Director Andrius Kulikauskas, ms@ms.lt, leads an investigation at the Minciu Sodas laboratory of the hypothesis:

Definitions of Sequences, Hierarchies and Networks Exist That are Most Natural for Arranging Thoughts

Overview of Investigation Members and nonmembers alike are invited to join our discussion group for this investigation: Minciu_Sodas_SHN@listbot.com  See rules and click here to join!

Abbreviations: S = Sequence, H=Hierarchy, N=Network, SHN=Sequences, hierarchies, and networks

Overview of Investigation

I am interested in the question, What definitions of sequences, hierarchies and networks are most appropriate for arranging thoughts?  I aim to describe in XML a preliminary version of a standard for the transfer of sequences, hierarchies, and networks of thoughts.  My major challenge is figuring out, from a human point of view, what is a sequence (S), what is a hierarchy (H), what is a network (N)? My investigation consists of the following steps:
  1. List Existing Standards We search the Internet to make a list of existing standards, such as XML, UML, HTML, that can be used to organize thoughts into sequences, hierarchies, and/or networks.  The examples we find also help build up our ongoing project Formats for Thinking.
  2. List Structural Questions Our list of existing standards helps make us aware of the structural possibilities, and thereby helps us develop a list of structural questions that we will need to resolve in defining sequences, hierarchies and networks, such as May the hierarchy be ordered?
  3. Apply Four Criteria We apply four criteria - functional, psychological, anthropological, philosophical - to each of our structural questions, and create a table to record our answers.
  4. Decide Structural Answers We use our table of answers, however tentative, to decide how we will answer each question in defining sequences, hierarchies and networks for the purpose of arranging thoughts.
  5. Describe Mathematically We produce a mathematical description of sequences, hierarchies and networks that accords with our answers.
  6. Create DTD in XML We express our mathematical description using a DTD (Document Type Definition) in XML (eXtensible Markup Language).
I welcome your help with this investigation!  Please write to me, Andrius Kulikauskas, at ms@ms.lt

List Existing Standards

I am considering how existing standards can be used to organize thoughts into sequences, hierarchies, and networks.  The table below lists the standards that I am aware of.  Many of the standards below are taken from Towards a Web Object Model, February 2, 1998, by Frank Manola, fmanola@objs.com, of Object Services and Consulting.

For each standard below, it would be useful to consider what they treat as a "capsule", or thought, and how they organize sequences, hierarchies, and networks of capsules.

Saulius Maskeliunas 1999.08.05:  In the journal "Informatica" Volume 10 Issue 2 there is an article: Sten Carlsson, Beneth Christiansson The Concept of Object and its Relation to Human Thinking: Some Misunderstandings Concerning the Connection between Object-Orientation and Human Thinking,   pp. 147-160. http://www.vtex.lt/informatica/Contents.htm  (or http://neris.mii.lt/mii/mii_engl/bndr_an/informat/intic_tr.htm ).  I think it may be of interest to you.

Help appreciated:  Do you know of any additional standards that we should examine?
Help appreciated:  For each standard below, what is a website with useful information, especially for figuring out the ways in which they use and define sequences, hierarchies, and networks?
Help appreciated: For each standard below, what is a listserv whose subscribers might be interested in the relation of their standard to the arranging and exporting of thoughts?
Help appreciated: How do the standards below use and define SHN?
 
Standard (and type of visualization) Capsule S = Sequence H = Hierarchy N = Network
XML (catalog)
HTML
HyTime
SGML
UML
OKBC
CORBA
COM
Conceptual Graphs
Cyc-L
KQML
Summary Object Interchange Format (SOIF)
Object Exchange Model (OEM)
Knowledge Interchange Format (KIF)
Extensible Markup Language (XML)
Dublin Core
Warwick Framework
PICS-NG
Meta Content Framework (MCF)
Resource Description Framework (RDF)
Document Object Model (DOM)
Embedded Objects
Web Interface Definition Language
OMG Property Service
Tagged Data Facility

Andrius Kulikauskas 1999.08.12: I did read Frank Manola's paper, but did not investigate or write up the standards in greater detail.  It does seem that each standard appeals to one or more of the six visualization types.  (For example, XML is designed as a sequence (to be processed as such) organized with a hierarchy that is supplemented with a network of links.  In other words, it is visualized as a chronicle (hierarchy on top of sequential processing), or as a catalog (network of links on top of hierarchy), or as a canon (network on top of sequential processing).  Thinking about the standards in this way should be helpful in actual implementing a solution, when we need to look for examples of existing solutions.  For example, HyTime is a multimedia standard that integrates temporal sequences with hyperlinking.  Other standards may show how to address, for example, issues with atlases.

List Structural Questions

How do the standards above differ in the ways that they define sequences, hierarchies, and networks of information?  These differences help us formulate questions that our standard will need to answer.

Andrius Kulikauskas 1999.08.17:  Thank you to Saulius Maskeliunas for his letters, which I include below: Supplementing SHN with Sets, An alternative System approach, Sketches, and Concerning Possible Application Area of SHN.  They have been very helpful in thinking through additional structural questions to raise.  More importantly, I have found them very helpful in priming my mind in pulling together a general explanation regarding the use of SHN, and especially the usefulness of a standard for them.

Saulius Maskeliunas: Supplementing SHN with Sets

Saulius Maskeliunas 1999.08.03:  Maybe it would be reasonable to supplement the SHN triplet with ' S e t '  (which has elements without any indicated links between them). Yes, that could be expressed as simple sequence (with elements aligned in any consecutive order) or hierarchy (Set + all elements of it). But similarly as Sequences and Hierarchies are not expressed as
partial cases of Networks - a Set could be included as independent case, too. That would give more fullness to SHN format. In reality we encounter cases when any order of elements of a set (sequence, hierarchy or network) is secondary, not so important to the fact that all elements belong to this set. E.g., inhabitants of some house can be enumerated in various Sequences (in alphabet order, according to flat numbers, according to their age, etc.), into Net (e.g. showing links of their friendship, collaboration relationships), into a Hierarchy (e.g., if this house is tenanted by some army subunit), but all such orders are less important than the main fact: there is a set with elements (which has various alternative possible inner orderings).
One more example: when we have some amount of notes on some topic without indicated any order between then and start to investigate it - a t  f i r s t  there is only Set (all sequence, hierarchy or network relations are probed to clear up gradually afterwards).

Saulius Maskeliunas: An alternative System approach

Saulius Maskeliunas 1999.08.03:  Listening Andrius' talks about SHN orderings - all the time it reminds me the idea: alternative to SHN could be  S y s t e m   a p p r o a c h or System Theory Approach (SysA).  In order to clear up possible relationships of SHN and SysA, here I'll probe to express my understanding of SysA :

According to SysA everything what is investigated (analysed, comprehended, under description, designed, etc.) is considered as a s y s t e m .

Each system:
-1- exists (operates, lives, ...) in an  E n v i r o n m e n t ;
-2- has it'  P u r p o s e  (aim, destination, goal, ...) and F u n c t i o n s ) ;
-3,4- has  I n p u t s  and  O u t p u t s  (I/O)  of information and/or materials.  I/Os are channels of interaction with 'Neighbours' (which are parts of Environment, too);
-5- consists of  C o m p o n e n t s  (subparts, elements, ...), i.e. is an aggregate of it' constitutive parts;
-6- has  I n n e r  s t r u c t u r e  (net of inter-connections of it components), destined for execution of system' functions. It describes statics of the system (i.e., [1] place of system in the Environment, [2] places of Components in the system), and is expressed by, e.g., structural schemes;
-7- has  M o d e  o f  a c t i v i t y  (again, destined for execution of system' functions). It describes dynamics of the system (i.e., [1] system activity in the Environment and [2] dynamic interactions of system Components), and is expressed by, e.g., algorithms, action diagrams, etc.

Main regularities of systems:

How SHN manifest in SysA : Considerations on this topic are presented in the next part on sketches.

Saulius Maskeliunas: Sketches

Saulius Maskeliunas 1999.08.03:  Do sketches (e.g. in architecture), work drawings, 3-dimensional views of inner composition of cars which are under construction can be named simply 'Networks' ?..  In such cases: [1] schemes are
expressing that something is inside something, [2] from such schemes anybody can clear up (by measuring) lengths - heights - forms - distances between any parts or points - relative positions - .... Such  _scaled_views_in_Cartesian_planes_or_spaces_  is something more than Net or combination of Net and Hierarchy (because naming it only as Net / Hierarchy  something essential is missed). Such sketches is peculiar sort of information' representation, in which Nets, Hierarchies, Sequences could be seen, but any combination of them expresses this new quality only partially. According to Chinese proverb: "One picture is more expressive than 1000 words".

So, SHN well fit for expresing relations, links, connections b e t w e e n  notes and/or figures, schemes, etc., but not the content of them.

From the other side, content of figures, schemes, etc. always can be expressed in textual form, showing SHN relations of constituent parts (which are expressed in thoses schemes).

Saulius Maskeliunas: Concerning possible application area of SHN

Saulius Maskeliunas 1999.08.04: In the 1st version of my thesis I've presented modes of information and knowledge classification [allowing to clear up: "what are the sorts of knowledge which is (or: 'should', 'will be', etc.) presented in various knowledge-based systems ?"].  Later on it was dropped out (because of immaturity and some change of thesis topic). But, in my opinion, having prepared modes of knowledge classification (sorting, typology, taxonomy) it is easier to evaluate: Here is 'refreshed' version of those knowledge classification ways:

ASPECTS OF INDICATING TYPES OF KNOWLEDGE, INFORMATION

1- Purpose (aim);
2- Character (nature): quantitative (indicating applied data types) or qualitative (symbolic), textual, graphic, visual (pictorial), audio, video, smell, taste, touch;
3- Range (common-ness): in a scale from concrete to abstract;
4- Mood: from descriptive (declarative) to imperative (procedural, operational, insistent);
5- Quality:

5.1-  Reliability (substantiation): from trustworthy (weighty) to doubtful,
5.2- Completeness: exhausted or incomplete in some aspect(s),
5.3- Indetermination: without inner contradictions or with (some) incompatibilities,
5.4- Formalization level: from  having one meaning (monosemantic) to  informal;
6- Indistinctness:
6.1- Vagueness: from  having clear boundaries  to  fuzzy,
6.2- Probability: firm or probable,
6.3- Exactness: strict (accurate, precise) or approximate;
7- Possibility of alternative views: presenting one view  or  allowing (supporting) various different views;
8- Deepness: expressing of empirical data, observed relations, etc. (i.e., presenting as "black box")   or  expressing goals,
  causalities, physical laws, formulae, structural models, etc. (i.e., presenting as "clear box");
9- Decomposition possibilities: from indivisible to simply decomposable to elementary constituents.

How all that (i.e., from "1-" to "9-") could be put into sequence according to their importance - I don't know; in addition, maybe it could be essentially enlarged (would be interesting to hear such propositions or criticism).

Here comes a question: "How SHN standard (which is now under preparation) could be classified in the light of presented typology ?..."

At first, it is possible (easier) to evaluate: "In what application area SHN usage was seriously investigated till now ?..."
Answer: "Usage by Andrius K."
Next sub-question: "How this area could be step-by-step classified?"
My first draft answer [which is prepared only looking from a very distant aside, so, sometimes incomplete, sometimes with very possible mistakes]:
1- for writing and ordering of Andrius' personal thoughts;
2- qualitative, textual;
3- abstract, with (accidental) examples;
4- descriptive;
5- in a process of evolution, so:

5.1- doubtful,
5.2- incomplete,
5.3- not very co-ordinated  (more strictly speaking:  in a process of tuning with help of SHN orderings),
5.4- informal;
6- rather indistinct:
6.1- often fuzzy,
6.2- probability was not evaluated,
6.3- exactness was not evaluated,
7- presenting view of 1 person;
8- middle deepness;
9- difficult decomposition (till ordering with SHN).

So, that belongs to the area of "wicked problems" [see, e.g.: http://www.gdss.com/wicked.htm (E.J. Conklin, W. Weil.Wicked problems: naming the pain in organizations, 1997)  or http://ksi.cpsc.ucalgary.ca/AIKM97/sbs/sbs-paper2.html (S. Buckingham Shum. Representing hard-to-formalise, contextualised, multidisciplinary, organisational knowledge, 1997).

C o n c l u s i o n :  for such sort of problem areas - SHN fit well.

But, what about problem areas of other possible sorts ?...

In my opinion, Andrius K. believes that SHN fits similarly good almost everywhere. But in order to substantiate such opinion -
additional investigation is needed: "how SHN orderings fit for other sorts of possible problem areas (from the list of 1-, 2-, ..., 9- alternatives) ?"

Apply Four Criteria

Organizing Thoughts into Sequences, Hierarchies and Networks, which I wrote with Saulius Maskeliunas, identifies four criteria to help decide how we should define sequences, hierarchies and networks for the purpose of arranging thoughts.

Functional criterion

Our SHN definitions should accord with the needs and preferences of users.  This is often the only criterion when there are well developed products and vendors simply need to come to agreement based on the products they have already developed and plan to develop.  However, ours is a case where the lack of a standard has set back the development of software tools.  That is to say, we should expect major advances in the tools and be careful not to make restrictions based on existing tools.

On the other hand, we can develop some very general guidelines based on our expectations of the relationship between our tools and the thoughts we are working with.

Psychological criterion

The psychological effects of arranging thoughts: Have you ever forced yourself to write a paper, only to notice how the act of writing helps sort out which ideas are strong, and which ideas are weak?  This psychological effect, of becoming sensitive to the distinction between strong ideas and weak ideas, appears when we organize thoughts in a sequence.  When we organize our thoughts in a hierarchy, we become sensitive to a different distinction: which ideas are broad, and which are narrow.  What is the effect of writing ideas in a network?  Such writing helps us distinguish which ideas are vague, and which are clear.  The SHN definitions that we are developing should heighten the polarization between strong and weak, broad and narrow, and vague and clear.

Designing a psychological experiment: I would like to design an experiment that would demonstrate the relation between the way we structure information and the distinctions that we discern amongst ideas.  Here are some ideas:

Restructuring Dilemma may explain the psychological effects: I have come up with one explanation of the source of the psychological effects.  It is based on the classification of visualizations in the paper Organizing Thoughts...  I have observed, based on the project Structures of Thinking, that in actual practice we do not find sequences, hierarchies, or networks by themselves.  Instead, they are always used in pairs, with a first structuring becoming restructured with a second structuring.  For example, as a sequence grows to be of meaningful length, it becomes more than we can handle, and so we can get it back under control by adding a hierarchy, yielding a chronicle.  There are six possible such restructurings, and we have observed them all: chronicle (S with H), evolution (H with S), catalog (H with N), atlas (N with H), canon (S with N), tour (N with S).  Introspection suggests that we do not visualize the first structuring, statically, only its growth.  For example, we do not visualize a sequence of any meaningful length.  Instead, we visualize its restructuring.  For example, we can imagine how elements of the sequence are being grouped together hierarchically.  Given a first structuring, such as a sequence, there are two ways it can be restructured, in this case: either with a hierarchy, yielding a chronicle, or with a network, yielding a canon.  The mind is encouraged to decide, which restructuring is taking place.  What is the effect of the choice in this example? This explanation is attractive in that it describes the polarizations as arising from a mental dilemma of having to decide, in the process of visualization, which restructuring is taking place.  It makes much more concrete psychological predictions and therefore should be easier to test.  The predictions are as follows: It seems not too difficult to ask subjects to rate their impressions of elements within diagrams, for example, on scales of -3, -2, -1, 0, 1, 2, 3, for weakness-strength, narrowness-broadness, vagueness-clearness. Help appreciated: Could somebody design and conduct a pilot of such an experiment?

Andrius Kulikauskas 1999.09.16:  I've been inconsistent in claiming that a hierarchy encourages us to distinguish the broad and the narrow ideas.  When I'm dealing with a single layer, I mean that the branchings closer to the root are taken to be broader ideas, and the branchings farther from the root are taken to be narrower ideas.  But when I'm dealing with a double layer, I mean that the broader ideas are synchronized across the tree (as in an evolution), and the narrower ideas are those involved in links from one part of the tree to another (as in a catalog).  I would think that these distinctions are compatible, in that associating broadness with closeness to the root gets replaced with synchronization across the tree, and associating narrowness with distance from the root gets replaced with linkings between various parts.  This suggests constructing the following table:
 
Structure and Effect Single layer Double layer
Hierarchy (broad and narrow) Close to root is broad, far from root is narrow. Synchronizing ideas across tree is broad, linking ideas from one part of tree to another is narrow.
Sequence (strong and weak) At front of sequence is strong, at end of sequence is weak. Hopping around subsequences is strong, grouping together into subsequences is weak.
Network (vague and clear) With many links is vague, with few links is clear. Establishing well formed subnetworks is vague, walking through a node is clear.

The descriptions in the double layer column may be thought of as growing out of the descriptions in the single layer column.

Anthropological Criterion

The anthropological criterion says that the definitions of sequences, hierarchies, and networks must accord with the ways of organizing information observed in human practice.

Philosophical Criterion

The philosophical criterion says that the definitions of sequences, hierarchies, and networks must accord with successful models of cognition.  In particular, they should be consistent with the classification of visualizations described in Organizing Thoughts into Sequences, Hierarchies, and Networks.  In my opinion, conclusions to be drawn from this model include:
 


I have worked for many years on a philosophical model that I will write up as Notes on Everything.  Some of the concepts from this model offer ideas on the roles that hierarchies, sequences, and networks play.  According to this model, the three structures give different ways that something can relate to everything.  The most basic way is a hierarchy, where each node is considered a local encapsulation of everything, and is a division of everything into zero or more disjoint perspectives.  In a sequence, there are nodes and links. Each node is considered a local encapsulation of everything, a sort of steady state available to everything.  Each link is a criteria, that is, a filter on everything.  In a network, there are two kinds of nodes (outgoing and incoming) and one kind of link.  An outgoing node is a local encapsulation of everything.  An incoming node describes a context for an outgoing node, and a link offers the means for providing the context.   (A small problem must be understood within the context of a larger system that includes neighboring systems).

What happens when we try to restructure a structuring with the same type of structuring?  For example, what happens if we restructure a sequence with a sequence?  Why is this not possible? How do the allowable restructurings relate to allowable actions on a structure?

Decide Structural Answers

The answers below are highly tentative, and meant to start up discussion.
 
Structural Question
S = Sequence
H = Hierarchy
N = Network		 Functional Criterion: SHN definitions should be the most convenient for organizing ideas. Psychological Criterion: SHN definitions should produce the most
dramatic psychological effects on thinkers. 		 Anthropological criterion: SHN definitions should best account for the
ways of organizing ideas reflected in human practice.		 Philosophical criterion: SHN definitions should be the most compatible
with successful models of cognition.
May there be infinitely many thoughts? No, human and computer memory are both finite.
May two thoughts overlap in any sense?
May two thoughts have the same position within a S? One thought per position, although each thought may have internal structure. It depends on how we understand evolution and tour.
May a thought have more than one position within a S? Thoughts can reccur in a stream of consciousness.
May there be several distinct Ss? Weak thoughts only relate to adjacent thoughts, strong thoughts can point to other sequences. Distinct Ss that need not fit within a common underlying sequence.
May a thought be in two Ss?
May distinct Ss refer to the same system of positions?
May Ss refer to different systems of positions?
Does an S have to be interpreted as time? No. Is single dimensional, but need not be one-directional.
May a thought be in two Hs?
May there be several distinct Hs?
May the branches of H be ordered or not? Atlas and catalog suggest order is arbitrary. Unordered, otherwise H is a chronicle and can be visualized!
May there be several distinct Ns?
May a thought be in two Ns?
May a thought be a node in N?
May a thought be a link in N?
May two thoughts have multiple links?
May two thoughts have a directed link?
May two thoughts have a nondirected link?
May a thought be in both S and H?
May a thought be in both N and S?
May a thought be in both H and N?

May there be infinitely many thoughts?

Human and computer memory are both limited.  There may be algorithms for generating infinitely many thoughts, depending on how we define thought.  However, we can focus independently only on a finite number of thoughts.  The functional criterion suggests that in practice we want to relate independent thoughts.  Therefore, our sequences, hierarchies, and networks are emphatically finite.  In particular, this means that every sequence has a definite beginning and end, and that every tree has a definite set of leaves.

May two thoughts have the same position within an S?

How do timelines deal with events in different places at the same time?  Typically, they draw parallel lines, for example, one line for each civilization.  One way to understand parallel timelines is to say that there is a single timeline, whose elements have internal field structure, each field corresponding, for example, to a separate geographic region.  In this case, I would say that at a given position there is a single thought, but it may have internal field structure. [7/99, Andrius Kulikauskas]

An evolution is one of the six visualizations that we encountered, the one given by restructuring a hierarchy with a sequence.  An example would be the tree of life: we start with a hierarchy giving the divergence of species.  Then we introduce time (a sequence) and synchronize the introductions of various species.  The time parameter lets us get a handle on the large tree.  A key question is, does a thought from a hierarchy belong to the sequence, or does it get mapped to the sequence?  If it belongs to the sequence, then we should say that two thoughts may have the same position within a sequence, just as two species may be attributed to the same time.  If it gets mapped to the sequence, then the sequence consists of different thoughts, such as times, and it seems confusing and unnecessary to think of this time sequence as having several elements with the same position.  The same question arises when we deal with a tour, which is a walk through a network. [7/99, Andrius Kulikauskas]

Saulius Maskeliunas 1999.08.05: Yes.  If we have a sequence of ideas, and we organize them according to strength (weight, priority, and so on) and if two ideas are according to this criterion equal, then they must take up the same position in the sequence.  Writing them in two neighboring positions one would have to have an additional comment that they should be treated as equal.

May a thought have more than one position within a S?

Saulius Maskeliunas 1999.08.05: It may.  For example, consider a sequence of all of the thoughts that pass into my mind in 1 hour's time, which you record as a stream of consciousness.  You can think about a certain thing more than once, and for examining later associations, it is important not to throw out duplicate thoughts from the sequence.

May there be several distinct Ss?

Several examples from human practice show that there can be several distinct sequences which should not be forced within a single larger sequence.  A tax form is designed as a sequence of steps to be made.  Some of these steps may include pointers to have us move back or move ahead along the sequence.  They may also include pointers to have us copy information to or from other tax forms.  It can happen that there are two or more tax forms which do not have to be completed in any particular order.  Each tax form can be thought of as a sequence, but we should not be forced to reconcile the sequences.  Similarly, steps in a math proof may point to other math results, but we should not be forced to position each step within a common time frame.

The above examples involve sequences in time.  In general, however, the sequence need not be in time or be related to time.  Consider an encyclopedia of measured quantities.  Such an encyclopedia may have one sequence providing examples of increasingly costly items, another of increasingly fast objects, another of increasingly massive things, and so on.  We should be able to consider these as distinct sequences.  In general, it seems that we should allow for eclectic collections of sequences. [7/99, Andrius Kulikauskas]

The Restructuring Dilemma suggests that thoughts are weak when they are related only to adjacent thoughts, necessarily existing within the same sequence, as in the case of a chronicle.  It seems out of character for a chronicle to group together thoughts from different sequences.  Thoughts are strong when they can be thought of as pointing to nonadjacent thoughts, whether within the same sequence, or within another sequence, as in the case of a canon.  The possibility for there being more than one sequence therefore heightens the distinction between weak and strong thoughts.

Saulius Maskeliunas 1999.08.05: Of course there can.

May a thought be in two Ss?

Saulius Maskeliunas 1999.08.05: Yes.  I don't imagine, that somebody could claim otherwise.

May distinct Ss refer to the same system of positions?

Saulius Maskeliunas 1999.08.05: Yes.  For example, two different sequences, organized by time.

May Ss refer to different systems of positions?

Saulius Maskeliunas 1999.08.05: Yes.  For example, a time sequence and a priority sequence.

Does an S have to be interpreted as time?

An encyclopedia of chess openings presents a hierarchy of the board positions that unfold as the chessplayers, White and Black, move their pieces from their starting positions.  The editors evaluate the positions that evolve, and indicate whether they are to the advantage of White or Black, and the size of the advantage.  The advantage may be recorded using a discrete scale (worse, slightly worse, roughly equal, slightly better, better) or, in this age of computer chess, using a continuous scale (where, for example, 0.0 is equal and 1.0 is a one pawn advantage for White and there are many subtle values in between).  When either a discrete or continuous scale is used, then we can think about the "identification" of positions of equal value, much as if we "synchronized" them.  This different kind of scale, value of position, achieves a similar effect as time, and is one-dimensional like time, but is not one-directional like time (a game can gravitate towards a win for White, a win for Black, or a draw).  This suggests that it should be possible to think of the parameter "value of chess position" as a sequence.  Also, the value of the chess position can be described qualitatively, which is important given issues of a chessplayer's style, what positions they are comfortable with.  Even such qualitatively described positions can be "identified", or so to speak, "synchronized".  The evaluation is no longer a one-dimensional parameter, and might be modeled with a multi-dimensional parameter.  Similarly, we could consider the evolution of species, and how they came to vary by length and height.  However, to visualize such an evolution, introspection suggests that we must focus on a single one-dimensional parameter.  This suggests that a sequence must be a one-dimensional parameter, but need not be associated with time, and in particular, need not gravitate in one-direction. [7/99, Andrius Kulikauskas]

Saulius Maskeliunas 1999.08.05: In general - no, it need not be interpreted as time.  For example, there may be a sequence by the alphabet or a sequence by priority.  But sometimes, yes.

May there be several distinct Hs?

Saulius Maskeliunas 1999.08.05: Perhaps hierarchies could be drawn together into a single one, and consider them all as distinct branches, but that is a matter of implementation, and in reality there exist several different ones.

May a thought be in two Hs?

Saulius Maskeliunas 1999.08.05: Yes.  I don't imagine, that somebody could claim otherwise.

May the branches of H be ordered or not?

Evidence suggests that hierarchies are not ordered of themselves, but are ordered only when there is an underlying sequential order, as in the case of a chronicle.  It therefore becomes important to consider visualizations where sequences are not involved, namely, atlases and catalogs.  For example, an atlas consists of a hierarchy of global and local maps.  The order of the local maps tends to be highly arbitrary.  A catalog consists of network links added to an underlying hierarchy, as in the case of a bureaucracy.  Here also, the order of the hierarchy tends to be arbitrary.  Are there counterexamples?  [7/99, Andrius Kulikauskas]

Saulius Maskeliunas 1999.08.05: [Re: May a hierarchy be unordered?] It may not.  This question comes across like "can there be hot ice cream?"  For if hierarchical relations have been indicated between thoughts, then there is a hierarchical order.  It might make sense to ask can hierarchical order be supplemented by some other order.  Then the answer could be "yes it can".

Andrius Kulikauskas 1999.08.06: I've reworded the question so that it asks "May the branches of the hierarchy be ordered or not?"

If the branches of a hierarchy are ordered, then resulting structure is simply a chronicle, in that it presumes an underlying sequence.  Furthermore, this would mean that a hierarchy could be visualized as such.  Whereas defining a hierarchy as having unordered branches is consistent with a theory that we do not visualize hierarchies, sequences, or networks directly, but that we need there to be a restructuring, as in the case of a chronicle.  [8/99, Andrius Kulikauskas]

May there be several distinct Ns?

Saulius Maskeliunas 1999.08.05: Of course there can.

May a thought be in two Ns?

Saulius Maskeliunas 1999.08.05: Yes.  I don't imagine, that somebody could claim otherwise.

May a thought be a node in N?

Saulius Maskeliunas 1999.08.05:  Of course.  This is the usual case.

May a thought be a link in N?

Saulius Maskeliunas 1999.08.05: Yes.  For example, when you look over a network and think that certain two ideas must be related.  This thought is a "link in N" or at least an explanatory remark for some relation in the network.  It is natural to hold that links can be of various kinds.

May two thoughts have multiple links?

Saulius Maskeliunas 1999.08.05: Yes.  For example, two thoughts "Socrates is a person" and "All people are mortal" are connected with links:
(1) They speak about people.
(2) They are used as descriptive sentences.
(3) These two sentences are used very often in articles about Logical programming.

May two thoughts have a nondirected link?

Saulius Maskeliunas 1999.08.05: In reality, yes, and in the implementation of a system the nondirected link can be represented as two links going in opposite directions.

May a thought be in both S and H?

Saulius Maskeliunas 1999.08.05: Yes.  For example, when two thoughts belong to any H or N and are placed in a sequence according to the date of creation.

May a thought be in both N and S?

Saulius Maskeliunas 1999.08.05: Yes.  For example, when two thoughts belong to any H or N and are placed in a sequence according to the date of creation.

May a thought be in both H and N?

Saulius Maskeliunas 1999.08.05: Yes.  For example, you take a thought belonging to any network, and write for it a more abstract (or more concrete) thought.

Describe Mathematically

The results above will be used to determine a conceptual, and then, a mathematical formulation of our standard. I imagine that the results we arrive at can be expressed in a flat table format, with one record per thought, one field for the text of the thought, and auxiliary fields for placing the thought within a sequence, hierarchy, or network.

Create DTD in XML

XML seems adequate for expressing our standard, and is becoming very popular.  There are already quite a lot of tools for working with XML.  It seems a natural and practical choice for expressing our standard.

I'm studying Sam's Teach Yourself XML in 21 Days by Simon North and Paul Hermans.  The authors recommend Structuring XML Documents by David Megginson, 1998, Prentice Hall PTR for architectural forms and DTD manipulation, and Developing SGML DTDs: From Text to Model to Markup by Jeanne El Andaloussi for heavy duty DTD development.  [http://www.samspublishing.com, 7/99, Andrius Kulikauskas]

Conceptual Knowledge Markup Language DTD is concerned with applying XML to artificial intelligence, and is an extension of the Ontology Markup Language.  The first versions of CKML followed the philosophy of Conceptual Knowledge Processing (CKP) that approaches knowledge representation and data analysis based on principles that "advocates methods and instruments of conceptual knowledge processing which support people in their rational thinking, judgement and acting
and promote critical discussion."  A basic theorem of CKP establishes the equivalence between the non-hierarchical structure of an incidence relation and the hierarchical structure of a (concept) lattice. The latest version 0.2 of CKML extends this approach with ideas from Information Flow (IF) and distributed systems, which Jon Barwise and Jerry Seligman describe in their book Information flow: The logic of distributed systems. Robert E. Kent, rekent@eecs.wsu.edu, is in charge of the website. [http://wave.eecs.wsu.edu/CKRMI/CKML.html , 7/99, Andrius Kulikauskas]

The IEEE Workshop on Integrating XML and Distributed Object Technologies, June 16-18, Stanford University, included a workshop report on discussions relating XML, JAVA, and UML. [http://www.cerc.wvu.edu/workshop2/xmlobjects.html, 7/99, Andrius Kulikauskas] [http://jeffsutherland.com/xml/IEEE_XML_Report_Draft.htm , 7/99, Andrius Kulikauskas]