This note is in reponse to the recent postings of Neil, Bob, and Steve. There is considerable ambiguity in our notions of 'semantics', even as the term is being used in our conversations. When AMS was invited to join this ERB, the goals of HTML-Math had been considerably extended over those of the older (1995), Plain-TeX-like approach. One can describe the goals functionally in terms of targets for transformation to and from HTML-Math, but I think it's also commonly agreed that the foundations for these superior transformational capabilities are 'semantical'. If TeX and other current-day notational systems are viewed as 'defective', I think the view of those defects is that they are ambiguities of expression which block mapping to other uses. When one uses the term 'ambiguity', I take it to mean that two disparate 'uses' appear as one. This is a simple *semantical* distinction. In this way, I think it is legitimate to say that the goals of HTML-Math have raised considerations about semantics in mathematical notation. We are not trying to ferret out whether to include semantics, but rather how and to what extent. We're speaking of semantics, not Semantics. I think everyone on this list realizes that the full problem of semantics is very difficult, and I don't know of anyone who has said that he or she would go to the ends of the earth to incorporate some huge formal specification. Speaking loosely (and guessing), my view of the spectrum of values attached to semantical attachments is less value more value higher value ---------------------------------------------------------------------- AMS Wolfram OpenMath Elsevier MINSE This says nothing about what 'less', 'more', and 'higher' come to. It also does *not* say that people in the groups mentioned lack understanding of the views of others. Neil and Steve from Wolfram have gone to some length to argue against some forms of semantics which I think no one on this list has pushed. Ping has indicated a strong interest in driving the various renderings from a disambiguated notation. I discussed what full semantics might mean, not to suggest doing it, but only to give it legitimacy. Bob has lobbied for the mere capability of including independently determined semantics within the HTML-Math notation. Bob's argument is for a tangent (or orthogonal --- the image is one of rooted intersection at a single point) semantics, not that our ERB has to define the semantics. With this in mind, I'd like to return to the matter of the goals of HTML-Math and how best to achieve them. The goals involve devising a notation (or a class of notations) each of which can be used for a variety of renderings (visual, audio, CAS, ...). The exactness with which these targets can be hit is very much under discussion. Standard TeX (and ISO 12083 and other forms of) visual markup allows at least two forms of ambiguity: (a) operator overload, and (b) unspecified expression structure. The Wolfram and MINSE approaches require that authors be much more careful about avoiding (b). MINSE asks that authors introduce new vocabulary to solve (a). The Wolfram proposal allows for 'macros' which disambiguate (much like the MINSE solution) and 'template-matching' which allows for late semantical binding and context-sensitive maps. Bob has indicated a desire to allow type- and context-information to be associated with notational objects. MINSE allows this underneath the surface-level notation (along with display and other rendering characteristics). The WP allows it, I believe, in the macro and template-matching specifications. I asked in a previous posting whether such information might be specified "on the fly" within the notation itself (perhaps no one sees a need to do so. -- If an object's name is unambiguous, type characteristics can be handled externally; otherwise the object will fit (WP assumes) a template which points to it uniquely and the type characteristics can be associated with that template.). To focus then: 1. Do we have objections to allowing for specification of externally defined information within our notational system? This could be semantics or other values associated with the 'objects' of our standard. 2. Must that specification (if permissible) lie beyond the surface-level mathematical notation we allow or can it be embedded directly within the mathematical notation? -RonReceived on Friday, 23 August 1996 15:57:58 UTC
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