Standard Generalized Markup Language: Mathematical and Philosophical Issues

The Standard Generalized Markup Language (SGML), an ISO standard, has become the accepted method of deening markup conventions for text les. SGML is a metalanguage for deening grammars for textual markup in much the same way that Backus{Naur Form is a metalanguage for deening programming-language grammars. Indeed, HTML, the method of marking up a hypertext documents for the World Wide Web, is an SGML grammar. The underlying assumptions of the SGML initiative are that a logical structure of a document can be iden-tiied and that it can be indicated by the insertion of labeled matching brackets (start and end tags). Moreover, it is assumed that the nesting relationships of these tags can be described with an extended context-free grammar (the right-hand sides of productions are regular expressions). In this survey of some of the issues raised by the SGML initiative, I reexamine the underlying assumptions and address some of the theoretical questions that SGML raises. In particular, I respond to two kinds of questions. The rst kind are technical: Can we decide whether tag minimization is possible? Can we decide whether a proposed content model is legal? Can we remove exceptions in a structure preserving manner? Can we decide whether two SGML grammars are equivalent? The second kind are philosophical and foundational: What is a logical structure? What logical structures may a document have? Can logical structures always be captured by context-free nesting?