A General Systems Theory Used as a Basis for a
Theory of Thesaurus Relationships
by Edward N. Baylin
is a working paper. I invite your comments and critique.
Last updated: January 25th, 2004
After working sporadically on a book over a period
of at least ten years, starting in the very late 1970's (when I
was still a systems analyst in industry), I officially went public
with my ideas on systems theory with three interrelated books,
especially Functional Modeling of Systems, published by
Gordon and Breach Science Publishers in 1990. Two concurrent
"satellite" self-published books accompanied that book,
one providing some examples, and the other going into more detail
on diagramming methods. My ideas in this area have continued to
develop since then.
A superficial reading of my ideas at the time led
many to believe that I was another author developing yet another
structured method of process modeling, rather than someone who was
developing something more along the lines of a general systems
Nowadays, my ideas are explained more in terms of
class/object structure diagrams and role playing, which may lead
some to believe that I has developed another method for
object-oriented computer system analysis, but using some
mathematical explanations. Although there is a degree of truth to
such claims, it would be more correct to say that I take the
approach of a philosopher looking far beyond computer information
systems into the realms of epistemology and ontology.
generic structural sub-distinctions within any dimension are possible. For
instance, within the flow function dimension,
programmers usually distinguish sequence, decision, and
looping structures (both accumulation and error
correction loops). Our books also analyze that dimension
in terms of other distinctions, in particular the
so-called "intertwine complexity," which constrains flow
functions to have the first input (supply acquisition)
flow function occur before the first processing
(transformation) flow function, and the last output
(delivery) flow function after the last processing one.
Within those constraints, more than one of each type of
flow function can occur in a procedural flow, in any
In addition to
the flow dimension, a second dimension is often included
by those who teach computer algorithms. This is the one
that distinguishes levels of control within what I
called the "adaptation" functional class. Modular
programming and distinguishing this second dimension are
the same subject insofar as the modules coincide with
control levels. Modules in the flow dimension are,
however, the ones that are emphasized by those who teach
algorithm theory. Again, this only provides two of about
seven dimensions of interest in creating generic
structure in algorithms.
sometimes ask myself whether my books are, in reality,
among the most advanced works in the area of algorithm
theory, although I'm not sure how others who have produced works
on algorithm patterns would react to such a claim. I'll
simply have to check out what has been done by others in
this area before coming to any kind of conclusions.
But, there is another way of identifying the area covered
by the books. This is to see them as being largely in the area of
advanced structured algorithm theory. It has always struck me that people
who teach computer programming tend to cover everything about algorithms
in just a single dimension, i.e., the dimension of what in my
books I call "flow functions" (see below). This
one-dimensional approach implies a huge lack of conceptual
structure, and makes the overall relationships in the flow
difficult to follow. My books approach the subject in an
way, thus providing a better way of conceptualizing the generic
procedural structure. Moreover, much leveraging of these ideas
is possible, since the patterns are recursive. The relation
between these various dimensions is discussed further below.
Further leveraging of the ideas comes from the fact that this
relation is fairly simple.
a simple example, applicable to a computer program, lets
us add a second dimension, say, to distinguish the
set-up (declaration of variables, opening of files,
allocation of memory, and so on) and wind-down
(de-allocation of memory, etc.) operations. These would
be in a separate dimension from the direct operations
(called "baseline" in my books). This provides a
two-dimensional structure to the conceptualization of
the algorithm, instead of putting all these operations
into a single, unstructured flow. In other words, you
are now looking at a table depicting the program
procedural structure with its rows (each depicting a
step in the program) divided into two columns.
To conclude this background section, it is important
not to lose sight of the fact that, although it may look as if the ideas are very
different from what they were in 1990, the core ideas are actually
the same as they have always been. What has changed is mostly that I
developed some badly needed perspective on them, along with
which came a different way of expressing the ideas and understanding
their relevance and connections with the ideas of others.
The role theory developed here is generally
applicable both to relationships between objects and to
relationships between object classes. However, some roles apply only
to relationships between object instances, while others apply only
to classes (types, kinds, categories, etc.) of objects. In fact, one
type of role provides the relationship between objects and object
To keep down the number of words in the rest of this
paper, although the discussion is generally phrased in terms of
object instance roles only, class roles are also implied unless
The latest expression of these ideas includes new
facets, and the use of some mathematical set theory. The ideas are
now expressed in terms of their providing a canonical, multi-level
scheme of types of roles that objects play in their
relationships to one another in a system or in modeling a system. An
object may also play these roles reflexively and recursively (back
on itself), and may engage in parallel in any number of roles in
relation to any number of objects.
The role classification is thought to be complete, and
Similarity/anti-similarity roles: Objects
can have roles that allow objects to represent one another. In
fact, such roles are the basis of modeling relationships between
objects. The relative similarity or dissimilarity of objects to
one another can be arranged on a fuzzy similarity spectrum,
where objects can range from being complete equivalents (e.g.,
synonyms) to complete opposites (e.g., antonyms) of one another.
"Primary" causal roles: Such
roles include those of:
Agent/instrument: That which carries out the
Input: The patient of an action; the
operand; that which is transmitted, transformed,
transfigured, transmuted, translated, etc.
Output: The product of an action; the output
of an event.
Pattern-provider: The pattern may be a
method to be followed, a spatial pattern, a value pattern,
or a pattern of meaning. A method, for instance, is
the flux pattern, procedure, or series of steps, that the
agent/instrument carries out to complete the process
involved in the event.
Context-provider: Time, space, population,
viewpoint/discipline/domain, giving the backdrops against
which the event happens.
respect to thesaurus systems, which involve word relationships,
a search that finds "lecture," which is a kind of
event, might also find the words for the corresponding:
Agents, which include teachers and
students (who actively participate in their own learning).
Inputs, which are the students, who
are the patients of the lecturing process carried out by the
teacher agent and their own participation in it.
Products, which are the students who
have now learned from the lecture.
Methods, which, for example, include
lecture notes to guide the teacher, and steps undertaken by
students to integrate the materials of the lecture into
their memory circuits.
Contexts, which include the school or
classroom, the time of the lecture, the academic community,
and so on.
Derived causal roles, i.e., the event role,
played by associative objects, derived from the intersecting
roles of objects playing the primary causal roles: Whenever an
event occurs, a number of objects are involved in these roles.
With respect to the previous example, the happenings during
the lecture, such as delivery of materials by the teacher,
absorption of the presentation by the students, and internal
reflections of people on the subject at hand.
Primary and derived
(event) causal roles are understandable only relative to a given
system. In the wider scheme of things, all objects (also known as entities)
are "eventities," i.e., associative objects as well as
"primary" objects (although the converse may not be true).
mountain can be seen as an event instead of a static object when
viewed over millions of years of change in the mountain
characteristics. Thus, the word
mountain may be understood
as being both a verb and a noun [ the many works of Kent Palmer at
Hierarchical roles: Hierarchical roles
Controller/subordinate roles: played in
superior versus inferior relationships.
Component/composite roles. Such roles are of
two kinds: 1) an object is completely and uniquely included
in another object; and 2) an object may be a component of
more than one other composite object, both of which share
the object as a component.
Super-class/sub-class roles: applicable only
to object classes; analogue of ancestor/descendant roles
played by object instances.
Ancestor/descendant roles: applicable only
to object instances; the analogue of super-class/sub-class
roles played by object classes.
The possible relationships of hierarchical roles (which
are the basis of mathematical ordering relations) to causality
is mentioned below.
Classification/Instantiation roles, i.e.,
roles based on the relationship between an object class and an
object that is an instance of that class. Object occurrences may
be classified, while object classes may be instantiated to
create object occurrences. In object-oriented programming, we
speak of instance creation and instance destruction operations
(usually referred to as methods),
each of which carries out a particular sub-type of instantiation
role. This idea can also be thought of in terms of object
classification and declassification.
I have applied this scheme of primary roles, along
with a simple event role, to several object/object class
relationship diagrams in the computer systems field, and might
provide an important enhancement to methods for creating such
diagrams, including the UML (Unified
Modeling Language) method that has now become the norm. Ignoring
such a scheme for assignment of roles to objects in their
relationships to one another may be to ignore basics in favor of
idiosyncratic schemes created in a helter-skelter way by a motley
crew of information system modelers.
As stated, this role
theory is basically just a very different way of presenting my
earlier ideas on general system process modeling. However, the
process modeling ideas in my 1990 books go considerably further, in
that they produce many sub-classes of the event roles played by
In fact, Functional Modeling of Systems
presents various ways of classifying associations (the event role). In that
book, a relation between these roles is developed, i.e., a sub-set
of the Cartesian product of the different sets of values associated
with each type of associative role.
Associative roles in the
relationships between associative objects themselves are first sub-classified
into baseline versus adaptation functions, based on
the factor of directness of relation to objectives.
Directness is in the sense used in accounting, rather than in the
sense of immediacy. Adaptation functions are those used to plan,
organize ("framework"), and control (direct, ensure) a system,
while the baseline functions directly carry out the essential
purpose of a goal-directed system.
From there, further levels of
sub-classification are based on concepts that include:
Decision-making versus decision-implementing
adaptation functions: orthogonal to other distinctions
applicable to adaptation functions described below.
Hierarchical control level of decision-making
(adaptation) functions: orthogonal to the distinctions based
on other factors described below in this list.
Adaptation function timing factors:
Time frame: long-term, medium-term, short-term, etc.
In its simple form, this leads to distinguishing control
functions, which are short-term, from planning and framework
(organizing) functions, which apply over a relatively longer-term
time horizon. Note: Baseline functions are always
short-term, by definition.
Time orientation of short-term adaptation
functions: initiative, interruptive,
and after-the-fact sub-classes, as well as further sub-types of
the interruptive sub-class.
Flow sequence functionality ("flow functions"):
Input, process, and output — applicable to
both baseline and adaptation functions, and thereby orthogonal to
other distinctions described below.
divisions of (adaptation) decision-making flow functions:
For instance, sub-types of adaptation process flow
functions include investigating a problem or opportunity, laying
out alternative solutions, and making an actual decision on what
to do. Generic sub-types of input and output flow functions are
Classification in this generic pattern leads to a
first-cut hierarchical functional decomposition of the system,
within which further decomposition is possible based on
non-generic factors until the required level of magnification of
details has been achieved for any purpose at hand. The
classification pattern itself is recursive (fractal), perhaps to
Let me now explain
mathematically, using simple set theory, how all these role types
are intersected with one another to obtain a general systems process
relation" is obtained by composing the set that contains the
various above values for primary roles with the relation that
describes the derived roles. (Note: As will eventually be seen, this
larger relation is still only a projection out of a still larger
relation, involving even more sets.)
mathematical terms, a model is usually thought of
as a relation that has a homomorphic relation to another
relation that is modeled by the model. In other words, it
is a relation between two similar patterns of objects. The
model is on the "one" side of this many-to-one
relation between relations, and so can potentially be at a
more abstract level than the relation representing the
system that is being modeled. A model can also be
understood to work in the reverse direction, as the
specification for a particular system that is constructed
based on a meta-model or a theory. The generic model can
be used for modeling in both senses. In either case, the
generic template can be viewed as a syntactic expression
of the patterns of structure and flux (behavior, process)
of a system.
The overall composite relation thus obtained can be
said to be a generic, or canonical one, since all the
sets provide categories that go back into the realm of
epistemological or ontological understandings. This generic relation
can also be viewed as a generic system model, i.e., as a
template or meta-model, or as a model of a general systems theory.
This model is domain and scale independent, i.e., can be used with
systems in any application area or of any size.
Using the idea of model in the first above sense,
system instances, or sub-classes of generic system models applicable
to generic system types (e.g., allopoietic, dissipative,
autopoietic, or reflexive systems, according to the to-be-described
Palmer's ontology) may be modeled by plugging in different detail
levels of more specific values. Thus, when the template is applied
either to model a particular system, or to specify a to-be-developed
system instance, semantic content is added to the various
placeholder positions in the template. In this addition, the
syntactic expression of structural and behavioral patterns is
supplemented with domain and application-specific semantic content
that expresses the patterns of value and meaning of a system
instance, as well as the details of the structural and behavioral
patterns giving that system occurrence its unique features.
Examples of application (instantiation of
placeholders) of the template to modeling systems are provided in
one of my two satellite books, Conceptual Prototyping of Business
Systems: A Templating Approach to Describing System Functions.
In that book, I showed that four apparently completely different
allopoietic business systems are actually isomorphic (equivalent) to
one another. For simplicity, the entire template was not applied to
these systems. Placeholders for planning and organizing (framework)
functions were left essentially unfilled. That is, by elimination, I
modeled only the "operating core" of these systems with
the template. This operating core includes the so-called
"transaction-processing" information systems, which are
part of the operating core control systems.
The general system model
in Functional Modeling of Systems book not only further
sub-classifies the event role, as described, but also applies the
time frame (one-shot, short-term, medium-term, long-term) idea to
engender different sub-classes of agent/instrument and method
pattern-provider causal role
General systems models
My generic meta-models can be usefully compared to
other attempts that have been made, mostly in the 1970's, to develop
general system models that are somewhat analogous to one another and
to my models. Examples of this way of thinking are found, for
instance, in books such as those authored by
or Stafford Beer.
However, those authors are as different from one another as they
each are from me with respect to how their ideas are developed and
expresses the ideas based on a model of the organism, which is a
kind of root metaphor used by us for a system (as we project our
own organization on ontic phenomena). Beer, on the other hand,
tends to approach the subject from the viewpoint of business or
other organizations and their management (command and control
structures). In both cases, the authors tried to stretch the
idea of the allopoietic system to fit what are perhaps better
modeled as autopoietic or reflexive systems.
My expression reflects the experience I had during
my career as a business computer systems analyst, during the era
when the structured approach to process modeling was in its heyday.
ideas are expressed in my books in terms of a new, very complex
diagrammed method called the "structure-flow chart."
The development of the latter coincided with some general
research on procedural diagramming, which was published in one
of my satellite books in 1990, namely, Procedural Diagramming
for System Development: From a More Scientific Viewpoint.
Thesaurus relationship theory
Application of something along lines that are
comparable to my role theory can be found in works on thesaurus
relationships, i.e., the theory of relationships between words.
A good paper on how this has been done can be found in an
article by Tudhope, Alani, and Jones, in the Journal of Digital
Information, volume 1, issue 8, February 5, 2001. To locate this
article, "Augmenting Thesaurus Relationships: Possibilities
for Retrieval," on the Web,
Beware in looking at this article that the similarities and
relationships to my role theory are not immediately apparent,
since the manner of expression and domain of study are quite
concentrate on similarity ("use for") and classification
(narrower/wider than) relationships between words. If the
thesaurus is for a particular discipline or domain, the context
relationship also becomes important, giving the viewpoint of that
domain. Any other word relationships are usually simply grouped
under the umbrella of "related-to" relationships. Note:
By "classification," librarians not only refer to the meaning of
the word just explained, but also refer to the context causal
role. These two roles are separated, as seen above.
Although it is focused in a very different way, the
core idea involved in my role theory can be roughly mapped to
four viewpoints for studying real-time systems, as well as to
Aristotle's theory of causality (perhaps as extended by the
differentiation of being from existence [
The latter's kinds of ideas have been extended to include:
The context role type, for objects
representing space, time, or population, and perhaps other types
Various sub-classes of all the role types,
whereby particular types of formal (pattern), material
(input), efficient (agent/instrument), and teleological (see
next) cause are delineated.
An arguably correct reinterpretation of
teleological cause in terms of different types of
hierarchical roles, including decomposition and classification
hierarchy sub-types. As well, the output role arguably maps to
Aristotle's teleological (final) cause. Hierarchical roles can
perhaps also be interpreted as related to teleological cause as
In the case of decomposition (part/whole)
hierarchies, the role of the part is to help fulfill the
role of the whole.
In the case of classification (typing,
specialization) hierarchies, the role of the ancestor or the
super-class is to form a cohesive, more core-centered
purpose for all its more specialized descendants, of which
the ancestor forms the core.
A different kind of treatment of Aristotle's
formal cause role type, whereby it is discussed at the level
of the object (what Palmer calls the "form"), as well
as below the level of the object, at what Palmer calls the pattern
level. Moreover, different "views" (for want of a
better term) of the object (form) or patterning are identified
Four kinds of pattern:
Not to distinguish too closely at this
point between the pattern and object levels (see below), the
four views are:
- Flux/Behavior: process, or flux
(Palmer's term for the pattern level), or behavior
(Palmer's term for the object level), or method, or
equivalent, seen against the context of time. Since
formal cause constrains/parameterizes the associative
event, it is possible to map control hierarchical
relationships to Aristotle's formal cause, and to
associate these relationships with method patterns. In
such a hierarchy, method constraints are given at
different levels of abstraction.
- Structure/Shape: seen against
the context of space.
- Value/State, e.g., economic
worth, seen against the context of population.
- Sign/Interface: symbolisms or
references that when arranged in certain strings or
other configurations give meaning, perhaps seen against
the context of population.
As described in Butchvarov's [
pre-entity theory (in Being Qua Being), specific
mappings of pattern type to patterning operation exist. Each
type of operation creates the specification for one of the
four kinds of pattern. That specification is used by the
object that plays the event (derived) role. Specifically,
the patterning operations specific to each kind of pattern
- Concatenation: specifies a flux
pattern to guide the temporal behavior of the
- Reduction: specifies a
structural pattern to outline the spatial shape
of the event object.
- Exclusion: specifies a value
pattern giving the state set of the event object.
- Reference: specifies a sign
pattern for constructing the interfaces (e.g.,
address references) of the event object.
As described by Palmer, the four kinds of
pattern of the pattern template that is part of our
tradition of understanding corresponds to four kinds of
object "views" at the level of the object template
(called the "form" template by Palmer).
- Pattern and object (form) are levels of
templates of understanding in Palmer's ten-levels of schemas.
These levels are: 1) facet, 2) monad, 3) pattern, 4)
form, 5) system, 6) meta-system (system environment), 7)
domain, 8) world, 9) cosmos, 10) pluri-verse. More is
said about this ten-level ontological hierarchy
in a frame below, where three special sub-levels between
levels 5 and 6 are identified. The form (object) schema
is the most traditional, while much work has been done
on the pattern and system schemas in the 20th century.
However, all schemas are important and part of our
tradition. Palmer's special area of interest tends to
lie from levels 3 to 7, with most interest at the center
of this hierarchy (where dissipative, autopoietic, and
reflexive system schemas are posited).
- Flux (method) and structure views of
patterns at the pattern level are the complementary
duals of value and sign views at this same level.
Flux and structure are percepts that depict the
totality of pattern contents, while value and sign are
(mental glosses) that depict the unity of the
- Behavior and shape views at the object
level are the corresponding complementary duals
of state and reference views at the object level. The
first two have to do with percepts, and the last two
with concepts, as for their counterparts at the pattern
The system meta-model
represented by my generic relation goes back to the levels of
ontology and epistemology, which are branches of philosophy. Going
back to these roots, here is a far more interesting and fundamental
further set that can be composed with my system relation, a set not
known to me in 1990. That further set can be seen as being at a
meta-level to the composed relation, since it affects how the
relation set itself is viewed.
This set is based on Palmer's theory of modes of
Being and Existence. Palmer proposes four modes of Being, one of
which allows us to see the world in terms of allopoietic systems. It
is the latter way of seeing the world, called Pure Presence by
Palmer, which is selected from this set in Functional Modeling of
Systems. However, for
and reflexive systems, other values of this set would be more
Other elements in this set provide us with an
increasingly less frozen kind of Being. Palmer calls these Process
Being (associated with dissipative systems), Hyper Being (associated
with autopoietic systems), and Wild Being (associated with reflexive
systems), successively. The fifth element of this set is Existence
itself, which can be seen as the null set. If Existence were to have
been selected as part of the relation in question, the relation
itself would be canceled, since Existence is emptiness, or the void,
where distinctions such as those made in the other sets in this
relation cease to have any meaning.
I would like to extend my theory of role relations
to include the ideas of types of systems and system environments as
developed by Kent Palmer. In this way, specific, canonical/generic
relation sub-classes can be specified. The extended theory would be
more appropriate for modeling dissipative, autopoietic, and
The application of the theory to these other kinds
of systems is a problem whose complexity has hardly been mentioned
so far. Although the popular term "system" is applied to
dissipative/autopoietic/reflexive systems, such mental templates
(schemas) may perhaps be more appropriately viewed as systems
inter-penetrated by the system environment in varying degrees. This
degree of environmental inter-penetration increases as we go from
dissipative, to autopoietic (self-organizing, organism), to
reflexive (social) systems.
My ideas are based on the
system schema (normally what we mean by a system), which has to be
unnaturally stretched for it to apply to phenomena that we have a
tendency to schematize as dissipative, allopoietic, and reflexive
systems. In Palmer's hierarchy of mental templates that we can
project upon phenomena (called the "ontological
hierarchy"), there are ten basic levels, with the system level
being near the middle. Palmer's three "special systems,"
the dissipative, autopoietic, and reflexive, actually form three
sub-levels above the system level, right at the center of this
hierarchy, between the system mental template and the mental
template of the system environment. (These templates of
understanding themselves are some sort of relation founded on the
Cartesian product of certain fundamental philosophical categories,
the kinds of Being, and another classification scheme that Palmer
calls "aspects of Being.")
Palmer has managed to put his insightful ideas into a kind of
"theory of everything" that is perhaps unlike anything
seen before except in the latest physics (with its 11-dimensional
string-based theory). His idea of autopoietic systems solves some
fundamental contradictions inherent in the explanations of such
systems in systems theory/science thinking.
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