Types vs. Sorts in HPSG

[Carl Pollard]

Hi Mark,

Just a couple of brief comments on the points you make.

> > To me "type" and "sort" are synonyms, at least in the context
> > of feature structures.
> >
> > Carl
>
> "Type" and "sort" are often used as synonyms, but I think that it
> makes sense to distinguish them the way that some logicans do:
>
> "sort" refers to a semantic distinction, where the objects that the
> language describes are segregated into several kinds or sorts.
>
> "type" refers to a syntactic distinction, where expressions from
> the language are separated into different categories or types.

Usage isn't uniform about this. Many authors use the term "sorted
logic" as a synonym for "typed logic" (in the sense that, say,
a given variable has a type/sort associated with it). Conversely,
"type" is often used semantically, e.g. Wand 1983 ("A types-as-sets
semantics for Milner-style polyomorphism") or Scott 1976 ("Data types
as lattices").

> I think the standard view about feature structures is that the
> relevant distinction is semantic.  Following the terminological
> suggestion I just made, we'd say that the objects are sorted, but that
> the description language is untyped.  Indeed, descriptions in which
> type clashes occur are not viewed as having violated the syntax of
> descriptions (which is what they would be if they were ill-typed),
> rather they just denote the empty set.  (Lots of other systems are
> formulated this way; e.g. LISP, which is sorted but untyped).

Exactly right. This is the same point I made in my followup note
to Lutz about not seeing why one would want to think of the
description language as sorted (or, in Mark's terminology, typed).
Another way to think of it is that when certain sentences in the
description language are interpreted as constraints, they IMPOSE
the typing (Mark's sorting) on the feature structures, e.g.


              noun => CASE:(nom or acc)

interpreted as a constraint means that any "grammatical" feature
structure (i.e. one that satisfies all the constraints of the grammar)
must have a CASE edge whose end node is labelled either nom or acc
if its start node is labelled noun; but the contradictory description

              noun and not (CASE = CASE)

is syntactically well formed, it just doesn't have any grammatical
satisfiers.

> However, to aid the development and maintainance of large grammars I
> think it _would_ make sense to impose type constraints.  If the
> grammar contains certain obvious type clashes, then I think it would
> be useful for the grammar development environment to identify these to
> the grammar writers as syntactic errors (the way a compiler does),
> rather than just silently fail!

Sounds reasonable to me, but some people (e.g. Martin Kay) object to
this idea quite virulently, for reasons which are not clear to me.
Mark, maybe you know the reason?

Carl