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Notes on a Visual Shorthand for Conceptual Graphs

© 2005 Robert McNally

Creative Commons License
This work is licensed under a Creative Commons License.

In his book Knowledge Representation, John F. Sowa describes a system he developed called Conceptual Graphs (CG).

I have been quite impressed by the expressive power of CG, but as I have studied them I have found myself wishing for a way of writing and reading them in addition to the two methods described in the proposed ANSI standard ("display form" (DF) and "linear form" (LF)). Such a third system would be a superset of DF that would attempt to achieve the following goals, which either maintain the benefits of DF, or improve upon them:

In addition, I feel that DF with its multiplicity of boxes and arrows, while concise and useful, feels stylistically "cold," and that a notation inspired by the human factors incorporated in traditional musical notation may provide a "warmer," and hence more approachable, experience of CGs.

What follows are preliminary notes on my approach to creating a visual "shorthand" for CGs. As I am relatively new to CGs and the CG community, I confess ignorance of any similar work that may have gone before, and would appreciate pointers to any such work. These notes indicate my direction, but I make no claim to having achieved any of the goals stated above, nor have I yet methodically covered the proposed CG standard. Much work remains, and I am particularly interested in finding out whether the CG community feels such work would be of value. If nothing else, I have found this to be a useful study tool for my own purposes, and I am open to feedback on any aspect of this exploration.

This document is not a tutorial on CGs or on the proposed shorthand. It assumes knowledge of reading and writing CGs. The definitions below are followed by a number of example graphs.

Modifications to Display Form

Concepts

Concepts may be notated as in LF or DF (brackets or rectangles), and additionally concepts not needing special grouping may be left bare.

Relations

Relations may be notated as in LF or DF (parentheses or ovals), and additionally may be represented by a glyph (see below).

Arcs

Darts are recommended when the arc distance is short because they require fewer strokes than arrows and they help create a “virtual box” at their origin, which is often a bare concept. Darts may drawn at any length or rotation as needed.

The last (away-pointing) arc of a relation may be omitted by juxtaposing the related concept. The relation and concept may be juxtaposed in any order, vertically or horizontally. The concept so juxtaposed may be omitted entirely if it is T.

Regular arrows may be used where necessary or desired.

Contexts

Bows are used to define contexts. The contents of the context appear "inside" (i.e. on the concave side) of the bow. Bows may be drawn at any length or rotation as needed. Only a single bow is needed to define a context.

Negated contexts are indicated by a stroke through the center of a bow:

Since bows visually divide space into two areas, nested contexts are indicated by placing the contents of nested contexts inside of bows smaller than the bows used to define the containing context.

The default context type is Situation unless stated otherwise. The type of context may appear juxtaposed on the convex side of its bow.

Regular boxes may be used where necessary or desired.

Coreferences

Coreference lines may be drawn directly to a relation if the related concept is T and has been omitted as described in Arcs, above.

Glyphs

Glyphs should be ideogrammatic yet terse (no more than 4 strokes total, and minimizing the number of times the pen must be lifted) and language-neutral. Similar relations should have glyphs that are visually distinct, yet harmonious.

Tenses

Glyph Relation Signature
Past Past(Situation)
Present Now(Situation)
Future Future(Situation)

Roles

The glyphs defined here are the ones described in the Appendix of Knowledge Representation and on the John Sowa's web pages describing Roles.

Glyph Relation Signature
Accompaniment Accm(Object,Object)
Amount Amt(Characteristic,Quantity)
Argument Arg(Function,Data)
Attribute Attr(Object,Entity)
Base Base(Attribute,Type)
Because Bcas(Situation,Situation)
Characteristic Chrc(Entity,Entity)
Child Chld(HumanBeing,HumanBeing)
Comparand Comp(Attribute,Object)
Manner Manr(Process,Entity)
Measure Meas(Attribute,Quantity)
Part Part(Object,Object)
Possession Poss(Animate,Entity)
Role Has(Entity,Entity)
Successor Succ(Occurrent,Occurrent)

Thematic Roles

The glyphs defined here are the ones described in the Appendix of Knowledge Representation and on the John Sowa's web pages describing Thematic Roles.

Glyph Relation Signature
Agent Agnt(Act,Animate)
Beneficiary Benf(Act,Animate)
Completion Cmpl(TemporalProcess,Physical)
Destination Dest(SpatialProcess,Physical)
Duration Dur(State,Interval)
Effector Efct(Entity,Entity)
Experiencer Expr(State,Animate)
Instrument Inst(Act,Entity)
Location Loc(Physical,Physical)
Matter Matr(Act,Substance)
Medium Med(Transfer,Physical)
Origin Orgn(Process,Physical)
Path Path(Process,Place)
Patient Ptnt(Process,Physical)
Point In Time PTim(Physical,Time)
Recipient Rcpt(Act,Animate)
Result Rslt(Process,Entity)
Start Strt(Entity,Time)
Theme Thme(Situation,Entity)

Example Graphs

The cat is on the mat.



Romeo marries Juliet.



A bus goes to Copenhagen.



Seize the day.



John kissed Mary.







Office 2 is between Office 1 and Office 3.



John goes to Boston on a bus.



If a farmer owns a donkey, then he beats it.



Sam is a good musician.



You are wet because it is raining.



Tom believes that Mary wants to marry a sailor.



Mary had a little lamb,
Whose fleece was white as snow,
And everywhere that Mary went,
The lamb was sure to go.
He followed her to school one day,
Which was against the rules,
It made the children laugh and play,
To see a lamb at school.