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Dynamic Semantic Web


Ontologies: Their Glory and the new bottlenecks they create.
The bottlenecks of the current web techology create
problems in searching information,
problems in extracting information,
problems in maintaining information, and
problems in generating information. Dieter Fensel

The advent of Web services, and the Semantic Web described by domain ontologies, highlight the bottleneck to their growth: ontology mapping, merging, and integration.
Stephen L. Reed and Douglas B. Lenat, Mapping Ontologies into Cyc

The Dynamic Semantic Web has to deal with the dynamics of the Web.

The Web is at a first glance at least distributed, dynamic, massive and an open world (Heflin, Hendler).

What is the Semantic Web? It is "a vision of the future in which the "web of links" is replaced by a "web of meaning" where the meaning is machine readable.

To introduce a web of meaning, ontologies appears as the main concepts and tools.

Therefore, the first job of DSW is to develop a dynamics of ontologies.

1 SHOE: Dynamic ontologies on the Web

"Dynamic ontologies on the Web" is the title of an approach by the authors of SHOE.

The dynamics of SHOE works with the constructs of ontology definition, modularization, revision and versioning with the help of the techniques "ID", "USE", "RENAME", etc. as methods of Evolution and Integration of ontologies.

All these concepts are realized and have their semantics in the framework of Hierarchy ruled by FOL.

Problems

Introduction, Navigation, Negotiation and Integration are restricted to hierarchical Unification.

2 Polycontextural Dynamics

DSW can not be realized by restricting it to this kind of ontological dynamics. In contrast to the mono-contextural approach of SHOE, DSW has to be realized in the framework of Heterarchy of polycontextural logics and ontologies.

How can we map ontologies onto Heterarchies?

A first but useful explication of the concept Heterarchy is given by the UML heterarchy diagram.

2.1 Heterarchies

Hierarchies are distributed and mediated by the rules of heterarchy.

Each hierarchy contains ontologies in the classical sense.

2.2 Proemial relationship

The mechanism of the interplay between different ontology is realized by the proemial relationship.

2.3 Poly-Semiotics

Signs in ontologies

signs relative to objects

signs relative to signs

signs relative to users

user: modeller, conceptionalist, instance etc.

Interaction between semiotics based on the immanent difference of "subjectivity" of the users between I- and Thou-subjectivity.

This leads to a post-Peircean semiotics of chiastic nature.

3 Short comparition of SHOE and DSW
Is it possible to develop a Semantic Web with its ontology and logics without having to forget and to deny everything we learned from philosophy, linguistics, logics, semiotics, grammatology and AI in the last century?

3.1 Multiple inheritance

Multiple inheritance can easily be modelled in SHOE:

<DEF-CATEGORY NAME="Chair" ISA="AdministrativeStaff Professor">

Here Chair has 2 parent concepts: AdministrativeStaff and Professor.

As long as there are no contradictions this construction is working. But there are no guaranties to avoid contradictions by means of multiple inheritance, as we know from all sorts of conceptual modellings. Simply change the definition of the organisation and the constellation is producing a conflict and later a contradiction.

3.2 Ambiguity and polysemy

All concepts in an ontology have to be disambiguated.

In SHOE, again, this is easily done by renaming.

<DEF-RENAME > CHAIR in furniture-ont to Seat

<DEF-RENAME > CHAIR in academy-ont to AcademyHead

As long as we live in a very small world this strategy will work. But it stops to work immediately if we accept the dimensions of the Web. The process of renaming runs into a non-stopping procedure.

3.3 Chiastic polycontextural modelling

Also because the renaming procedure to avoid polysemy and ambiguity is not surviving the dynamics of a Dynamic Semantic Web the chiastic modelling is introduced as another more dynamic way of modelling the situation of polysemy and ambiguity.

Instead of domesticating the foreigner ontology into the home ontology by renaming the disturbing concepts a poly-contextural modelling is accepting the new ontology as such but has to offer a mechanism which allows to deal with the new double face situation of accepting and of mediating both ontologies. The process of mediating ontologies accepts the ambiguity between the concepts but rejects its logical conflicts and contradictions because now ambiguity is distributed over two ontological contextures ruled by two logical systems.

In accordance with the constructiviste point of view of conceptualizing as a semiotic process, in contrast to the neo-Aristotelian fundamentalist position of GOL, terms, objects, concepts have to be understood as relative to their use (Wittgenstein, Derrida) and not as pre-given entities of the world (universe).

4 Architectonic Parallelism of DSW

Navigation

Negotiation

Interactivity

Complexity

Reflectionality

5 Dynamics in the Semantic Web Context

There are many attempts to bring more dynamics into the Web. Some answers from the authorities: W3C, DARPA, MIT, ETH ZŘrich and McLuhan Institute

5.1 Dynamic Ontologies (Heflin, Hendler)
http://www.cs.umd.edu/projects/plus/SHOE/pubs/#aaai2000

The Web is dynamic.

The Web is massive.

The Web is an open world.

in: Towards The Semantic Web: Knowledge Representation In A Dynamic, Distributed Environment, Heflin 2001

Ontology Mapping and Translation

Will the inevitable proliferation of ontologies really solve the semantic interoperability problem? The answer is clearly no. The widespread adoption of ontologies only gets us half-way to semantic interoperability nirvana by forcing the use of explicit semantics. The other major challenge is mapping from one agent's ontology to another agent's ontology. The approaches to solve this problem range from static manually created ontology mappings to dynamic ondemand agent-based negotiation of ontology mappings.

in: Hendler, Semantic Web Technologies for Aerospace

Diagramm 12

Dynamic Ontologies on the Web

5.2 Water: Static and Dynamic Semantics of the Web

http://web.media.mit.edu/~lieber/Lieberary/Dynamic-Semantics/Dynamic-Semantics.pdf

Less concern has been given to dynamic semantics of the Web, which is equally important. Dynamic semantics have to do with the creation of content, actions which may be guided by

User-initiated interface actions

Time

Users' personal profiles

Data on a server

and other conditions.

5.3 Cultural dynamic Web

http://semanticweb2002.aifb.uni-karlsruhe.de/proceedings/Position/veltmann.pdf

Towards a Semantic Web for Culture and Challenges for a Semantic Web

Kim H. Veltman, McLuhan Institute, Maastricht

Logic is, of course, an excellent starting point. Tim Berners-Lee has a conviction, which can be traced back to early history of Oxford from which he comes, that logic is a way to separating the wheat of truth from the chaff of idle claims. Logic is universally applicable: it reflects the scientific spirit. It represents the dimension concerning which there ought, in theory, to be no debate.

5.4 Dynamic Semantic Web

In contrast to the precedent approaches the PCL based contribution to a Semantic Web and its dynamics is not accepting the limitations of expression, computation and interactivity forced by logic and its logical systems.

Peter Wegner has clearly analyzed the reason of the failure of the Japanese 5th Generation project: its believe in logics and its logic based programming languages, like Prolog. We have not to accept all the thesis about the change of paradigm in computer science proposed by Wegner, but I agree fully with his analysis of the role of logic. But again, Wegner and his school is not able to think about changing logics, instead he proposes some more empirical concepts to develop his intuition of paradigm change based on interactivity.

It is not necessary to repeat history again and again.

5.5 Dynamics with Modularity

Farshad Hakimpour, Andreas Geppert, Ontologies: an Approach to Resolve Semantic Heterogeneity in Databases

This ontology dynamics is based on a constructivite epistemology not naively presuposing data systems. Different communities with different ontologies are introduced.

This Global schema of ontology integration is not telling us what happens with the presupposition of the difference of the ontologies p and q, namely their different Community P and Q.

It maybe of no special problem to integrate DBp1 and DBp2, simply because they are objects of the same community P. What happens to Community Q after merging ontology q with ontology p via merging schema p1, p2 with schema q1?

In this way of thinking, not many possibilities are open: Community P may disappear, or Community Q or a new super-community R will be constructed.

Merging companies, fusions of organizations, always have to deal with this problem. It seems to be an everyday problem, but there are no global solutions in sight.

Diagramm 13


A nice vizualitation of a merging is given by robert lee

ai.kaist.ac.kr/~jkim/cs570-2003/ lecture-tp/SemanticWeb.ppt

Diagramm 14


Diagramm 15


Obviously, for this scheme of Degrees of Similarities of Ontologies, everything Joseph Goguen mentioned abaut classic semiotics is true in an even more strict sense for ontologies.






Semiotics and Ontologies
Semiotics, as the general theory of signs, would seem a natural place to seek a general HCI framework. However
(1) semiotics has not developed in a precise mathematical style, and hence does not lend itself well to engineering applications;
(2) it has mostly considered single signs or systems of signs (e.g., a novel, or a film), but not representations of signs from one system by signs from another, as is needed for studying interfaces;
(3) it has not addressed dynamic signs, such as arise in user interaction; and
(4) it has not paid much attention to social issues such as arise in cooperative work.

A new project to address such problems has so far developed precise algebraic definitions for sign systems and their representations, and a calculus of representation providing laws for operations that combine representations as well as precise ways to compare the quality of representations. Case studies have considered browsable proof displays, scientific visualization, natural language metaphor, blending, and humor, while social foundations are grounded in ideas from ethnomethodology.
Joseph Goguen, Algebraic Semiotics and User Interface Design, 2000

http://www.isr.uci.edu/events/dist-speakers00-01/goguen00.html

Dynamics in Ontologies and Polysemy


1 Dynamic Ontologies in SHOE

SHOE is a well established approach to the Semantic Web emphasizing dynamics of ontologies.

http://www.cs.umd.edu/projects/plus/SHOE/

The dissertation of Henflin gives us a perfect introduction.

http://www.cs.umd.edu/projects/plus/SHOE/pubs/#heflin-thesis

Diagramm 16

Ontology Scheme

Generally, an ontology is a tupel O = (V, A)

V: Vocabulary

A: Axioms

Dynamics of SHOE-Ontologies are given by the operations of

Ont-Building

Ont-Revising

Ont-Versioning

Ont-Perspectiving

Short: Ont-Dyn = {Build, Rev, Vers, Persp}

The dynamics Ont-Dyn don't change the general definition of ontology. The operation of Ont-Dyn is closed, that is, Ont-Dyn(Ont-Dyn(Ont)) = Ont

Ont-Dyn(Ont-Dyn) = Ont-Dyn

The USE-Ontology operation is the key for modularity in SHOE. USE is building ontologies out of other ontologies. That is, ontologies are understood as modules.

Ontology = (Module0 , Module1, ..., Modulen)

Module0 contains the general base-ontology

The USE-ontology operation is producing a vertical and hierarchic chain of ontology extensions.

Ont-Dynamics: Ont --> Ont: Oi --> Oi : Oi1, Oi2 --> Oi1+2

Linear Modularization: Oi --> Oi: Oi1+2 --> Oi1, Oi2

Examples of modules (ontologies)

A SHOE Module can be any ontology which is not a base ontology and which is fulfilling the syntactic definition of an ontology.

http://www.cs.umd.edu/projects/plus/SHOE/onts/index.html

general-ont = (Web-Res, Agent, PhysObject, Event, Location, Address, Activity)

document-ont = (Document, unpublished, published)

university-ont = (Faculty, Student, University, Department)

agents-ont = (sequentiell, parallel)

Ontology Dependencies (SHOE)

Below is a tree showing the dependency of ordering of the most recent versions of each ontology.

Base Ontology, v. 1.0

Dublin Core Ontology, v. 1.0

General Ontology, v. 1.0

Beer Ontology, v. 1.0

Commerce Ontology, v.1.0

Document Ontology, v. 1.0

University Ontology, v. 1.0

Computer Science Department Ontology, v. 1.1

Personal Ontology, v. 1.0

Measurement Ontology, v. 1.0

Commerce Ontology, v.1.0

TSE Ontology, v. 1.0

http://www.cs.umd.edu/projects/plus/SHOE/onts/index.html

1.1 Dissemination of Ontologies, a more formal description

Polycontextural logics enable to add a new operation to extend ontologies. The horizontal operation of mediation MED is used to add ontological Modules not vertically like the USE operation but horizontally and therefore is producing a heterarchic organisation of the ontological modules.

Diagramm 17





USE(USE(USE))

Diagramm 18

MED (ont1, ont2, ont3) = ont (3)

MED (ont1, ont2, ont3) = ont (3)

MED(USE) /= USE(MED)

The mediation of USE ontologies is not the same as the use of mediated ontologies.

MED (Ont) /= Ont

The mediation of ontologies is surpassing the definition or type of the given ontologies.

The interplay of USE and MED defines the ontology grid in its vertical (iterative) and in its horizontal (accretive) dimensions. The grid is produced by the operation DISS (dissemination) which is the interplay of USE and MED, or in other words, the interplay between hierarchy (HIER) and heterarchy (HET).

DISSaccretive (ONT) = MED(USE(ONT)) and

DISSiterative (ONT) = USE(MED(ONT))

DISS(ONT) = DISSiterative DISSaccretive (ONT) = GRID (ONT)

Mediated ontologies are opening up the possibility for metamorphic changes of the basic categories of the ontologies involved in the interaction.The most basic change surely is the exchange between a base ontology, Mod0, and a core ontology, say Modi. What is basic and primary in one ontology can be simultaneously secondary in another neighbor ontology.

This type of ontology-change is ruled by the proemial operator (chiasm) PR.

PR(Mod0, Modi, Ont1, Ont2)

Example: Disseminating basic concepts

Basic concepts like time, numbers, truth-function are defined in a base-ontology, which is by definition not to be transformed by any operations of Ont-Dynamics.

Veltman who is engaged to enrich the current trends of the Semantic Web toward a much more cultural and historical Semantic Web. He is criticizing SHOE of having implemented only the western model of calender. The real problem seems not be to add different cultural modules of chronology, topography and languages etc., but who to add them. If they are added vertically, in the sense of an iterative hierachical addition of modules, nothing has changed at all.

Only in the case of horizontal organisation of the basic ontologies a simultaneous multi-cultural and multi-lingual use can be processed and interaction between the different world views can be realized without restrictions by a ultimate upper ontology of what kind ever.

My thesis is, not the content but the very structure of the whole ontology is under question. If the modules of whatever content are added vertically, we stay in the western-centred paradigm of thinking. If we allow horizontal organization of the ontologies we are leaving this empire of hierarchical power to a heterarchical world of chiastic interplay of world views.

1.2 Computational complexity of hierarchy and heterarchy

(This is only a very first appraoch to the topic of complexity!!!)

Compl (USE(Ont1...Ontn) > Compl (MED(Ont1...Ontn))

Compl (HIER) > Compl (HET)

The tree of Ont1 may contain 2m knots, and Ont2 may contain 2n,

Compl(HIER(Ont1, Ont2)) = 2n+m

Compl(HET(Ont1, Ont2)) = 2m + 2n

This gives the number of knots for isolated parallel mediated ontologies Ont1 and Ont2. Additionally to this we have to calculate the number of interactions between Ont1 and Ont2.

2 Polysemy: Ontology Extension with the procedure rename

An interesting case of combining ontology modules together arise if the ontologies contains equal terms. In contrast to simple multiple inherence the situation of polysemy is introduced.

Remember:

The Web is distributed. One of the driving factors in the proliferation of the Web is the freedom from a centralized authority. However, since the Web is the product of many individuals, the lack of central control presents many challenges for reasoning with its information. First, different communities will use different vocabularies, resulting in problems of synonymy (when two different words have the same meaning) and polysemy (when the same word is used with different meanings).

One of the hardest problems in any integration effort is mapping between different representations of the same concepts - the problem of integrating DTDs is no different. One difficulty is identifying and mapping differences in naming conventions. As with natural language, XML DTDs have the problems of polysemy and synonymy. (12)

Recall that the Web is a decentralized system and its resources are autonomous. As a result, different content providers are free to assign their own meanings to each nonlogical symbol, thus it is likely that multiple meanings will be assigned to many symbols. Different axiomatizations for the same symbolsmay result fromthe polysemy of certain words, poor modeling, or even malicious attempts to break the logic. (23)

The main principle of ontology is demanding for disambiguating the polysemy of the used term. The simplest and historically oldest method to do this is given by renaming the terms. This is working perfectly in a very small world. But as we have learned, not only the weather system is massive, complex, open worlded, but also our WWW.

It is probably not very difficult to find, even if restrict ourselves to the english language, hundreds of different meanings of a term, here in the example of "chair". Therefore the renaming procedure can easily explode to a massive and complex topic in itself, destroying the aim of the simple and innocent procedure of renaming.

The problems of synonymy and polysemy can be handled by the extension mechanism and use of axioms. An axiom of the form P1(x1; : : : ; xn) $ P2(x1; : : :; xn) can be used to state that two predicates are equivalent. With this idiom, ontologies can create aliases for terms, so that domainspecific vocabularies can be used.

For example, in Figure 3.1, the termDeptHead in OU2 means the same thing as Chair in OU due to an axiom in OU2. Although this solves the problem of synonymy of terms, the same terms can still be used with different meanings in different ontologies.






Diagramm 19

Figure 3.2

There are many open questions. How does it fit together to have an ontological relation "isa" and an obviously linguistic operation "rename"? To bring the modules furn-ont and furn-ont2 and also univ-ont and univ-ont2 together we need at least a mediation third module, which is reflecting the terminology of both. But this linguistic ontology would produce itself similar possibilities of polysemy.

Polysemy means:

A=C and

B=C and

A /=C

Do it again

There is no reason to not to start the game of polysemy again with the term Seat as furniture and Seat as seat, e.g. position, in the hierarchy of a department. And we can disambiguate this polysemy again with the help of the term Chair. A seat as department is a chair and a seat as furniture is a chair. And now we can turn around as often as we want...

Extension of ontologies by renaming is not violating the principle of verticality, that is hierarchy. Therefore, the tree is growing and with it its computational complexity.

It becomes obvious that the procedure of renaming is part of the broader activity of negotiation. Without a proper mechanism of solving the problems of renaming the amount of not machine-assisted negotiation is growing in a contra-productive way, conflicting the very aims of the Semantic Web to support machine-readable semantic information processing.

Diagramm 20


http://www.mindswap.org/cgi-bin/2002/searchdamlont.pl

ONTOLOGY HYPER-

DAML DUMP

ONT Convert to OWL Color n3 HIT ON

1 NSO-ont [H] [H] [D] OWL color view n3 view ChairmanOfTheJointChiefsOfStaff

2 NSO-ont [H] [H] [D] OWL color view n3 view ViceChairmanOfTheJointChiefsOfStaff

3 UNSPSC [H] [H] [D] OWL color view n3 view Bedpans-or-commode-chairs-for-people-with-disabilities

4 UNSPSC [H] [H] [D] OWL color view n3 view Camping-chairs-or-stools

5 UNSPSC [H] [H] [D] OWL color view n3 view Chair-lifts-or-chair-transporters,-for-people-with-disabilities

6 UNSPSC [H] [H] [D] OWL color view n3 view Chairs

7 UNSPSC [H] [H] [D] OWL color view n3 view Coxit-or-arthrodesis-chairs-for-people-with-disabilities

8 UNSPSC [H] [H] [D] OWL color view n3 view Mechanized-chairs-to-assist-with-sitting-or-standing-for-people-with

9 UNSPSC [H] [H] [D] OWL color view n3 view Patio-chairs

10 UNSPSC [H] [H] [D] OWL color view n3 view Restaurant-chairs

11 UNSPSC [H] [H] [D] OWL color view n3 view Vibrating-chairs-for-training-deaf-people

12 UNSPSC [H] [H] [D] OWL color view n3 view Wheelchair-accessories

13 UNSPSC [H] [H] [D] OWL color view n3 view Wheelchair-lifting-platforms

14 UNSPSC [H] [H] [D] OWL color view n3 view Wheelchair-ramps

15 UNSPSC [H] [H] [D] OWL color view n3 view Wheelchairs

16 cs1 [H] [H] [D] OWL color view n3 view Chair

17 cs1 [H] [H] [D] OWL color view n3 view Chair

18 cyc-transportation [H] [H] [D] OWL color view n3 view ElectricWheelchair

19 cyc-transportation [H] [H] [D] OWL color view n3 view Wheelchair

20 univ1 [H] [H] [D] OWL color view n3 view Chair

20 hits in 186 ontology files

Douglas B. Lenat

The success of the Semantic Web hinges on solving two key problems:
(1) enabling novice users to create semantic markup easily, and
(2) developing tools that can harvest the semantically rich but ontologically inconsistent web that will result.
To solve the first problem, it is important that any novice be able to author a web page effortlessly, with full semantic markup, using any ontology he understands. The Semantic Web must allow novices to construct their own individual or specialized-local ontologies, without imposing the need for them to learn about or integrate with an overarching, globally consistent, master ontology.

The resulting Web will be rich in semantics, but poor in ontological consistency. Once end-users are empowered by the Semantic Web to create their own ontologies, there will be an urgent need to interrelate those ontologies in a useful way. The key to harvesting this new semantic information will be the creation of the Semantic Web-aware agents that can cope with a diversity of meanings and inconsistencies across local ontologies. These agents will need the capability to interpret, understand, elaborate, and translate among the many heterogeneous local ontologies that will populate the the Semantic Web.

http://www.cyc.com/cyc/cycrandd/areasofrandd_dir/sw

These agents will not only "need the capability to interpret, understand, elaborate, and translate .." but they also have to be non-human agents, that is programs. What┤s difficult to master for human beings should be a fine job for our new agents. It seems that the unsolved problems of AI are emerging again in a new setting.

3 Polycontextural modelling of polysemy
The Internet is a giant semiotic system. Sowa


Polycontextural modelling can be made more transparent if we don┤t forget that the concept of ontology is only a very reduced case of general semiotics. (I leave it for further reflections to abandon also semiotics in favor of polycontexturality.)

Exposing a polycontextural modelling of polysemy I am forced to use semiotic distinctions not available in the Semantic Web language SHOE.

3.1 Semiotic Diagram

Remember Charles Sanders Peirce:

A sign, or representamen, is something which stands to somebody for something in some respect or capacity. It addresses somebody, that is, creates in the mind of that person an equivalent sign, or perhaps a more developed sign. That sign which it creates I call the interpretant of the first sign. The sign stands for something, its object. It stands for that object, not in all respects, but in reference to a sort of idea, which I have sometimes called the ground of the representamen. (CP 2.228)

Sowa:

Many of the ontologies for web objects ignore physical objects, processes, people, and their intentions.
A typical example is SHOE (Simple HTML Ontology Extensions), which has only four basic categories: String, Number, Date, and Truth (Heflin et al. 1999).
Those four categories, which are needed to describe the syntax of web data, cannot by themselves describe the semantics. Strings contain characters that represent statements that describe the world; numbers count and measure things; dates are time units tied to the rotation of the earth; and truth is a metalanguage term about the correspondence between a statement and the world. Those categories can only be defined in terms of the world, the people in the world, and the languages people use to talk about the world. Without such definitions, the categories are meaningless tags that confer no meaning upon the data they are attached to.

Ontology, Metadata, and Semiotics

John F. Sowa

http://users.bestweb.net/%7Esowa/peirce/ontometa.htm

Diagramm 21


A nice semiotic picture of our world of semantic knowledge. It is surely better than the lack of any semiotic knowledge.

Diagramm 22


Pure logic is ontologically neutral
It makes no presuppositions about what exists or may exist in any domain or any language for talking about the domain. To represent knowledge about a specific domain, it must be supplemented with an ontology that defines the categories of things in that domain and the terms that people use to talk about them. The ontology defines the words of a natural language, the predicates of predicate calculus, the concept and relation types of conceptual graphs, the classes of an object-oriented language, or the tables and fields of a relational database. Sowa
Diagramm 23


Everyone who has studied polycontextural logics know that logic isn't as neutral as it is believed by the community of logicians and computer scientists. At least, logic is presupposing a special type of formality to be accessible to formalization, and this formality as such can turn out as logics restricting content. But it is crucial to understand this neutrality statement because it describes exactly the situation as it is established in contemporary (western) thinking.

Ask for other opinions and paradigms Charles S. Peirce or Gotthard Gunther.

3.2 Reflectional semiotic modelling of polysemy

A reflectional analysis of polysemy is an analysis of the semiotic actions or behaviors of agents which is leading to the phenomenon of polysemy and its possible conflicts with other semiotic or logical principles. Therefore, such an analysis is more complex, because it has to describe the situation intrisically, that is from the inside and not from the outside from the position of an external observer.

Mono-contextural introduction of "isa":

S1: Chair is part of a furniture ontology

S2: Chair is part of a department ontology

S3: Chair is part of a vocabulary

Poly-contexturally we have to distinguish the situations "isa as":

O1S1: Chair as such, that is, as an object "Chair"

O2S2: Chair as such, that is, as a person "Chair".

O3S3: Chair as such, that is, as the token "Chair"

Here, "as such" means, that the ontologies Person, Object and Vocabulary can be studied and developed for their own, independent of their interactivity to each other but mediated in the constellation of their poly-contexturality, that is, their distribution over 3 loci.

Voc O3S3 in Furn O1S3 : The token "Chair" as used to denote the object "Chair"

VocO3S3 in Dept O2S3 : The token "Chair" as used to denote the person "Chair"

Chair O2S2 in Dept O1S2 : The object Chair as used in the person ontology Dept

Chair O1S1 in Furn O2S1 : The person Chair as used in the object ontology Furn

Diagramm 24


Reflectional situations

Chair O2S2 in Dept O1S2:

System O1S1 has in its own domain space for a mirroring of O2S2. This space for placing the mirroring of O2S2 is the reflectional capacity realized by the architectonic differentiation of system O1. In other words, O1 is able to realize the distinction between its own data and the data received by an interacting agent. Data are therefore differentiated by their source, e.g. their functionality, and not only by their content.

Chair O1S1 in Furn O2S1:

System O2S1 has in its own domain space for a mirroring of O1S1.

Some exclusions

Some more fascinating possibilities, which are excluded in this construction:

The word Chair as a DeptChair: (empty chair): Voc O3S3 in Dept O2S2

The word Chair as a Furn: (decoration): Voc O3S3 in Furn O1S1

The DeptChair as an object Chair (in a game): Dept O2S2 in Furn O1S1

The DeptChair as a token Chair (as a symbol): Dept O2S2 in Voc O3S3

The FurnChair as a person Chair (Breschnijew) :Furn O1S1 in Dept O2S2

Diagramm 25


A (re)solution of the problem

The solution of the (new) problem is in the (old) problem which the (new) problem is the (old) solution.

The department Dept for itself has no conflict with polysemy. This conflict between Dept and Furn is mediated by the Voc. That is, the Person of the Dept as Chair are persons and nothing else.

The furniture Furn for itself has no conflict with polysemy. This conflict between Furn and Dept is mediated by the Voc. That is, the Chairs as objects of the Furn are chairs and nothing else.

The vocabulary Voc for itself has no conflict with with polysemy between Dept and Furn.

The meaning of the polysemic situation is realised by

Meaning of (O3S3) = interaction of (O1S3, O2S3)

The conditions for a conflict arises excactly between

O1 (S1,2,3) and O2 (S1,2,3) mediated by O3S3 as visualized by the blue triangles.

Both Furn and Dept are using Voc and both are using the string Chair. Both are different and are mapping the Voc differently relative to their position, thus the Voc has to be distributed over different places according to its use or functionality. The Voc used by Furn is in another functionality than the Voc used by Dept.

Until now we have not yet produced a contradiction but only a description of the situation of polysemy, that is, the necessary conditions for a possible ontological contradiction.

A user-oriented or behavioral-oriented approach to the modelling of polysemy has to ask "For whom is there a conflict?". Therefore we have additionally to the semantic and syntactic modelling of the situation to introduce some pragmatic instances. In our example this can be the user of a Query which is answering in a contradictional manner.

Query┤s contradiction

Now we have to deal with the contextures: (Query, Voc, Furn, Dept).

In the classic situation the Query answers with a logical conjunction of Chair as Person and Chair as a Department member, which are logically excluding each other and therefore producing for the user a contradictorily answer. Logic comes into the play also for the polycontextural modelling, but here conjunctions too, are distributed over different contextures. And therefore, a contradiction occurs only if we map the complex situation all together onto a single contexture. If we give up all the introduced ontological distinctions of polycontexturality and reducing therefore our ontologies to a single mono-contextural ontology we saved our famous contradiction again. But now, this contradiction is a product of a well established mechanism of reduction. And sometimes it isn't wrong to have it at our disposition.

Extension by mediation

The procedure of renaming can now be understood as an accretive ontology extension, using another additional ontology, by the procedure MED-ontology.

To change from Chair as a furniture to Seat and from Chair as Dept to DeptHead is not only a linguistic procedure of renaming in the vocabulary it is also the use of two other ontologies in which these terms are common.

From the point of view of the new ontologies the conflict between Furn and Chair becomes obvious and transparent as a linguistic conflict of using a Voc. Only from the point of view of DeptHead and Seat the conflict appears as a conflict of synonymy. From the positions of Chair as Furn and Chair as Dept their is only a conflict per se. Without the possibility of an insight into its structure and kind of the conflict and therefore there is also no chance for a solution of the conflict.

Diagramm 26


Chiastic situation of the polysemy example:

Person becomes Object and Object becomes Person both relative to their common Vocabulary, that is the word "Chair".

4 Some Polylogical Modelling of Polysemy

To each ontology we have a corresponding logic (or logical system).

Ont ---> Logic

Med(Ont1, Ont2, Ont3) = Ont(3) ---> MED(Logic1, Logic2, Logic3) = Logic(3)

A contexture is the common framework of a logic and its corresponding ontology.

Conjunctive connection of ontological modules A, B, C, D in each contexture:

L1: A and B and C and D

L2: A and B and C and D

L3: A and B and C and D

L(3) : A(3) and and and B(3) and and and C(3) and and and D(3)

The binary case for short: L(3): (A and B); (A and B); (A and B)

As we see, the possible places for reflecting the neighbor systems are empty, marked with "#" in the case of the monoform junctional distribution.

Diagramm 27


This corresponds to the purely parallel situation of the ontologies as such without any interaction at all. But nevertheless, these logics are distributed over three places and mediated together in the architectonics of the logical frame L(3).

Diagramm 28


Additionally to the intra-contextural realizations of conjunctive chains we observe a first interaction from the logical system to its neighbor systems. Again, this interaction is not overriding its neighbors but is offered by the neighbors logical space to succeed realization. In other words, the neighbor systems are mirroring, that is, reflecting the interactivity of the logic system L3 in a place or locus of their own systems.

How is this realized? Also no conjunction or disjunction or other intra-logical operation is able to leave its place, we are not lost in the cage of mono-contexturality, because by construction, logical operations which are crossing the borders of their systems are accessible, this is the family of transjunctions.

A transjunction has a continuation simultaneously in its own and in its neighbor systems.

For short, we have in L(3): (A and B; A and B; A trans B)

In L3 the transjunction is crossing to logic L2 simultaneously to logic L1 and staying with other parts of the formula in its own logic L3.

It is easily to see, that the classical conflicts of multiple inheritance would be produced if the mapping would not be transjunctional and reflectional but a simple mapping onto the systems as such, that is, mapping of O3S3 onto O1S1 and O3S3 onto O2S2.

The same argumentation is used for the logical operator "implication" and works in the same sense also for meta-logical constructions like the inference rule(s).

Therefore inferencing in poly-contextural systems is architectonically parallel.

Diagramm 29


L(3): (A trans B); (A trans B); (A trans B)

Diagramm 30


Even more interesting interactions are possible with the introduction of transjunctional mappings from O1S1 to O3S1 and from O2S2 to O3S2.

In these cases, reflectionality enters the domain of the vocabulary Voc. The Voc , again, is not only a collection of facts which exist per se in a dictionary. A vocabulary exists in being used. Therefore the other system s are influencing the system of the vocabulary. The difference is, that these lexical influences are not yet incorporated by the vocabulary in the sense of O3S3. That the reason way they occur in the reflectional ebvironment of Voc as reflecting and accepting the interactive influence of Furn and Dept to the domain of Voc.

4.1 Inconsistency, Contradiction and Polysemy
Building, Sharing, and Merging Ontologies, John F. Sowa
Figure 14 shows a "bowtie" inconsistency that sometimes arises in the process of aligning two ontologies.
On the left of Figure 14, Circle is represented as a subtype of Ellipse, since a circle can be considered a special case of an ellipse in which both axes are
equal. On the right is a representation that is sometimes used in object-oriented programming languages: Ellipse is considered a subclass of Circle, since it has more complex methods. If both ontologies were merged, the resulting hierarchy would have an inconsistency. To resolve such inconsistencies, some definitions must be changed, or some of the types must be relabeled. In most graphics systems, the mathematical definition of Circle as a subtype of Ellipse is preferred because it supports more general transformations.

http://users.bestweb.net/~sowa/ontology/ontoshar.htm#Formal

For whom are this two positions a contradiction? Where does the inconsistency appear? Obviously both positions are clean in themselves. The inconsistency or logical contradiction occurs only by the mixing both and mapping them into a third general common position. What happens? The merging produces a new object which involves both different positions and at the same time denies the autonomy of those positions.

Again, for the case of managing a small household, the strategy of subordination maybe accepted for the one or other short termed practical reasons. But, by whom? For more official, and serious solutions, the idea of resolving by the device "To resolve such inconsistencies, some definitions must be changed, or some of the types must be relabeled." is not a proof of profound thinking and knowledge about practicability.

4.1.1 From merging to mediating interactivity

From an actional point of view in contrast to an entity ontology standpoint it is more apprpriate to consider the process of merging as a process of conflict resolution. This type of modelling is reasonable only if we accept the relevance of the two different point of views, if both positions have their own reason to exist. Otherwise it would only be a question of terminology and adjustments (renaming, relabelling).

The above example of a "bowtie inconsistency" can easily modelled as a chiastic interaction between two different positions offering at least a conceptual description of the situation as introduced.

Chiasm (Ellipse, Circle, Pos1, Pos2):

OrdRel(Ellipse1, Circle1)

OrdRel(Circle2, Ellipse2)

ExchRel(Ellipse1, Circle2)

ExchRel(Circle1, Ellipse2)

CoincRel(Ellipse1, Ellipse2)

CoincRel(Circle1, Circle2)

To model the full picture of the chiastic situation we can move to the Diamond Strategies.

4.1.2 Diamond strategies and merging inconsistent ontologies

A framework of the distribution of places needed to merge inconsistent or dual ontologies is given by the Diamond Strategies.

Position: a given ontology.

Opposition: the dual ontology to the positioned ontology, short, the contradicting ontology.

Neither-Nor: the position which is neither one nor the other ontology, but in respect to this two ontologies. It is the place of the rejection of both ontologies. Positively, it is the empty place which is common to both in respect of rejecting the ontologies.

Both-And: the position which gives place for both, the first and the second ontology at once. At this place, the position as well as the opposition is accepted, that is, the contradiction between both ontologies is accepted as such.

I hope it becomes slowly clear that the diamond strategies are not at all identical with the tetra-lemma of Buddhist philosophy despite some analogy in the wording.

Rejection of an alternative and acceptance of an inconsistency has nothing to do with negation or set theoretic union of concepts. One of the main differences is that the tetra-lemma is not reflectional at all. It is a good starting point but only as a configuration about the world as it is without including any observational reflectionality.

It is obvious too, that the acceptance of inconsistency is not understood in the sense of para-consistent logics. Nevertheless, it is interesting for other reasons to deal inconsistencies in a para-consistent setting.

Today it shouldn't be a technical problem to represent complementary objects at once on a screen or where ever.

The discipline which would have to deal with such complementary objects and their theories would be called "Dynamic Diagrammatics" as a further development of the Peirceian based Diagrammatics.

Politics of examples

Examples and metaphors are not as harmless as it seems to be.

Some more realistic examples instead of innocent circles and ellipses, chairs, penguins and kilts etc. should be introduced. A simple example of renaming is globally introduced by Bush┤s doctrine of pre-emptive war.

Logic of execution:

Human beings, animals

allowed to be killed, not allowed to be killed

Friedensfighter, terrorists

The Christian problem of executing humans in a non-war situation is pluntely solved by Bush and Sharon with the not at all rhethorical decision, that terrorist are animals.

In the more theological terminology, animals are replaced by the evil, because animals too are creatures of God.

5 Polycontextural modelling of multiple inheritance
Ontologies differ in how they handle the case of inheriting multiple properties.
Robert Lee

There are no problems neither with polysemy nor with multiple inheritance if you chose your examples carefully and then run away after you have been paid.

The multiple inheritance of CHAIR being a AdminStaff member and a Faculty member as Professor in the example of SHOE is surely innocent of any logical violations, leading to contradictions. SHOE is even excluding logical negations to avoid contradictions. But this is not the situation a Semantic Web designer should be concerned about.

It is simply bad propaganda and contra-productive advise if I have to read in different Web Semantic papers that they have solved the multiple inheritance problem properly.

Let┤s have a short look at the scenario.

Several proposals have arisen for thesauri interchange formats based on either RDF or DAML+Oil. The major problems with these is that either they cannot accommodate the multiple inheritance common in many multilingual thesauri or that the semantics of thesauri in the ISO standards are not as precise as these languages require. The links in thesauri hierarchies define the top term in the hierarchy, and the broader or narrower coverage of terms down the hierarchy. There are also links between hierarchies to show equivalence in different languages, or similar meaning in the same language.

http://www.ercim.org/publication/Ercim_News/enw51/wilson.html

A more optimistic view is here. You simply have to do it before the game.

Very flexible ways of combination, such as multiple inheritance, can be specified for types in simple ways. Since agreement on supplied and required interfaces is all that is needed for the exchange of data in a distributed environment types already provide the glue for many useful applications.

The Quaker Example

Most Quaker are Pacifists

Most Republicans are non-Pacifists

Dick is a Quaker

Dick is a Republican.

Query: Is Dick a Pacifist?

Diagramm 31

Multiple Inheritance

There are many serious attempts to deal with multiple inheritance in the AI literature (Lokenda Shastri: Semantic Networks: An Evidential Formalization and its Connectionist Realization, Pitman London 1988)

It is not the place here to discuss Shastri┤s solution. What we can learn is the introduction of different relevance criteria and multiple views on a token. It is only a simple step further to combine multiple views with multiple contextures and introducing irreducible polysemy into the very concept of "person".

Therefore, Dick has multiple personal identity, one as a Religious Person (REL-PER) and one as a Political Person (POL-PER).

With the introduction od POL-PER and REL-PER the simple question "Is Dick a Pacifist?" is wrongly placed and not well-formed because the particle "as" giving his perspective and role is excluded.

We have to ask "Is Dick as a POL-PER a pacifist?" and "Is Dick as a REL-PER a Pacifist?" And additionally, which is a very different question, we can ask "How is Dick as Dick, which is neither a political nor a religious person, dealing with his two positions of being a POL-PER and a REL-PER?" And here, we would have to consider the relations of interactions between the different ontologies.

Only if we are reducing the two perspectives and eliminating the as-category, we are reconstructing the contradictions of this multiple inheritance situation. This maybe well known, but because of the lack of a logic which is genuinely dealing with different and mediated perspectives, like polycontextural logic, the implementation of the complex conceptual modeling is lost for mono-contexturality.

I can not go into the details here, but obviously, the polycontextural approach of modelling the multiple inheritance situation has to separate and then to mediate the ontologies REL-PER and POL-PER in a heterarchical interacting poly-ontology.

Obviously, the SHOE trick for multiple inheritance we have learnt before with Chair= (Dept, AdminStaff) doesn't work anymore. Because Dick as (REP, QUAK) is producing a contradiction by definition. By the way, the same can happen with the Chair example, we simply have to change the rules of the organization to a more strict regime.

Again, a hint is given by the following chiastic metapattern diagram.

Diagramm 32


I added to the list of

Quaker

Penguine

Whale

Oistrich

Fleuve

etc.

the very neglected case of Kilts.

Diagramm 33


Kilt as an instance of female clothes proposed by the Eurpean Administration, that is as a skirt and therefore female, is surely in contradiction to the Scottish definition of Kilts. A chiastic resolution of this crucial conflict has simply to understand that Kilts are Instances of a very different Concept2. It doesn't mean that the Instance1 "Kilt" becomes itself a Concept2, but that the contradiction in system1 with Instance1 and Kilt gives reasons to a switch to system2 with concept2 as maybe "folklore" and Kilt as an Instance2 of Concept2. But both systems are as mediated systems not isolated.

Is the Grid of the Dynamic Semantic Web a confused Grid?
Why linearizations? In a class-based object-oriented language, objects are instances of classes. The properties of an object - what slots or instance variables it has, which methods are applicable to it - are determined by its class. A new class is defined as the subclass of some pre-existing classes (its superclasses - in a single-inheritance language, only one direct superclass is allowed), and it inherits the properties of the superclasses, unless those properties are overridden in the new class. Typically, circular superclass relationships are prohibited, so a hierarchy (or heterarchy, in the case of multiple inheritance) of classes may be modeled as a directed acyclic graph with ordered edges. Nodes correspond to classes, and edges point to superclasses.
It is possible that an inheritance graph is inconsistent under a given linearization mechanism. This means that the linearization is over-constrained and thus does not exist for the given inheritance structure. An example of an inconsistent inheritance relationship appears in example 1c. <confused-grid> is inconsistent because it attempts to create a linearization that has <horizontal-grid> before <vertical-grid>, because it subclasses <hv-grid>, and <vertical-grid> before <horizontal-grid>, because it subclasses <vh-grid>. Clearly, both of these constraints cannot be obeyed in the same class.

-----------------------------------

Kim Barrett et al, A Monotonic Superclass Linearization for Dylan

http://www.webcom.com/haahr/dylan/linearization-oopsla96.html

define class <grid-layout> (<object>) ╔ end;

define class <horizontal-grid> (<grid-layout>) ╔ end;

define class <vertical-grid> (<grid-layout>) ╔ end;

define class <hv-grid> (<horizontal-grid>, <vertical-grid>) ╔ end;

define method starting-edge (grid :: <horizontal-grid>)

#"left"

end method starting-edge;

define method starting-edge (grid :: <vertical-grid>)

#"top"

end method starting-edge;

Example 1a: A simple use of multiple inheritance

define class <vh-grid> (<vertical-grid>, <horizontal-grid>) ╔ end;

Example 1b: Reversing classes in the linearization

define class <confused-grid> (<hv-grid>, <vh-grid>) ╔ end;

Example 1c: An inconsistent class definition

6 Query, questions and decisions
"Only undecidable questions have to be decided by man" ? HvF

As long as our queries are answering our questions with only non-ambiguous, non-polysemous statements, we are dealing with a very reduced case of semantics. It is semantics reduced to a machine-readable and machine-understandable situation, therefore there is no need for cognitive reflectional decisions.

If i am asking for the earliest flight to Frankfurt/M and the answer is "6.30h", then i have to accept it as the answer to my question. And nothing has to be interpreted, understood or decided. (Except, that the flight is much to early for my rituals.)

Semantics as a reflectional system is not dealing primarily with facts but with meanings. Meanings are at least reflectional multi-leveled, or as we know from Second-order Cybernetics, second-order concepts. That is concepts of concepts (of facts).

What is the purpose of a query system? A query system has to support and to assist decision-making for humans and as far as possible also for machines.

It seems reasonable to make a distinction between machine- and human-decidable decisions. Machine decidable decisions are on the level of dis-ambiguous dis-ambigue meanings, that is zero-level or 1-level meaning.

ambiguous ambigue

dis-ambiguous ambigue

ambiguous dis-ambigue

dis-ambiguous dis-ambigue

To make it easier, a simpler correlation to polysemy is possible by one-to-one, many-to-one, one-to-many and many-to-many relations. All well known in rhethorics and linguistics since Aristotle.



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