Graph characterization of overlap-only TexMECS and other overlapping markup formalisms

Yves Marcoux - Balisage 2008 1

Graph characterization of overlap-only TexMECS and other overlapping markup formalisms

Yves MARCOUX

GRDS – EBSIUniversité de Montréal

Visiting researcherUniversitetet i Bergen


Overview of the talk

1. Graph representations of structured documents

2. Overlap, in markup and structure

3. OO-TexMECS (N.B.: Overlap-Only ;-)

4. Node-ordered DAGs (noDAGs)

5. Results and consequences

6. Future work


1. Graph representations of structured documents


XML document = tree

top

b

c

<top> <a> <b/> </a> <c/></top>

a

Embedding in markup Child-parent in tree


Any tree an XML document

top

b

c

<top> <a> <b/> </a> <c/></top>

a


Any tree an XML document

top

b

c

<top> <a> <b/> <d><e/></d> </a> <c/></top>

a

e

d

Perfect isomorphism !


Document Object Models

• DOMs are essentially graph representations of structured documents

• "Patched" for attributes, namespaces, etc.

• DOM manipulations = graph modifications

• It suffices to make sure that the graph remains a tree


2. Overlap, in markup and structure


Problem of overlap

• In real life (outside of XML documents!), information is often not purely hierarchical

• Classical examples:– verse structure vs sentence structure– speech structure vs line structure

• In general: multiple structures applied (at least in part) to same contents


Overlap


Two views of overlap

• Geometric view: overlapping markup

• Common contents view: non-tree graph structure


Example (markup)

(Peer) Hvorfor bande? (Åse) Tvi, du tør ej!Alt ihob er tøv og tant!

<vers> <peer>Hvorfor bande?</peer><åse>Tvi, du tør ej!</vers><vers> Alt ihob er tøv og tant!</åse></vers>


Example (graph)

(Peer) Hvorfor bande? (Åse) Tvi, du tør ej!Alt ihob er tøv og tant!

vers vers

peeråse

Alt ihob er tøv og tant!Hvorfor bande? Tvi, du tør ej!


Embedding Child-parent

vers vers

peeråse


<vers> <peer>Hvorfor bande?</peer><åse>Tvi, du tør ej!</vers><vers> Alt ihob er tøv og tant!</åse></vers>


Still perfect isomorphism?

• Not for graphs in general... cycles !

• Maybe for acyclic graphs ?

• Let's try more examples...


What if the last verse is saidin chorus by Peer & Åse ?

vers vers

peeråse



What if the last verse is saidin chorus by Peer & Åse ?

vers vers

peer åse


Still acyclic, but no corresponding markup !


So, imperfect isomorphism

• Some acyclic graphs have corresponding documents (i.e., are serializable)

• Some (apparently) don't...

• Manipulations of the graph (DOM) may leave it non-serializable !

• Which acyclic graphs are serializable?


3. OO-TexMECS


TexMECS

• A particular proposal to address the overlap problem with overlapping markup

• MECS (Huitfeldt 1992-1996)– Multi-element code system

• TexMECS (Huitfeldt & SMcQ 2003)– "Trivially extended MECS"

• Markup Languages for Complex Documents (MLCD) project


Overlap-only TexMECS

• TexMECS allows overlapping markup...

• but also much more:– virtual elements, interrupted elements, etc.

• OO-TexMECS 101– Start-tags: <a|– End-tags: |a>– Overlapping elements allowed– Natural notion of well-formedness


4. Node-ordered DAGs (noDAGs)


Contents ordering

• In a serialized document, contents appears in some order

• The order is often significant– Procedure steps, verses in a poem, etc.

• Thus, the order must be present in graph representations– XML: children ordered in the tree


Node-ordered DAGs

• Node-ordered directed acyclic graphs

• Essentially a DAG with children ordered

• Why "node-ordered" (and not "child-ordered") ?– Provisions for further ordering of nodes


Examples

A

B C

E F G H

D

B

C

D

E

A


5. Results and consequences


Main results

1. A noDAG is serializable in OO-TexMECS iff it is completion-acyclic (essentially)

2. Any OO-TexMECS well-formed document can be obtained by serializing some completion-acyclic noDAG

3. You don't gain any expressivity by allowing node-ordering over and above children-ordering


Consequences

• We now know how to define a DOM for overlapping markup

• A DOM-based editor is complete

• Round-tripping is possible between noDAGs and OO-TexMECS

• Results also apply to similar formalisms– TexMECS with more features except virtual

and interrupted elements


Completions

• Intuition: combination of parent-child relationships & children-ordering informs on the relative positioning of tags in an eventual serialization

• If contradictory information is derivable: the graph is not serializable


Example: "starts-before"

A

B C

E F G H

D


Example: "ends-after"

A

B C

E F G H

D


Contradiction = cycle !

A

B C

E F G H

D

Completion-acyclic each completion is acyclic


Future work

• Optimal algorithm for verification

• Optimal serialization algorithm

• Relaxing conditions on the graph

• Relationships with GODDAGs (SMcQ & Huitfeldt 2004)

• And, yes...

• Intertextual semantics of overlap !


Thank you !

Questions ?

<[email protected]>