Semantics and information capability

Concepts and objects, high order objects. Modeling, modeling tools, modeling capability, universality principle, self-reference, MENTION-USE principle. Relevant elements of knowledge explication in the framework of lessons learnt from Interim Project.

= Concepts and objects =

Concepts – 1st approximation
• Concepts are identical to intensions : linguistic expressions denoting intensions are names of concepts

Concepts are functions from possible worlds (Possible-world) and time points (Time) to any types above EB (elementary believes).

Criticisms of the 1st approx.:

A.

-Concepts arestructured

-Intension is a function, thus an object. An object, as well as a function, is not structured, it is “flat”.

-What seems to be structured about a function is a way of its declaration – its construction.

=>concepts could be identical to constructions of intensions.

B.

-It is necessary to separate precisely the world of objects from the world of their constructions, as we have no objects in our Memory – therefore we need trivialisation:

• it is about elaboration and expansion of the definition of atomic construction

• TRIVIALISATION constructs objects simply by pointing them.

1.Simple Theory Of Types:

– constructions are out of the focus of our research

– constructions are only tools for a research of the World-of-objects


 * Simple Theory of Types deals only with OBJECTS OF ORDER 1 and works with type hierarchy which is infinite but still in limits of order 1.

-Construction is unable to be mentioned as object of interest in Simple Theory of Types; Constructions need to be included into observed objects of interest …

=> Ramified Theory of Types is needed !

2.Ramified Theory Of Types (Bertrand Russell):

-This is a complete apparatus of constructions which allows to describe also a self-reference (and what happens in the Fundamental Hierarchy)


 * Ramified theory of types is built above used cognitive base, above EB introduced in Simple Theory of Types.


 * Ramified Theory of Types includes constructions asobjects, thus it adds a new (infinite) hierarchy of orders. HIGHER ORDER OBJECTS

Concepts – 2nd approximation
• Based on the use of Ramified Theory of Types:

• Concepts are closed constructions

(Rules of l-calculus)

Concepts – 3rd approximation
• Concept is a closed construction belonging to a class of quasi-identicalclosed constructions.

As constructions from a given class are not distinguished in theUSE mode, we will not distinguish them in theMENTION mode.

(Closed constructions c1 and c2 are quasiidentical if they are alpha- or beta- or gamma equivalent. We say that c1 and c2 are in relation Quid.

If ( c1 Quid c2 ), then c1 constructs the same object as c2, or both c1 and c2 are improper.)

CONCEPTUAL SYSTEMS
Primitive Concepts (simple concepts)

-Simple concept is atrivial construction of anobject (which is not a construction!!) or of anvariable

-Simple concepts pointobjects

Vs.

Derived Concepts

!RELATIVITY of Primitive/Derived!

What is primitive within one domain can be derived in other domain!!


 * How we evaluate the situation depends on a CONTEXT.

The semantics is given by the couple: (Domain, Conceptual System).

=> !CONCEPTS are context INDEPENDENT; selection of CS is context DEPENDENT!

JAK poznáváme

 * vždy pomocí modelů
 * model dynamického systému:

-jiný dynamický systém (v reálném světě)

-pomocí pojmů a představ (v ideálním světě)


 * pojem: identifikační procedura dohoda na významu
 * pojmový (konceptuální) model
 * model v ideálním světě (ideální model)


 * dynamické systémy reálného světa mapujeme statickými pojmovými modely

-vytváříme základní modely pozorováním

-odvozujeme sekundární modely přemýšlením

https://kore.fi.muni.cz/pub/index.php/File:ODM.jpg


 * 1) procesy (vnímáme z reálného světa)
 * 2) věci (vyabstrahujeme se na čas)
 * 3) události (navnímané koincidence procesů)
 * 4) kontejnery (sbalení do vyššího celku za účelem pořádání)

= Higher order objects =

• If α is a type of order n, then every X Є α is an object of order n.

• Objects of order n, where n > 1, are called higher order objects.

• The class of all constructionsof objects of order ncomposes a type of order n+1.

• Every construction of order nis an object of order n+1.

Higher order objects and their constructions, especially trivialisation, provide the inspiration for MENTION and USE of connections, categories, operations and rules which are fundamental constructs for modeling.

• Knowledge is principally recursive !

• To understand (or to model, to execute) a knowledge-intensive Service System

No construction can be found among objects of order 1.

• Simple Theory of Types deals only with objects of order 1 and works with type hierarchy which is infinite but still in limits of order 1.

• Ramified Theory of Types includes constructions as objects, thus it adds a new (infinite) hierarchy of orders.

= Modeling =

Role of objects and constructions in conceptual (data) modeling

• OBJECTS – what is focused on

• CONSTRUCTIONS – what identifies focused objects

(for all participants in a communication so that they have the same objects in the mind during this common communication)

• Conceptual (Data) Model contains constructions of objects (constructions which identify objects) corresponding especially to non-trivial intensions

• Database contains linguistic EXPRESSIONS (of a special language) which denote some objects (corresponding to extensions)

 Objects are defined and they are defined by concepts

Attention Focusing

-over EB we choose particular types and we focus our attention to objects belonging to this types only

-the model than contains constructions of these focused objects

-The focused objects are: HIT attributes and sorts

What a conceptual modeling is in fact

• Discovering of suitable concepts identifying objects in the Domain under Discussion (DuD).

• Creating pragmatically a proper conceptual system.

• Step-by-step designing of a hierarchy of languages with respect to the conceptual system.

• Real understanding to DuD through previous steps, i.e. by creating of semantics of words connected to the domain.

Process of Modeling

1. Focus on objects >> base of categories

2. Focus on relationships >> list of relationships

3. Simulation of behaviour >> list of operations

4. Statements of consistency >> list of rules

Conceptual Modeling is the way to understand


 * 1) domains
 * 2) environment
 * 3) systems

= Modeling tools =

• Let MT=(CAT, CNN, OPE, RUL) be a dynamic model such that

– every category from CAT Є CNN could be filled by instances,

– every operation from OPE could be executed

• Then we say that MT is modeling tool.

• By modeling using MT we can create a dynamic model M, which we can use again as modeling tool.

• The creation of model M by modeling tool MT means, that we simulate M by game with instances of dynamic model MT.

• Definition of MT is fundamental. It corresponds with intuitive approach of model creation in modeling tool and also with common praxis in available SW, which are considered as modeling tools.

Available modeling tools (MT)
CASE tools (Computer Aided Software Engineering)

– any computer-based tool for software product planning, development, and evolution.

(Editors, Compilers, Debuggers, Code Generators, Documentation Generators,Requirements Tracing, Change Management (CM), Defect Tracking, Collaboration tools, Access Control)


 * Oracle Designer, System Engineer, Enterprise Architect, Rational, Power Designer, …

BPM tools (Business Process Model)

– help enterprises map out their existing processes and optimize them


 * Aris Tool Set, Corporate Modeler

PM tools (Project Management)


 * MS Project, Primavera

Available MTs (modeling tools) are not satisfactory for needs of current service oriented business.

Bottom-up building MT

• MT is created for specific particular problem

• … according to current needs and requirements

• … without any analysis of a position of a problem within other problems (already modeled or worthy to be modeled)

• In the given specific situation it is a pragmatic and effective approach.

= Modeling Capability =

• Let MT1 and MT2 be modeling tools.

• If all M ((M can be created by MT1) => (M can be created by MT2)) then

MT1 has lesser modeling capability than MT2

(i.e. modeling capability of MT1 is lesser or equal, or “at least the same as” modeling capability of MT2.)

• If MT1 has lesser modeling capability than MT2 and MT2 has lesser modeling capability than MT1, then MT1 and MT2 have the same modeling capability.

Modeling Capability properties

Relation „has lesser modeling capability than“ on set MMT of all modeling tools is partial quasi-ordering.


 * Reflexivity and transitivity leads from definition, antisymetry does not work.

Relation „have the same modeling capability“ on set MMT is equivalence.


 * Reflexivity, tranzitivity and symetry comes directly from definition.

= Universality principle =

Requirement of universality

• Process of management of knowledge in business is continually switching between MENTION and USE

• To achieve continual switching MENTION->USE->MENTION->USE…, modeling tool has to allow to model itself as a model.

What we focus our attention to, by using a modeling tool, is an OBJECT

• Modeling Tool MT is a universal one if:

(1) it has capability to model any model (in accordance with modeling tool definition)

(2) let MT = (CAT, CNN, OPE, RUL), then there exist MENTION and USE operations in OPE, which have previously stated properties.

Diamond of Attention Focusing ("to See") - Universality principle implementation

https://kore.fi.muni.cz/pub/index.php/File:Diamond_ot_Attention_Focusing.jpg

Universality Principle Implementation • Edges R1, R2, R3 and R4 are together called R-edges. R-edges serve to perform transitions between mentioning and using and vice-versa. • If we focus on a concrete object of the class #Object, which was spoken of in a way (MENTION), then by the operation USE we will pass the relevant R-edge and we will reach represented sequence (#Connection) or operation (#Operation) or category (#Category) or rule (#Rule), which could be then directly used, or we will reach nothing. • If we focus any vertex of the Diamond graph on the other hand (which we used in a way - USE), then by the operation MENTION we will pass the relevant R-edge and we will reach this vertex representing object, which we can speak of directly.

= Self-reference =

What if we focus on a construction as an object of interest?

Self-reference - when a model refers to itself as a modeling tool.

= MENTION-USE principle =

MENTION operation

• MENTION operation applied on an object, that we have focused our attention on, allows us to

directly „speak about“, „describe“ and „elaborate on“ anything that we commonly use,

e.g. to model/simulate business processes.

MENTION has to enable development and update of anything, that (in use mode) supports

knowledge acquisition and manipulation.

MENTION has to provide possibility to continually develop knowledge about what knowledge we need’ and ‘how to manipulate it.

• MENTION operation returns focused object in mention mode

USE operation

• USE operation applied to an object, that we have focused our attention on, allows us to directly use anything that we have designed in mention mode. It has to provide possibility to carry out what the object is for.

• USE operation returns focused object in use mode

The Nonaka-Takeushi Life-Cycle in a relation with a MENTION and USE switching vs. Cyclical paradigm



• Process of externalization: this is about creating a model.

• The best way to perform a combination is to do it by means of an appropriate modeling tool.

• Internalization and socialization can be more effective when supported by an appropriate dynamic model or modeling tool.

• We externalize tacit knowledge and combine the result into created (mentioned) model

• We internalize and socialize explicit knowledge by using model

MENTIONing means creating a MODEL of a part of reality (a DOMAIN)