a few approaches5
to the problem of mappings between objects and their features as assembled
in tabular datasets: (1) information systems (RST), (2) contexts (FCA) and
(3) classifications (DIL).
The way FCA looks at concepts is in line with the international stan-
dard ISO 704 that formulates the following definition: “A concept is con-
sidered to be a unit of thought constituted of two parts: extent and intent.”
The extent consists of all objects belonging to the concept, whereas the in-
tent comprises all attributes shared by those objects. Thus, the definition
of a formal concept is based on the dual nature of the assignment func-
tion of features to objects but, from a strictly linguistic point of view, it is
important to mention the fact that this duality cannot be found without
the “opposition system” or, in FCA terms, without their “contexts” (tables
of binary data).
The research of Karl Erich Wolff (2009) might serve as an interesting
example of the use of several fields of data science with the aim of creating
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Concepts and Categories: A Data Science Approach to Semiotics
a relational semantic theory. Let me quote the extended Formal Concept
Analysis.
... we combine the structure of a many-valued context and the structure of
a power context family in the notion of a Relational Data System such that
each many-valued context, each power context family, and each concept graph
can be represented by a Relational Data System. They will be used to define
Relational Semantic Systems which offer a clear way of relational scaling
(Wolff 2009: 67).
On the schema below, it is shown that formal concepts are dual pairs
of sets of features as projected on objects. The duality is provided by the
two functions f(A) = Band g(B) = Aknown as Galois Connection. This
definition lies at the basis of the FCA theory by Rudolf Wille (1982, 2005)
and by Bernhard Ganter and Rudolf Wille (1999).
Schema 1. The Definition of a Formal Concept as a Galois Connection
For the convenience of linguists, it may be handy to represent the model
of systems with formal concepts as in the following triple:
(1) C= (A, α, a)using the terminology as follows:
Ais the opposition system to which a given semiotic unit belongs,
αis a subset of features ({intent}) describing the language units of
that system,
a– is a subset of language units ({extent}).
Most importantly, however, the concept defined this way, besides meet-
ing the expectations of semioticians, has an important characteristic feature:
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Andr´e Włodarczyk
it is obtained automatically by the dual function which combines features
with internalised traces of signs (s-objects). Let us compare by way of exam-
ple two classic (logic and linguistic) analyses of such a simple expression like
“white cat”. Following the syntax of the First Order Logic (FOL) language,
we get the following formula:
(2) ∃xwhite(x)→“there exists an xsuch that xis white”
which after interpretation (i.e. after applying this formula to a set of cats)
gives:
(2a) ∃cat white(cat) →“there exists a cat such that this cat is white”.
It goes without saying that only two layers are necessary for this analy-
sis: a lower (elementary) layer of individuals and a higher (derivate) one of
relations. Moreover, to make the interpretation happen, logics needs some
application domain. In the case of FOL, logicians use set theoretical notions
with respect to which their logical formulae take the truth values.
Now, in the proposed conceptual approach, signs being defined as pairs
comprising “traces of expressions” and “features”, we get the following anal-
ysis (for the sake of brevity, only two out of 5 layers will be exemplified).
Layer 3 – Words: two semiotic units “white” and “cat” with their two un-
derlying concepts:
concept 1 = ({white},{set of white objects}) and
concept 2 = ({cat},{pet}).
Layer 4 – Phrases: one semiotic unit “white cat” with its underlying concept:
concept “cat” = ({cat},{white}).
On every layer of the system, I propose to use the combination of
the notion of scaling of concept systems (FCA) with that of approxima-
tion (RST) thanks to the fact that the formal concepts (FCA) correspond
to B-definable subsets of objects (RST). Given that perception relies merely
on partial views of objects, due to the synergy of (a) semiosis operating
mostly on sense with (b) encapsulation operating mostly on form, semi-
otic representations help to improve (refine, deepen) these views through
alignments not only with ordinary knowledge but also with data and in-
formation being acquired during the communication processes thanks to
all the sensory devices of individuals. For this reason, one way to model
these processes might be the utilisation of the lower and upper approxima-
tion techniques. Thus, combining the power of approximation (RST) with
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Concepts and Categories: A Data Science Approach to Semiotics
that of scaling (FCA), it might become possible to process formal con-
cepts associated with signs and, perhaps, even use them very successfully
for modelling the underlying conceptual components of non-semiotic (ordi-
nary) systems.6
The aim and meaning of Formal Concept Analysis as mathematical theory
of concepts and concept hierarchies is to support the rational communication
of humans by mathematically developing appropriate conceptual structures
which can be logically activated (Wille 2005: 2).
The Formal Concept Analysis actually provides the mathematical ca-
pacity for defining concepts and scaling datasets. In FCA, all kinds of real-
world entities (objects), once registered in datasets, are treated as formal
objects. Indeed, in more general terms, formal concepts are very useful
mathematical representations of both real/fictitious and concrete/abstract
objects. The combination of FCA with RST is fruitful because the RST
also presents a similar mathematical power in scrambling decisions while
taking advantage of the ability to use approximation techniques.
Another reason for using data science technology in modern linguistics,
is the fact that, being equipped with autonomous knowledge processing
systems, humans use both extensional and intentional information which
form their knowledge defined as an internal mental model of the external
world. However, for clarity’s sake concerning the feasibility, note that to
make judgements and assertions, given that knowledge is inconsistent in face
of the immense complexity of the world, man neither needs always to refer
to the real world nor to be entirely rational.
4. Signs in the conceptual semiotic theory
It is namely Uta Priss (2002, 2020), a German mathematician, the au-
thor of the relational formal concept analysis (RFCA), who has formalised
the traditional Peircean semiotic theory. She has also written many pa-
pers on the linguistic applications of FCA. Undoubtedly, one of the most
interesting of them concerns language studies (especially contrastive lin-
guistics) and treats human language expressions as intents. But in struc-
tural linguistics (the general theory of human language as a system), we
need to account for the fact that (1) human language expressions exist
in the real world in acoustic form, hence they also should be treated as
objects, or perhaps more precisely, as “traces” of objects or formal ob-
jects (following the FCA framework terminology) and, consequently, that
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Andr´e Włodarczyk
(2) signs should be treated as one-element extents of formal concepts, not
as their intents. For some linguists, this problem is similar to the one of
meta-language for the sole reason that the objects of their investigations
actually are languages. Some other linguists use the term meta-language
to indicate special kinds of expression of their object language itself. How-
ever, even in the latter case, the definitions are often too large as they
also cover problems which can be better captured using the term meta-
information (cf. Włodarczyk 2013; Włodarczyk and Włodarczyk 2016a,
2016b, 2019a and 2019b).
As a matter of fact, applied to semiotic systems (and a fortiori to hu-
man languages), during the process of concept analyses (i.e. during commu-
nication), solely the formal concepts whose extents are composed of unique
elements (singletons) are functionally efficient within the whole system.
Note however that, although the formal concepts which underlie the
categorisation of semiotic objects are the result of their recognition in the
real-world7and memorisation as “traces” in the mind, it is clear that, using
traditional terminology, one may say that signs are “vehicles” or “support”
of information about not only real but also fictitious (abstract, mythical,
symbolic etc.) objects. However, in the present approach to semiotics, the
classical pair of notions form/sense is being replaced by the formal concept’s
pair ({extent}, ({intent}), the latter being generalised as an outcome of its
application to the expressions of all the layers of the information process-
ing system. As will be shown below in section 6, processing signs consists
in the awareness of the 5-layered emergence of semiotic units which are:
(1) phonetic, (2) syllabic, (3) lexico-grammatical, (4) syntactic and (5) sen-
tential (see Fig. 4). At this point again, I claim that this knowledge indeed
needs to be, first of all and at least partly, treated in terms of ontologically
grounded formal concepts, namely concepts whose extents have proto-
objects as referents. Consequently, as is argued below, it is impossible to
reduce either Form to extent or Sense to intent.
4.1. Semiotic and ordinary objects as formal objects
The distinction between semiotic formal objects (traces of signs) and
ordinary formal objects (traces of things) is crucial for any theory of semiosis
which supports the hypothesis of the existence of mental code, the struc-
ture of which is certainly more systematic (hence it is even more suitable for
formal modelling) than the structure of human languages. Moreover, from
the logic point of view, these two sorts of objects are linked together. Hypo-
thetically, the correlation between both kinds of objects can be seen as an
alignment rather than as any deductive system. In addition, both the com-
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Concepts and Categories: A Data Science Approach to Semiotics
munication within human societies (macro-cognitive, social systems) and
the common-sense knowledge of their members (micro-cognitive, individ-
ual systems) are better modelled using distributed systems than centralized
ones. As languages undergo constant evolution, they form systems in which
semiotic and noemic objects coexist in the distributed networks of knowl-
edge. Intuitively, during the processes of conceptualisation (thinking and
communicating) s-objects and o-objects both follow general laws of infor-
mation transmission systems, hence, they can be assimilated to the merged
clusters of smaller groups of concepts which can be represented by lattice
diagrams.8In functional linguistics, such collections of language units, where
concepts are definable by the dual function as in FCA, are known as oppo-
sition systems.
4.2. Linguistic signs as objects and para-objects
In the proposed conceptual semiotic theory, formal objects are consid-
ered firstly as ‘traces’ of semiotic objects (objects per se) and, only in the
second place, as aligned with ordinary objects or, more precisely, as para-
objects (objects per alia) with the senses historically drawn from the percep-
tion of ordinary objects which are aligned with them (see Fig. 1). Linguistic
signs are therefore objects and para-objects at the same time. Their pe-
culiarity consists in that – in addition to conveying their proper (per se)
semiotic information – they are aligned as objects per alia with the ordinary
(non-semiotic) mental code constructs.9Judging on the basis of analyses of
human language signs seen as objects could perhaps make it possible to hy-
pothesise that semiotic and ordinary objects, both being mental code units,
are processed in the mind in a similar way (i.e. within hierarchies of layers)
passing from lower (micro-) layer categories to higher (macro-) layer cat-
egories through multiple synergies between (1) features per se themselves,
(2) features per alia themselves and between (3) features of encapsulation
and those of semiosis (see Fig. 1, Fig. 2, and cf. section 6).
However, before this problem is properly solved, I will concentrate here
on semiotic objects only, proposing to take advantage of the set-theoretical
notion of formal concepts with one-element set of objects in extent and of
the category-theoretical notion of monoids. Fig. 1 suggests that signs are
processed “within” the layers of activated memory spaces10 where they are
represented by (1) families of semiotic formal concepts (semions) and
(2) semiotic categories (semiotic units). On the right side of fig. 1, ordi-
nary real-world objects are represented by formal objects (“traces”) of fami-
lies of ordinary formal concepts (noemata). In spite of all this, it is more than
probable that semions and noemata are NOT processed in a similar way.11
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Andr´e Włodarczyk
Figure 1. The Tetradic view of Emergence within Semiosis and Noesis and
between them
Semioticians and linguists who traditionally consider that signs are ob-
jects which stand only per alia focus on the universal character of signs as
substitutes of objects being themselves representations of elements of sit-
uations regardless of their belonging to the fragments of the world “out
there” or their essentially abstract (only epistemic) nature. Contrariwise,
linguists who restrict their views to signs as objects only per se, consider
that signs determine specific mental representations (“the mind”) of exter-
nal world objects; hence, departing from the common ontological ground of
languages, thus paying attention mostly to the diversity of world languages.
Both points of view appeared in the history of linguistic investigations as
antagonistic, the first one is known as universalistic, and the second one as
relativistic. In the present approach, introducing the distinction between
objects (objects per se) and para-objects (objects per alia) makes it possible
to “reconcile” the relativistic and universalistic points of view. It is impor-
tant to mention that, just as semiotic categories sometimes differ very much
in human societies speaking different languages, so ordinary (non-semiotic)
categories are not the same for all societies and for all individuals because
not only semiotic but also ordinary knowledge both depend on different
cultures (different social and individual experiences). Hence, the ongoing
cognitive investigations into ontology cannot have but a normative char-
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Concepts and Categories: A Data Science Approach to Semiotics
acter. For this reason, we shall hopefully learn more about the problem of
the alignment of semiotic categories with ordinary ones from neuroscience
(of the brain), where active research is underway, than from cognitive psy-
chology or cognitive linguistics.
Although linguistic signs should also be treated as physical objects, it
is important to emphasise that concepts which represent signs (having their
historically determined “literal” meanings) play an additional role, that of
being aligned as semiotic para-objects with ordinary objects. This stand-
point prevents me from treating as semiotic entities the indices which Peirce,
in his semiotic theory, treated as a type of signs (e.g. smoke as an “index” re-
ferring to fire). As a matter of fact, due to human language ambiguity, there
is a still prevailing misunderstanding of the important difference between
signs (proper semiotic objects) which are aligned with mental representa-
tions (e.g. the English word “fire” referring to the mental representation
of the object fire) and indices which should be classified as resulting from
such cognitive capacities of human beings as learning and pattern matching
(e.g. after having experienced a fire, one knows that – in the physical world –
smoke (effect) is produced by fire (cause)). The issue here is that the nature
of signs (semiotic units) lies in their reciprocal oppositions but that of ob-
jects (ordinary units) is still unclear. Nevertheless, semiosis should be seen
as the dynamics of the “semantics (of signs)” in contrast to the dynamics
of the “ontology (of things)” in perception.
5. Concepts and categories in human languages
As mentioned above, it is necessary to distinguish between the two
following sorts of concept families:
1. Families of ordinary formal concepts (noemata), which are en-
coded in a sort of internal mental code and whose extents are “traces of
things” (e.g. the category of an adult female person emerges amongst
others from the underlying ordinary formal concept:
{{image of a human being}, {sex: female}}.
2. Families of semiotic formal concepts (semions) which are in-
ternally encoded but can be exteriorised (either in the form of human
language expressions or, more generally, in the form of diverse signs)
and whose extents are “traces of signs” (e.g. the category of the English
word “woman” emerges amongst others from the underlying semiotic
formal concept:
{{trace of the word "woman"}, {gender: feminine}}.
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Andr´e Włodarczyk
Indeed, I assume that (1) both semiotic objects (traces of signs) and
ordinary objects (traces of things) are represented in the human mind by
s-categories (semiotic units) and o-categories (ordinary units) respectively
and that (2) these units are aligned with each other (see fig. 1). What
is traditionally called denotation refers to the relationship between signs
“in the mind” and objects in the world “out there”. What I propose is
two kinds of relationships between signs (semiotic objects) and things (or-
dinary objects), both being internalised “in the mind” as (1) singleton
extents of s-concepts and o-concepts, on the one hand, and as (2) unique
objects of a special sort of categories (monoids); namely between semiotic
categories (s-categories) and ordinary categories (o-categories), on the other
hand. Hence, it is easy to predict the usefulness of notions such as alignment
and/or refinement to characterise these two relationships between semiotic
units and ordinary units.
Table 1
Elementary and Integrative Units of Language and Mental Codes
Semiotic Units Ordinary Units
Space of CATEGORIES SIGNS OBJECTS
Space of CONCEPTS SEMIONS NOEMATA
S-concepts and o-concepts constitute the building blocks of semions and
noemata respectively and underlie the units that perhaps could be mathe-
matically represented as monoid categories (i.e., categories having a unique
object) that, in turn, integrate many of their features in the form of arrows
pointing to themselves. Note that the proposed setting is an important
paradigm shift in semiotic theory (table 1). As a matter of fact, once inter-
nalised, signs are characterised here as aggregates built as the result of the
emergence of categories from a synergetic interaction between encapsulation
and semiosis.
Classifications and their infomorphisms form a category in which classifications
are objects and infomorphisms are morphisms (Burgin 2010: 473).
As will be shown below, all the conceptual “ingredients” of signs have
singletons (one-element sets) as their extents within the dually defined pairs
of ({extent},{intent}).
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Concepts and Categories: A Data Science Approach to Semiotics
Concerning semiotic formal concepts, their features are of two kinds:
1) semiotic semantic (traditionally considered in structural linguistics
as displaying only ‘distinctive’ features of ‘form’) + features per se tra-
ditionally considered as displaying only ‘significative’ features of ‘sense’
and
2) ordinary semantic or ontological semantic (traditionally consid-
ered in structural linguistics as belonging only to ontology) with links
per alia to noemata.
However, although the extents of semiotic concepts taken as objects
per se have their proper semiotic features, the nature of their relationship
as objects per alia with noemata is based on some sort of free unification that
I will call provisionally alignment, not on interpretation. In other words,
semiotic systems – judging from their most representative sort which are
human languages – convey their own quasi-autonomous semantic ‘contents’
(information) and only align with ordinary knowledge.
5.1. Linguistic signs as categories (monoids)
The vertical arrows on Fig. 1 above indicate two kinds of inverse opera-
tions (recognition/production) which are at work between various layers of
semiotic objects hierarchy. Hypothetically, operations of the same kind (re-
ferred to as perception/action) occur between layers of ordinary objects.
The semiotic formal objects (“traces”, singleton extents of semions)
should be treated as bearing their proper features, i.e. they form concepts
which underlie the categories of the given layer in two ways: (1) as objects
per se through synergies between encapsulation and semiosis giving rise to
emergence, on the one hand, and (2) as objects per alia within a space of
complex unifications (alignment, refinement and the like) with ordinary
formal objects of noemata, on the other hand.
Operations such as the optimisation of formal concept systems under-
lie both the conceptualisation and categorisation of semiotic (and a fortiori
perhaps also of ordinary) object systems. As represented on Fig. 2, con-
cepts underlying signs of the lower (micro-)layer are subject to operations
which result in the emergence of higher (macro-)layer signs. I propose to
call this process of synergetic interaction between encapsulation and semio-
sis conceptualisation, while the process of building the higher layer units
out of the lower ones I propose to call categorisation, which consists of free
but complex unifications. The processes of categorisation are therefore due
to the synergetic dynamics of concepts, making it possible to reduce signs
and messages to solely relevant contents (see Fig. 2). Thus, categorisation
concerns the construction of more complex units out of simpler ones on each
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Figure 2. Information as the result of two kinds of processes (conceptualisation
and categorisation) passing through multiple layers of its emergence
from data to knowledge
layer (in section 6, see the discussion in more detail of the multi-layered
structure of human language utterances).
The rotating arrows (inside box Ion Fig. 2) depict the synergy (cre-
ative interaction) between (a) semions themselves and between (b) noemata
themselves, in particular, and between (c) semions and noemata, in general,
resulting in the formation of higher layer units (macro-categories) from the
lower ones (micro-categories). Let us call category emergence the synergy
(1) which occurs between all kinds of concepts (conceptualisation) and, de-
pending on the context12 in which new concepts are created, (2) gives rise
to the essentially partial integration of the result into more or less complex
units. Emergence is defined as a phenomenon that occurs between multiple
layers of nature.
In philosophy, systems theory, science, and art, emergence occurs when an
entity is observed to have properties its parts do not have on their own, proper-
ties or behaviours that emerge only when the parts interact in a wider whole.
Emergence plays a central role in theories of integrative levels and of com-
plex systems. For instance, the phenomenon of life as studied in biology is an
emergent property of chemistry. (https://en.wikipedia.org/wiki/Emergence),
last access: September 1st, 2022.
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Concepts and Categories: A Data Science Approach to Semiotics
Applied to semiotics, and particularly to linguistics, this phenomenon
sheds new light on the socio-natural ability of humans to communicate
using very complex systems. Given that semions (defined as families of
semiotic formal concepts which underlie the emergence of categories) have
single element extents (language expression units), the language categories
which result from emergence constitute a special kind of categories; they are
monoids (i.e. categories known in mathematics as having a unique object
with arrows pointing to itself only).
In fact, as described in section 6 below, the processes of transforming
expressions seen as data into their meanings (information) and their impli-
cations into knowledge pass across a stratified system of components where
the same operations (emergence and application of combination and recom-
bination rules) are repeated at every layer. It is also noteworthy that besides
Formal Concept Analysis (for concepts scaling) which inspired the founda-
tions of the research program presented, two other data science approaches
(a) Rough Set Theory (for data approximation), and (b) Distributed Infor-
mation Logic (for categories distribution) are at work during the processes
of information transmission/acquisition. And although the protagonists of
these theories sometimes attempt to cover the whole domain of data science
while extending their theories, in my view, all three mentioned approaches
should be used altogether rather than as alternative competing ones. And
in the same way as concepts and categories cannot be treated separately,
so data science objects need to be processed together though on different
stages of processing.
Table 2
The universal nature of Data-Information-Knowledge (DIK) Hierarchy
(every intelligent system acquires knowledge by the transformation
of data into information)
Domain The DIK Pyramid
Knowledge Engineering Data Information Knowledge
Intermediary
Cybernetics Support Comprehension
Transformations
Link suit Soft suit Complex
Granular Computing Hard suit Granules Granulation granules
Primary Sensory Higher Order
Neuroscience of Brain Association Area
Area Association Area
Formal Concept Distributed
Data Science Rough Set Theory Analysis Information Logic
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Andr´e Włodarczyk
In the proposed theoretical setting, information appears to be the re-
sult of an interface-like device (an invertible system) between boxes Dand K
(Fig. 2). Given that human languages can be seen as information trans-
fer devices resulting of the conceptualisation and categorisation of signs,
the new approach to language processing within the investigation methods
should adopt the name of “human language processing” (HLP) defined as
“encoding/decoding of information within the multi-layered semiotic data
processing device”, instead of “natural language processing” (NLP) which
has existed for at least half a century.
5.2. Encapsulation in human languages
The problem of encapsulation can be formulated as follows: while sign-
objects are “public”, referent objects are “private” i.e. sign-objects en-
capsulate referent objects, which causes underspecification or partiality
of meaning. Para-objects represent partial views (selected fragments) or
compressions (e.g. some conjoined parts of a whole) as opposed to their
counterparts (e.g. wholes) of object representations.13 This corresponds
to the pragmatic principle in accordance with which – in order to make
their statement effective and concise – speakers should not “say every-
thing” about a given situation but only what is relevant for their current
purpose.
As concerns the partiality of linguistic utterances, we showed in our
previous research (cf. Włodarczyk and Włodarczyk 2013, 2019) that the
information they convey does not consist exclusively of ortho-information,
which would reflect the whole knowledge of speakers about the situation
they talk about. What we called meta-informative devices14 make it possi-
ble to communicate only some chosen aspects of the situation and to high-
light them among other parts of the same situation which are treated as
secondary and can remain implicit (because “it goes without saying”), since
they may be easily reconstructed on the basis of the common knowledge
shared by users of a language and by the participants of a given conver-
sation. Moreover, any chosen linguistic unit is “virtually” linked to other
units belonging to the same subsystem. Let me call para-information such
information that refers to that which is activated in memory though, us-
ing linguistic terminology, not “actualised”. As an example, let me evoke
the meaning of the definite article “the” in English which results from the
fact that it can be chosen among other articles (the indefinite “a” or even
the absence of any article). Lexical units also belong to para-informative
networks, e.g. saying that “someone divorced” entails that this person was
previously married. Thus, both para-information and meta-information are
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Concepts and Categories: A Data Science Approach to Semiotics
important components of linguistic information, making it possible to make
linguistic messages as concise as possible. This property of human language
utterances is seen as a defect by logicians whose formulae do not entail any
implicit content. However, although it is difficult to model and formalise
meta-informative and para-informative devices for language processing, it
appears that native speakers are trained to use them unconsciously seem-
ingly without special effort.
5.3. Semantics as alignment of semiotic categories with ordinary
categories
Let me return now in more detail to the problem of alignment, in par-
ticular so far as it concerns human language semantics. Both semiotic and
ordinary objects are analysed/produced by the cognitive systems of intel-
ligent agents. Instead of the commonly accepted direct mapping between
signs and objects of the world, I claim that semantics consists in the align-
ment of two different sorts of formal (mental) objects: semiotic units (semi-
otic para-objects) and cognitive units (non-semiotic objects). This point of
view makes it possible to shed new light on the distinction between literal
and proper senses not only from the point of view of the pragmatic use of
language in human communication.15 As a matter of fact, the distinction
between s-concepts and o-concepts can be seen as a step forward to the
formalisation of the traditional opposition of literal and proper meaning.
In Fig. 3, horizontal arrows represent the alignment of semiotic ontology
with ordinary ontology, that of semiotic information with ordinary infor-
mation and that of semiotic knowledge with ordinary knowledge. Thus, in
the semiotic framework I proposed, alignment is one of the proper semantic
functions of language.
In fact, as a result of this theoretical shift, linguistic expressions have
two sorts of semantics: semantics per se and implications of semantics
per alia. From the point of view of logics, propositions undergo both in-
terpretation (satisfaction) and derivability (admissibility). But in the
case of human language utterances, the semantic content of semiotic units
(semions and categorie) draws from reciprocal dependencies (e.g. depen-
dency of decisions from conditions) (a) between themselves and (b) between
them and ordinary units (noemata and o-categories). Consequently, the se-
mantic content of linguistic expressions is defined neither from a purely
realistic viewpoint nor from a purely nominalistic one. Indeed, using for-
mal concepts makes it possible to provide a quite new and more complete
definition of semantics, namely, it enables us to treat jointly extent and
intent from the very start.
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Figure 3. Relations between the multi-modal and multi-sensory Data (D),
the Literal and Proper Senses (I) and the integrated semiotic and
ordinary Knowledge (K)
Taking the above theoretical position makes it possible to replace the
foundational issues of possible world semantics (ex. the problem of mythical
beings like Pegasus) and even to cope with (apparently) deficient constructs.
For example, the fact that the non-semiotic categories without alignments
with the semiotic ones are felt as unnamed or unspeakable, and vice versa,
that the semiotic categories without alignments with the non-semiotic ones
are referred to as incomprehensible (ex. abracadabra). In formal terms, not
all ordinary objects are paired with semiotic objects (i.e. are named) and,
vice versa, not all semiotic objects designate ordinary objects (this is known
as the coverage problem).
5.4. Ambiguity of category alignments
The alignment of semiotic categories with ordinary categories is (most
probably always) problematic. For example, some signs are synonymous
(designate the same referent) and some others are polysemous (designate
more than one referent). As an example, let us show how we can resolve the
problem of sense and meaning (Frege’s Sinn und Bedeutung) caused by the
use of two different signs to refer to the same object of the world out there.
The planet Venus is named the “morning star” when observed at dawn and
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Concepts and Categories: A Data Science Approach to Semiotics
the “evening star” when observed at dusk. Hence, the distinction “morn-
ing star” / “evening star” concerns the semiotic categorisation (with respect
to the observer’s location on the scale of daytime) regardless to the fact that
there are one or two ordinary objects. For this reason, it becomes possible
to attach these attributes to the semiotic category and not to an ordinary
category. Speakers using the expressions “morning star” and “evening star”
may know or not that these expressions are signs aligned as para-objects
with the same ordinary object, however when choosing one of them they
select a different point of view to which different images, feelings and emo-
tions are attached. “Morning” is used in human languages as a metaphor
of beginning, renewal, optimism etc. while “evening” calls to mind opposite
notions. To explain why metaphors are so important in human language
(Lakoff and Johnson 1980) the distinction between semiotic concepts and
semiotic categories, on the one hand, and ordinary concepts and ordinary
categories, on the other hand, appears to be crucial. As another example, no-
tice how poets and writers make use of the literal meaning of the expression
“the sun is rising” although everyone knows since the times of Copernicus
(and today, everyone can even see it on satellite pictures) what is the real
ontology “hidden” behind this expression.
6. The multi-layered arrangement of semiotic categories
in human languages
Conceptual semiotics constitutes the theoretical foundation of concep-
tual linguistics. It had its roots in multiple experimentations with lan-
guage data within the computational framework of interactive linguistics
(Włodarczyk and Włodarczyk 2019b) elaborated on the basis of data sci-
ence methods. The results obtained in my research within this framework
showed that a special kind of lattice is equivalent to a kind of neural net-
work with regard to human language. This observation suggests therefore
that the multi-layered arrangement of semiotic categories in human lan-
guages corresponds to a cascade of neural networks. More advanced ex-
perimental work is needed however in order to prove that it is possible to
get two complementary models of the conceptual processing of data which
underlies semiotic categories: one conceptual (qualitative, “symbolic”) and
the other one neuro-mimetic (quantitative, “statistical”). Let me also as-
sume that, here again, the qualitative and quantitative processes are most
probably both active in parallel during the data-information-knowledge
processing.
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6.1. Multi-layered pairwise patterning of human language
utterances
The processes of encapsulation and semiosis I sketched out above made
it possible to reconsider the problem of double patterning as it is usually
understood in classical structural linguistics. As a consequence, this led me
to work out a new model of the layered patterning of information during
the processes of communication in human language. My approach is close
to some theses of stratificational linguistics (Lamb 1999) but, in general,
it follows the philosophy of functional linguistics and should be seen as
the attempt to systematise the points of view of structuralist theories of
phonology, morphology and syntax, and to fill their gaps.
Indeed, the main characteristics of the structure of this new model of hu-
man language components is its multi-layered pairwise patterning. In
structural linguistics, phonemes are considered to be distinctive units with-
out meaning; consequently, the structural theory of double patterning (con-
cerning the opposition of distinctive function vs. meaning function) draws
a sharp limit between the first and second patterning, between phonemes
(viewed as “distinctive units”) and all linguistic categories of superior lay-
ers beginning with morphemes up to whole utterances viewed as “meaning
units” (see part A on the left of Fig. 4). Yet, considering that units on each
layer can be treated as categories, it should also be possible to process the
concepts which underlie them as having both extent and intent. I claim that
it is possible to generalise the idea of “distinction/meaning” relationship at
each structural layer of linguistic units (part B on the right of Fig. 4).
Thus, phonemes can be represented by families of formal concepts of
the phonic layer making it possible to interpret voice sounds as arranged
into language units (categories) of a higher layer: syllables. Similarly, cate-
gories of successive layers composing linguistic utterances (words, phrases
and utterances) are conceptualised by families of formal concepts, in this
case, forming the units (categories) of successive higher layers (morphemes,
phrasemes and predicemes). On each layer of the hierarchy, new categories
emerge due to synergy (i.e. multiple interaction processes between encap-
sulation (per se) and semiosis (per alia) operating on formal semiotic con-
cepts). Therefore, (1) syllables and chains of syllables emerge out of voice
sounds conceptualised as phonemes, (2) words emerge out of syllables and
chains of syllables which undergo conceptualisation processes as morphemes,
(3) phrases (chains of words) are conceptualised as phrasemes and, on top
of all these layers, (4) utterances (chains of phrases with characteristic
prosody) emerge from phrases conceptualised as the families of formal con-
cepts I call predicemes.
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Concepts and Categories: A Data Science Approach to Semiotics
Figure 4. Essential Layers of Utterance Construction Architecture: (A) Double
Patterning theory vs. (B) Multi-Layered Pairwise Patterning theory
As a matter of fact, in order to process a chain of sounds as a syllable,
a chain of syllables as a word, a chain of words as a phrase and a chain
of phrases as an utterance (information) speakers need to use their knowl-
edge of the given language consisting in layers of phonemes,morphemes,
phrasemes and predicemes (see Fig. 4). Indeed, only competent speakers of
the language in which an expression is uttered have at their disposal con-
cepts which are necessary for encoding/decoding units (expressions) of each
succesive layer of utterances in a given language. Persons who do not know
the language in which an utterance is being uttered perceive only chains of
physical voice sounds without any meaning.
From a more general perspective, let me just mention that be-
sides the main functions of the human brain there are a large number of
intellectual faculties (functions) which enable the speakers/hearers to en-
code/decode meaning (structured information) into/from linguistic units
such as sounds,syllables,words,phrase and utterances. These units are due
to three kinds of processing moods. They are: (a) products of grammar
rules, (b) results of realisations of schemes (such as verb and/or noun va-
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Andr´e Włodarczyk
lences) which are ready-made (in the widest sense, ‘idiomatic’) expressions
(as alternative to products of grammar rules) and (c) optionally, results
of recombination rules as applied, first of all, to schemes but also to the
products of grammar rules.
6.2. Concepts and categories of utterance layers
At this point, it seems necessary to add a few precisions about the
need to distinguish thoroughly between observable linguistic categories and
their underlying concepts. In the history of language science, the problems
covered by the “category/concept” couple of notions was explicitly intro-
duced first in the domain of phonetics, giving rise to the notion of phoneme16
as it is now used in linguistics. Phonemes are defined in the present frame-
work as families of formal concepts, their intents consist of features which
determine mostly the distinctivity of voice sounds within the given sys-
tem. At first sight, this idea may seem misleading ... especially for linguists
and other specialists working on language problems outside the data mining
community for whom the wording phonemes are not supposed to be concepts
would certainly be more than evident.17 The discrimination of phonemes is
possible solely when one takes into consideration the system of “phonolog-
ical oppositions” which can be represented by datasets to which the dual
function (Galois connection, see the schema 1 above) can be applied in or-
der to find out the formal concepts consisting of extents (objects i.e. sound
traces) and intents (the latter being known in linguistics as “distinctive
features” of phonemes). Nevertheless, from the viewpoint of data science,
given that every object has properties, specialists assume that it is always
possible to build datasets using features. Phonemes are concepts which can-
not be directly observed, what speakers and hearers experience are different
realisations of phonemes as sounds in different speech acts and different
languages.
Let me address another important issue of structural linguistics: the
definition of the category word. Surprisingly, the category of word has been
definitively abandoned and replaced by that of morpheme, although recently
some researchers consider that both concepts are necessary for the descrip-
tion of human languages. The main reason which was put forward for re-
moving word from the inventory of linguistic notions was that it is difficult
(if not quite impossible) to provide a formal (hence universal) definition
of what speakers intuitively perceive as words in any language. In my ap-
proach, I keep both terms however within different ranges; words are treated
as categories emerging from the layer of syllables thanks to the concept of
morpheme, thus they are what is perceived and produced by language users
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Concepts and Categories: A Data Science Approach to Semiotics
while morphemes are families of concepts underlying the emergence of words
out of syllables.
It is also necessary to mention how the term phraseme is used in my
model since it is understood differently in other linguistic theories.18 In this
approach, phrasemes are sets of concepts determining the internal structure
of phrases. Phrases emerge out of word chains. The features defining the
category of noun phrases in a language make it possible to distinguish them
from verb phrases whose features are different. The bundles of features char-
acteristic of different types of phrases in a given language constitute their
phrasemes. In human languages various phrasemes underlie different types
of phrases.
In a similar way, predicemes19 are families of concepts underlying
the emergence of utterances of a given language (regardless of whether
these utterances are complete or not). Importantly, predicemes provide
closure frames for predications, thus making it possible for utterances to
emerge out of phrases (cf. Włodarczyk and Włodarczyk 2019a). The basic
schema of predicemes is the subject-predicate structure which may be ex-
pressed in different ways in different languages, e.g. word order (SOV and
SVO being the most frequent orders in all the languages of the world);
gender and number agreement between subject and verb is a mark of
the predicative structure in many European languages, etc. At this point,
it is important to emphasise that one of the most innovative contribu-
tions of conceptual linguistics consists in highlighting the pragmatic na-
ture of predication in human languages, understood as meta-information
(cf. Włodarczyk and Włodarczyk 2013, 2016b, 2019a). In linguistic utter-
ances, meta-information itself combines with ortho- and para-information.
Indeed, all the complexity of linguistic utterances aims at making them the
most efficient vehicles of information.
7. Conclusion
From a philosophical point of view, it is interesting to note that the
computer tools for data mining created to advance research on all sorts of
objects, not just languages, have been used here to represent the supposed
functionality of linguistic systems. This is not a paradox, however, since
the formalisms (e.g. logical notation conventions or Programming in Logic
language Prolog) that in science underlie the symbolic representations are
to a great extent inspired by the study of natural languages. In short, the
functionality of tools is borrowed for elucidating the functionality of objects.
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Andr´e Włodarczyk
To conclude, let me outline the most salient theses of the proposed
tetradic conceptual theory of semiotics:
– Mental systems are layered information processing devices forming
a stratified configuration of spaces.
– Within mental systems, in the same way as ordinary objects, signs as
semiotic objects are code units (I adopt the idea of ‘mental code’ in spite
of the fact that its real existence is still to be proved by neuroscientists).
– Code units are components of conceptual systems; hence they have char-
acteristics of morphisms.
– Within mental systems, objects within ordinary code units are traces
of ordinary things, while objects within semiotic code units are traces
of semiotic things.
– Code units representing ordinary objects preserve traces of objects of
the world “out there”, however code units representing semiotic objects,
in addition to features their traces also preserve, have their “proper
semantic” features per se.
– Signs – like all other objects – are physical things of various kinds:
articulatory, acoustic, graphical, material etc. As such, they are objects
per se, but – in addition – unlike the ordinary (non-semiotic) objects,
signs are also para-objects: they are objects per alia.
– Signs should be treated as categories within a layered system of in-
formation processing. In structural (Saussurean) linguistic terminology,
objects of such categories are seen as ‘signifiers’ and all their features
correspond to the ‘signified (face)’ of signs.
– Ultimately, the meaning of signs (or semantics) is obtained in the pro-
cess of integration of information (most importantly assemblages of
ortho-, meta- and para-information).
The above proposal opens a new perspective on the hierarchy of suc-
cessive layers of semiotic objects which are building blocks of information
as conveyed by language utterances. I propose to replace the explanation
of the so called “double patterning” problem of classical linguistics, which
draws the dividing line between “distinction” and “meaning” of signs, by
that of multi-layered pairwise patterning reflecting the hypothesis according
to which every linguistic unit at each successive layer building up an ut-
terance can be at the same time both distinctive and meaningful, though
to varying degrees.
Clearly, in addition to their quality as objects per se characterised by
their own ‘material’ (physical) ontology augmented by their own seman-
tic features, signs are objects per alia which are aligned with ordinary ob-
jects. For this reason, they draw their features from ordinary ontologies.
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Concepts and Categories: A Data Science Approach to Semiotics
Due to their social nature, signs are more conservative than ordinary cate-
gories. Indeed, languages undergo fewer changes than cognition within the
same period of time. From the point of view of their systemic nature, it
is important to keep in mind that language ontologies are not the same
in different languages, especially so when these languages belong to differ-
ent families and cultural areas. For this reason, translating from one lan-
guage to another is a hard task (theoretically not always feasible), espe-
cially as regards literary works of art which rely heavily on the literal sense
of expressions.
Linguistic signs are used as data that need to be recognised and pro-
cessed by cognitive systems as both concepts and categories. The undergoing
operations should include, amongst others, emergence (due to the synergy
of encapsulation and semiosis) of concepts themselves and optimisation
(approximation and disambiguation) of underlying concept opposition sys-
tems. These kinds of operation should happen while passing through differ-
ent layers of a hierarchy of sign or sign combinations in which the highest
layer constitutes bunches of information giving rise, in turn, to the acqui-
sition of knowledge. Human languages, as semiotic objects (i.e. seen as ob-
jects and para-objects), are proper to humans and have a social character,
i.e. they rely on an inter-subjective consent between their bearers. Lan-
guages enable humans to fuse their reciprocal knowledge during instances
of communication (Stacewicz and Włodarczyk 2020). This remark suggests
the hypothesis about the existence of a sort of elementary presemiotic stage
of communicative ability within the brains of certain species of animals but,
as for now, more research needs be de done to acquire constructive knowl-
edge on this problem.
What is specific about human languages is that language units or ex-
pressions (categories as defined here) are (1) conceptual, their underlying
concepts being drawn from the ontological and epistemic references of noe-
mata, (2) self-consistent though (3) not self-sufficient (they play their role
exclusively when aligned with noemata). In our model, the structural lin-
guistic definition of signs as pairs of ‘signifiers’ and ‘signified’ is enhanced
by the adoption of a special kind of category (a monoid category). Although
semiotic objects and ordinary objects are both represented by their traces
within mental systems, traces of signs are not simply classic ‘signifiers’ (they
are families of dual pairs of extent and intent) and the ‘signified’ face of signs
cannot be simply elucidated by the classic notion of “concepts” (they are
equally families of pairs of extent and intent, too).
The presented conceptual approach to semiotics fills the gap between
the theory of signs and that of linguistic messages (sentences, utterances),
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Andr´e Włodarczyk
providing a new research paradigm for specialists of many disciplines (lin-
guists, philosophers, logicians, neuroscientists, psychologists and computer
scientists) about any semiotic system in an integrative manner.
N O T E S
*I would like to thank Reviewers and Editors for all valuable comments and suggestions
which helped me to improve the quality of the manuscript.
1Taking the referent for an ingredient of the theory, Saussure’s approach is, in
fact, rather triadic, too. The difference lies in that while the Saussurean pair “signi-
fier/signified” is located in memory, the Peircean pair representament/referent seems to
be situated in the real world, i.e. it is outside the memory.
2More generally, living beings or, as Henryk Greniewski [1903–1972] put it, “organisms
possessing central nervous systems endowed with the capacity to process information”
(Engl. trans. AW, Greniewski 1968: 30).
3Computer scientists proposed multiple (about 20) formal approaches to grammars
of natural languages. One of them, the Lexical-Functional Grammar (LFG), has – how-
ever without much success – laid at its basis some principles of the generative grammar
elaborated by Noam Chomsky.
4We called “interactive linguistics” (Włodarczyk 2007, 2015; Włodarczyk and Włodar-
czyk 2019b) the methodological computer-aided approach of the research area on human
languages which is deeply rooted in the forthcoming data science.
5Their nomenclature is sometimes rather strange, e.g., the not cited above “institutions”
(Goguen and Burstall 1984; Goguen 1991).
6Note however that this claim does not preclude the possibility of modelling concepts
using quite different definitions which would be more suitable for the purposes of other
applications.
7Incidentally, it is worth mentioning that for reasoning, agents and figures have a double
“embodiment”, one is (a) objective (existing “out there”), the other one is (b) subjective
(represented “in the mind”). In fact, an inter-subjective nature should also be envisaged
because while, in the case of (b), representations located in the mind of individuals (with
traces of objects), the inter-subjective nature of representations is imaginary and is the
result of all kinds of ontology unification-like processes which occur in the mind of com-
municating agents.
8As an example of such an opposition system, I built data tables of personal pronouns
in English using FCA and decision logic and the result was a lattice whose upper nodes
are attributes (speaker,masculine,feminine,human) and lower nodes objects (I,you,
he,she,it). Note that he resulting latticework suggests a strong structural analogy with
neural networks.
9Note however that ordinary objects may perform two functions: they form ordinary
categories (with objects on their own behalf, per se), but they may also be incidentally used
as if they were objects of semiotic categories (as objects per alia), e.g., a fan on the door
sometimes used to indicate the ladies’ restroom in Japanese restaurants.
10 Note that this suggests that there are two kinds of operational (“working”) memory
(“short-term working memory” and “activated portion of long-term memory which is
subject to undergo some alterations”) at work during the processes of utterance analy-
sis/synthesis.
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Concepts and Categories: A Data Science Approach to Semiotics
11 Neither the neural nature of semions nor that of noemata are known, as yet. However,
to hypothesise about their supposed analogy might be arbitrary because of at least the
two following reasons: (1) traces of signs have a double functionality (per se and per alia)
and (2) they are combining in one dimension while traces of objects can develop their
representations in the 3D space.
12 Usually, two types of emergence are distinguished: weak and strong. Weak emergence
occurs when objects of higher layers arise as a result of applying rules, while strong
emergence arises due to additional factors coming from the environment (context) in which
the system operates. Additional factors may include information from the environment
coming through the senses (traditionally sight, hearing, taste, smell, touch).
13 By partial view, I mean any part of an object representation, not merely partially
ordered sets.
14 In our previous research, we showed that meta-informative markers which point
to aboutness (choice of the subject and direct object as global and local centres of at-
tention, partition of the utterance into subject and predicate, selection of some temporal
parts of situations as opposed to their whole development) are not only lexical (e.g. to say,
as concerns etc.) but also grammatical (e.g. aspect of verbs etc.), cf. Włodarczyk and
Włodarczyk 2013.
15 Marek Tokarz provided a modern pragmatic interpretation of this traditional linguistic
problem (Tokarz, 2006, section “Znaczenie dosłowne i niedosłowne” [Literal and Non-
literal Meaning]).
16 At the beginning of the 20. century, Nicolas Trubetzkoy (1939) introduced the notion of
phoneme. This fact can be seen as a decisive step into the scientific approach in linguistics.
Although phonetic sounds have an audio-articulatory nature (“language forms”), they are
processed in the mind not only as “traces” of (physical) objects but also as ones of fully
meaningful concepts.
17 To the best of my knowledge, it is Velina Slavova and her research team (at New Bul-
garian University – Sofia) who provided the most reliable statistical results on the prob-
lems of sound symbolism and iconicity (2020).
18 Currently, most linguists understand phrasemes as collocations or idioms (as opposed
to “free phrases”). In my approach all the combinations of the Word Layer which are NOT
due to the weak emergence underlie the construction of coined phrases. The most con-
strained phrasemes are said to be coined, while some collocations allow for the free choice
of at least one component.
19 As far as I know, the term prediceme was coined by Leon Zawadowski (1966).
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