We are developing a CMS including document authoring feature based on wiki to publish structural mathematical documents on the Web. Using this system, users can write documents including mathematical expressions written in LATEX notation and explicitly stated characteristic structures of mathematical articles such as definitions, theorems, and proofs. Documents input to the system is published on the Web as not only XHTML files to be browsed but also XML files complying with NLM-DTD, which is used to exchange articles electronically. Not only single wiki page document, users can build a document which consist of more than one pages and is described its structure semantically by the system. In order to do this, we also propose an application of OAI-ORE and RDF vocabularies to describe structures of documents consisting of several resources.
Today, many documents are published on the Web. The term “documents” here includes articles of news or blog, wiki pages, journal articles, and any other web pages. These documents are published as HTML or XHTML to be browsed, or as PDF or PS file to be printed out. Sometimes one document is published as several formats.
Some documents consist of several resources. One of examples is a document including a graphic image. Here, we assume that body text of the document is written in a HTML file and the image is a JPG file. On the Web, each of them is independent resource and given unique URI. When URI of the image is put on src attribute of an img element in the HTML file, we should treat the document as not just referencing but including or embedding the image. In this case, this document is an aggregation of two resources that are HTML file of body text and JPG file of graphical image.
Sometimes documents include not only graphic images but also whole of other (more small)
documents. In general, this is called transclusion. HTML does not have this transclusion feature in itself,
but MediaWiki, for example, has templates feature to extract content of other wiki pages to the page [
Furthermore, we sometimes build a document by integrating several documents. In this case, not
only a large document is just split into several documents, but each of documents is independent and
has their own URI, and they can be referenced directly. In general, parts, chapters, or sections of a
document are able to be independent documents. MathML specification by W3C [
Open Archives Initiative Object Reuse and Exchange is standards to describe and exchange
aggregations of web resources [
At f i r s t , we g i v e Taylor ’ s theorem and p r o o f o f i t . [ [ theorem i d =” t a y l o r t h e o r e m ” t i t l e =” Taylor ’ s theorem ” j Let $f$ be a f u n c t i o n which i s d e f i n e d on t h e i n t e r v a l $ ( a , b ) $ and s u p p o s e t h e $ n $ t h d e r i v a t i v e $ f ˆ f ( n ) g$ e x i s t s on $ ( a , b ) $ . Then f o r a l l $x$ and $x 0$ i n $ ( a , b ) $ , $$ R n ( x ) = n f r a c f f ˆ f ( n ) g( y ) gfn ! g ( x x 0 ) ˆ n $$ w i t h $y$ s t r i c t l y between $x$ and $x 0$ ( $y$ depends on t h e c h o i c e o f $x$ ) . $R n ( x ) $ i s t h e $ n $ t h r e m a i n d e r o f t h e T a y l o r s e r i e s f o r $ f ( x ) $ . ] ] ( O r i g i n a l t e x t o f t h e theorem i s h t t p : / / p l a n e t m a t h . org / e n c y c l o p e d i a / TaylorsTheorem . html , r e t r i e v e d a t 2 0 1 1 . 0 5 . 0 8 ) aggregations of representation files such as PDF or PS. In this article, on the other hand, we propose describing documents as aggregations of constituting resources and relating the documents with their representations apart from describing aggregations.
With a background like that, we are developing a content management system Matherial, which manages and publishes mathematical documents and other resources. One of the purposes is developing a system which assists to write documents consisting of several resources, and publishes as web pages with appropriate metadata to describe its structure and publishes as XML files complying with NLMDTD for further reusing.
Matherial provides authoring assistant feature based on wiki engine. Users of the system can write a wiki page including chapters, sections, mathematical statements, and expressions, or they can write some of them as independent wiki pages and integrate them into one document and publish it. Relationships between documents and included resources, and between documents and wiki pages representing them, are modeled as aggregations of OAI-ORE, and they are described in XHTML representation of documents by RDFa. Matherial can output documents into not only one or more XHTML pages, but also XML files complying with NLM-DTD. Therefore, other systems supporting NLM-DTD are able to re-use documents by Matherial.
The paper is organized as follows: In section 2, we present an example of mathematical structural documents on Matherial. In section 3, we propose an application of OAI-ORE and RDF vocabulary to describe structural documents on Matherial and more generally on the Web. Finally, section 4 concludes the paper. 2 2.1
One of major features of Matherial, developed in this study, is assistant authoring mathematical
documents. This is based on so-called “Wiki Engine”, so users can write documents by simple markup
notation and publish them on the Web. They can put mathematical expressions written in LATEX notation
into texts, and our own MathML library [
The most simple type of documents created on Matherial is one consisting of a wiki page. When users need to write mathematical text structures, such as definitions, theorems, and proofs, using functional markup for them, they can expressly provide that segments have such property.
For example, Listing 1 is a document written in wiki markup including a theorem. When users write theorems in their document directly like this, URIs of theorems are hash URIs, appending
We b e g i n w i t h Taylor ’ s theorem and i t s p r o o f . [ [ i m p o r t w i k i / TaylorTheorem ] ] [ [ i m p o r t w i k i / ProofOfTaylorTheorem ] ] For a f u n c t i o n $ f ( x ) $ , $f$ i s T a y l o r e x p a n d a b l e when $n l i m fnn t o n i n f t y gR n ( x ) =0$ where $R$ i s r e m i n d e r term o f [ [ [ w i k i / TaylorTheorem j t h e theorem ] ] , and we have b e l l o w . [ [ i m p o r t w i k i / T a y l o r E x p a n s i o n ] ] Even i f complex f u n c t i o n $ f ( z ) $ i s n o t h o l o m o r p h i c a t a p o i n t $c$ , i f $f$ i s h o l o m o r p h i c i n an a n n u l u s around $c$ , we g e t L a u r e n t s e r i e s bellow , $$f ( z ) = nsum fn=n i n f t y gˆfn i n f t y g a n ( z c ) ˆ n$$ where $$a n =n f r a c 1 f2n p i i gn o i n t ngamman f r a c f f ( z ) dz gf( z c ) ˆf n+1gg $$ and $ngamma$ i s a c l o s e d c u r v e i n t h e a n n u l u s ( f i g . [ [ r e f a n n u l u s ] ] ) . [ [ f i g u r e f i l e / A n n u l u s O f L a u r e n t i d = a n n u l u s ] ] T h i s i s e x t e n s i o n o f [ [ [ T a y l o r E x p a n s i o n ] ] ] f o r f u n c t i o n s which a r e n o t h o l o m o r p h i c . their IDs as fragment to URI of the document. In this case, assuming a URI of a document is http://mw2011.matherial.org/wiki/Taylor, a URI of a theorem itself in the document is http: //mw2011.matherial.org/wiki/Taylor#taylor_theorem.
For important definitions, theorems, and proofs, considering we discuss about them or reuse them from other documents, they should be independent documents and referenced by their own URI. On wiki of Matherial, users can set type of page, for example set that page is a theorem, the system treats the document by the wiki page as if it is described a theorem. In this case, URI of the theorem is URI of the document by wiki page. Detail about URIs and relationships of documents and wiki pages in Matherial are illustrated in section 3.
With Matherial, users can write documents importing and extracting mathematical statements which have been created as independent document. Moreover users can put images which are managed in Matherial into documents in the same way, and they can use descriptions of images which were input when images were upload to the system instead of writing new descriptions in the page. Listing 2 is a document importing statements which are already published and going on to describe a statement following them. In that example, an image referenced in the text will be imported with its description.
Moreover, aggregating these documents as sections, chapters, or parts, users can build a new document. In Matherial, users input enumeration of sub documents with metadata of the document such as title, author’s information, and so on into form to build the document. Detail of semantic structure of documents which consist of several resources is described at section 3. 2.2
Matherial output documents as XML files. XML schemas of output XML files are XHTML [
For XHTML files, metadata are described as RDF graph [
Listing 3: A part of an NLM-DTD XML version of a document Discussion forum for The Document
Taylor Theorem mt:discussedAt mt:discussionAbout mt:hasRepresentation
Laurent Series XHTML
Wiki Markup Text shown at Fig.2.
For XML files complying with Archiving and Interchange Tag Set [
The documents authoring feature of Matherial is based on wiki engine. Users write texts by wiki markup
of Matherial. The most simple document is one consist of only body text but not any other resources.
Matherial converts an input wiki markup text to XML files complying with XHTML and NLM-DTD, and
publish them on the Web. Wiki source files, XHTML files, and XML files should be given different URI,
and a URI of each files is different from the URI of the document itself (we call a URI for a document
itself platonic form URI) [
In Matherial, users can write documents which include other resources, too. This does not means that documents just reference other resources. As \includegraphics command or \input command of LATEX, users can embed images or extract contents of other documents into the document. Matherial generates XHTML files which include contents of other documents and is embedded images by img elements, and generates XML files of NLM-DTD which include other documents and is embedded
mt http://www.matherial.org/terms/ rdf http://www.w3.org/1999/02/22-rdf-syntax-ns# ore http://www.openarchives.org/ore/terms/ images by graphic elements, from wiki sources written like that.
This document structure on Matherial is described as an RDF graph whose nodes are platonic form
URI of the document, URIs of resources included in the document, URIs of representations of the
document, and so on (Fig.1). Matherial describes this structure by Resource map of Open Archives Initiative
Object Reuse and Exchange (OAI-ORE) [
The structure of a document which consists of several resources and which is represented by several representations could be applied to not only documents in Matherial but general documents on the Web. In following subsection 3.1, we will introduce OAI-ORE to describe Aggregations of resources, then in subsection 3.2, we will show a model of the document structure and metadata schema to describe the structure. RDF namespaces and its prefixes used in this article are shown at table 1. : s a x h
N ore:proxyIn e x t t N s x e x : h a
Open Archives Initiative Object Reuse and Exchange (OAI-ORE) provides a model to describe aggregations of resources. In OAI-ORE, a resource which consists of one or more resources is called an Aggregation. A resource which is a member of an Aggregation is called an Aggregated Resource. An aggregation is defined as a conceptual construct, so it does not have a representation. Therefore, information about an Aggregation should be described by other resources different from the Aggregation. Such a resource which describes an Aggregation is called a Resource Map. For example, relationships between an Aggregation and Aggregated Resources are described in a Resource Map for the Aggregation.
OAI-ORE provides a mechanism named Proxy to relate Aggregated Resources with properties which are given only in the Aggregation. In an Aggregation A-1, for example, we assume that two Aggregated Resources AR-1 and AR-2 have order AR-1 ! AR-2. Moreover, we assume that they have different order AR-2 ! AR-1 in another Aggregation A-2. In this case, if we describe directly the order relationship between AR-1 and AR-2 in AR-1, it conflict to relationship in AR-2. This is because we describe relationship which is available only in AR-1 independently of AR-1. To resolve this problem, we use Proxy resources which act as Resources in the Aggregation to describe relationships available only in the Aggregation between Aggregated Resources and other resources. For example, relationships between AR-1 and AR-2 in A-1 is described using their Proxies like fig.3.
For more detail of OAI-ORE, see [
3.2.1
Document and its Members In this study, a Document is an Aggregation consisting of one or more resources. A resource which is a constituent of a Document is called a Member of Document, or simply a Member. An image embedded into a Document is familiar example of Member. A Member of a Document could be another Document different from the aggregating Document. In other words, aggregating several Documents, we can build a new Document. Relationships between a Document and its Members are described by RDF triples whose predicates are ore:aggregates. Document Content. A Document could have a resource as one of Members which is described the content of the Document itself. We call such a Member a Document Content. A content of a Document is body text of the Document. When a Document includes other resources, indications to include them are written into the content. One example of Document Content is a HTML file, which is a source file of a web page. We can write not only marked-up body text, but also indications to embed images into the page using img elements. In this case, the Document consists of a HTML file as Document Content and images indicated. When we browse this document, web browser get a HTML file from a server, recognize it, get other resources to embed into the page, and display the completed web page. For another example, text files written in wiki markup for any wiki engines. They are described body text and embedding indications different notation from HTML. The system may convert it to a HTML, or create a PDF file which contains image files. Relationship between a Document and a Document Content is described by a RDF triple whose predicate is mt:hasContent, which is sub property of ore:aggregates. Order of Members. When Document has the Document Content, positioning of other Members is described in the Document Content. On the other hand, when Document is simple Aggregation of resources and does not have a Document Content, we may want to describe positioning or order of Members. Furthermore, we may want to give Members complicated and non-linear order relationships such as tree structure. In this article, we propose mt:hasNext predicate to describe order relationships of Members in the Document. This property takes URIs of Proxies of Members for subjects and objects of triples to describe linear or complicated order relationships of Members of the Document (fig.4) Type of Members. We may want to give Members any role in a Document. In an “article” document, for example, the first Member is abstract of the article, following some Members are Sections of the article, and the last Member is References of the article.
mt:partType predicate is to describe these roles of Members in a Document. This property takes URIs of Proxies of Members for subjects, and URIs of sub-classes of mt:PartType which represent roles of Members in Documents. Sub-classes of mt:PartType are mt:Preface, mt:Abstract, mt:TableOfContents, mt:Part, mt:Chapter, mt:Section, mt:Acknowledgment, mt:Appendix, mt:References, and mt:Index. 3.2.2
Mathematical Element Mathematical documents may contain distinctive elements, such as mathematical expressions (especially display math style), definitions, theorems, proofs. When we write a mathematical document, preparing these elements as independent resources and including them in the Document as Members, we can reference these import elements individually and reuse them.
When we create a Document containing mathematical elements, we can show type of the Document explicitly using sub-classes of mt:MathematicalObject. Sub classes of mt:MathematicalObject aremt:Expression, mt:Definition, mt:Theorem, and mt:Proof. mt:Theorem has more detailed sub classes, that are mt:Lemma, mt:Corollary, and mt:Proposition.
A resource of type mt:Proof describing mathematical proof should show explicitly which theorem is proved. mt:proofOf is predicate for RDF triples to relate theorems and its proofs. This property takes URIs of resources of type mt:Proof for subjects and URIs of resources of type mt:Theorem or its sub classes for objects (fig.4). : s t m h a
N e x t mt:partType mt:Section In this article, Documents are Aggregations of ORE, so Documents are abstract resources and do not have entities. Therefore, to browse Documents, Documents should be related with other resources which Documents are serialized in any formats which we can browse. A resource which is serialized from a Document and has URI different from URI of the Document is called a Representation of the Document. When a Document is related to a Representation of the Document, We say a Document has a Representation. a Document Content may be one of Representations of the Document. Some Representations include all Members of Document any way like PDF files, other Representations include only indications and references to other Members like HTML files. Relationships between Documents and its Representations are described by RDF triples using mt:hasRepresentaion predicate (fig. 1). 4
In this article, we introduced a CMS developed for authoring and publishing mathematical documents, and we proposed background semantics to describe structures of documents consisting of several resources. Using the system, we can publish not only small documents but also large documents consisting of several resources by writing in easy mark-up. Structures of documents consisting of several resources are described as RDF graphs based on Resource map of OAI-ORE, and they will be reused by Semantic Web Technologies.
Some applications of OAI-ORE are describe an article as an aggregation of OAI-ORE. The
FORESITE [
The OMDoc format is a content markup scheme for mathematical documents [