S3DM/R3DM

(Signified-Sign-Signifier) or (Resource-Representation-Realization)

2013-10-01 Semantic_Web

Introduction

S3DM/R3DM is a conceptual framework that formalizes the architectural design of data modeling process in software engineering. It is founded on the concept of Sign from Ancient to Modern Semiotics. S3DM/R3DM framework is based on the powerful theory of the semiotic triangle, a.k.a triangle of reference. We use numerical vectors (signs), to encode abstract things in our mind (signified) to which the sign refers, e.g. Person, name, Car, model. We associate these with data containers-forms that the sign takes for the storage of data values (signifier), i.e. primitive data types (see wikipedia Signified and Signifier article). This trilateral principle of S3DM/R3DM framework permits a uniform treatment of semantics, syntax and storage of information based on a symbolic representation. Next we define a fundamental, atomic information resource unit, (AIR). Those units, in turn, can be easily shaped to form any tabular, hierarchical, or graph data structure in a unified way. Data granularity can be also deeply connected and related to the definition of a fundamental unit of processing.

Computational Semiotic Triangle

First illustration with porsche
Second illustration with
- information resources
- information representation
- information realization
Third illustration with
- concepts
- code
- computer storage
Illustration with real-world object (green leaves)
Illustration with an event (traffic lights)

The Core Terms of S3DM/R3DM

There are two sets of base terms one starting with the letter ‘R’ and the other with the letter ‘S’ that we can use in order to convey the fundamental principles of R3DM. Both of the sets are outlined hierarchically into three levels. Each level is described with one or more characteristic words that are useful for memorizing and recapitulating the distinguishing features of R3DM.

STerms

S3 : Signified, Sense, Semantic - Signify
- Signified, in Greek “σημαινόμενον”, to mean something
S2 : Sign, Symbol, Syntax, Structure - SymbolizeS2 : Sign, Symbol, Syntax, Structure - Symbolize
- Sign, in Greek “σημείο”
S1 : Signifier, Storage (String) - Store
- Signifier, in Greek “σημαίνον”

RTerms

R3 : Information Resource - InfoRes (Enity) - Originate
R2 : Information Representation - InfoRes (Symbol) - Represented
R1 : Information Realization (Datum) - Realized

Other Terms

There are also other terms that are often used when we describe relations, operations and features in R3DM these are:

Referenced
Interpreted
Formatted
Expressed
Decoded
Encoded
Parsed

Trilateral Relations

The trilateral schema of relations between R1, R2 and R3 or equally between S1, S2, S3 defines the core mechanism of semiosis. We will use the terms we defined in previous section to build simple sentences that convey the full meaning. We will also use three prepositions “from”, “through” and “in” that accompany RTerms and STerms in a specific order that signifies the left to right direction of abstraction

Direction from S1 through S2 in S3
- Data from S1 are Symbolized through S2 and Signified in S3
- Data from S1 are Decoded through S2 and Interpreted in S3
- Realization from S1 is Parsed through S2 and Interpreted in S3
Direction from S3 through S2 in S1
- Information Resources from S3 are Represented through S2 and Realized in S1
- Information Resources from S3 are Represented through S2 and Encoded in S1
- Information Resources from S3 are Represented through S2 and Formatted in S1

S3DM/R3DM Dogma

With the term dogma we want to bring together a set of R3DM principles laid down by an authority as incontrovertibly true. R3DM dogma serves as part of the primary basis of R3DM modelling system, and it cannot be changed or discarded without affecting the very system’s paradigm. R3DM is serving one purpose to become the paradigm of paradigms, the metamodel of metamodels.

S3DM/R3DM Formalization v2.0

S3DM/R3DM is a conceptual model of an information processing system based on semiosis. S3DM/R3DM fundamental construct is the uniform information RESOURCE (UIR), i.e. a parent class of the following three derived subclasses :
A Term Information Resource (TIR) models any concept, subject, topic, idea at a highest level, S3, i.e. sense, context level, of abstraction. TIR is also called the signified information resource
On the next, intermediate level, S2 - sign level, a Sign Information Resource (SIR), models the notion of the sign in semiotics. Therefore (TIR) is REPRESENTED by (SIR).
Finally at level, S1, i.e. data level, (SIR) conveys information that are encoded inside a data container, i.e. Datum Information Resource (DIR), signifier. The content inside (DIR), i.e. data, is expressed with an atomic or complex data structure and REALIZED with operations on data. Therefore (SIR) is REALIZED by (DIR).
In all the levels, S3, S2, S1 of abstraction references are created and maintained for the context of the signified concept (S3), the construction of signs (S2), and for the addressing of containers and the indexing of content that express signifiers (S1). Thus, information resources are REFERENCED differently depending on the level of abstraction by a Reference Information Resource (RIR).

There is also a hidden level S0, machine-system level, where everything is encoded and expressed with a sequence of binary digits but this currently out of our scope.

Memorizing the formula

In a concise way S3DM/R3DM can be described in any of the following memorable ways

S3DM/R3DM Edges - Duality of Sign
- Any Sign at level S2 is correlated to a Signifier at level S1 and the Signified at level S3
S3DM/R3DM Nodes - Triadic Relationship
- Any information RESOURCE at level S3 can be REPRESENTED at level S2 and REALIZED at level S1 using a different REFERENCE mechanism at each level.
S3DM/R3DM Nodes - Triadic Relationship
- Information RESOURCES are REPRESENTED, REALIZED and REFERENCED
S3DM/R3DM Nodes - Triadic Relationship
- Information RESOURCES are originated FROM level S3, are represented THROUGH level S2 and encoded IN level S1

S3DM/R3DM Formalization v1.0

In fact it occurs that this formalization is also the first attempt to formalize the notion of the word “plerophoria”, i.e. information translated in Greek, using Aristotle’s semiotic triangle of meaning.

S3DM/R3DM models any concept C at a highest level, L2, of abstraction.

Information RESOURCES about that concept are REPRESENTED and consequently encoded using a combination of signs S at an intermediate level, L1, into a message M.

Then at the lowest level, L0, the content of M is expressed with a complex data structure D and REALIZED with operations on data containers.

In all L0, L1, L2 levels of abstraction, we maintain REFERENCES for the context (L2), for the construction of signs (L1), and for the addressing of containers and the indexing of content (L0).

The Trilateral Principle

Resource, symbol and data, each plays a distinct role but they are united with a trilateral relationship and act as one thing. They are present at every level of R3DM as

In fact you cannot separate these three things in any computer engineering architecture, the signifier (the concept, semantics), the symbol (serialization, syntax), and the signified (storage, data form, i.e. strings, numbers, bits). They stay together from the lowest level of abstraction, to the highest level. You can only link these meaning triangles side by side and move in two directions, specialization or generalization, Sowa Ontology, Metadata, and Semiotics.

Symbol’s Duality Principle

There is a duality on the characteristics of a sign. Symbols play two roles at the same time that of a container and content. These roles cannot be separated, they always come in pairs. You may think in terms of how computer memory works to understand this. In digital computers EVERYTHING is represented with a sequence of bits, but this sequence is stored in an array of memory cells. Therefore any such fundamental construct, i.e. data structure, that can be build at a higher level should comply with a symmetrical design, i.e. Types, Instances, Values, and Relations-Associations all of them have to be constructed from these atomic fundamental constructs.

The Threefold Tower of Babel in Information Technology

A concise synopsis of the chaotic situation that is present in information technology is this:

The user is experiencing a threefold Tower of Babel

in semantic web and linked data - conceptual modelling,
in computer programming - symbolic modelling
in persistent or temporary storage and retrieval of information - data modelling.

Cross-References

Upper_ontology Semantic_Web Topic_map Formal_ontology Sign_(semiotics) Triangle_of_reference Signified_and_signifier Information Computational_semiotics