SUO: 15 May 2002 -- Abstract Syntax & Set Theory
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Abstract Syntax
I have noticed people increasingly bandying about
the words "abstract syntax", for instance in the
Conceptual Graph Standard (Working Draft):
http://www.jfsowa.com/cg/cgstand.htm
Also in the CLog papers (sorry, but the identifier "CL" has
long been pre-empted by the subject of "Combinatory Logic"):
| Well, maybe we have different understandings of the notion of an
| abstract syntax. The way I understand it, an abstract syntax is
| a specification of a general abstract structure that can have many
| instances. Thus, I view the abstract syntax as analogous to the
| definition of a boolean algebra, e.g., a BA is a set A on which are
| defined binary operations + and x that satisfy the laws of idempotence,
| commutativity, associativity, absorption, mutual distributivity, a unary
| complementation operator ~ and such that A contains a maximal element 1
| and a minimal element 0 satisfying the usual stuff. This is not picking
| out any particular BA, it is just describing the structure common to all
| of them. In the same way, the abstract syntax for CL doesn't describe
| a particular language, but rather the structure common to all of them --
| any CL language must have a lexicon, there must be a one-to-one
| operation App that generates the set of terms of the language,
| a set of operations that generates the formulas, etc.
|
| Chris Menzel -- http://philebus.tamu.edu/pipermail/kif/2002-May/001128.html
This appears to be a poorly labelled repackaging
of a standard subject in formal language theory --
twenty years ago it was commonly referred to as
"Allied Families of Language" (AFL's), but I'm
sure the name has changed six times since then.
At any rate, an AFL by any other name is just
a category of formal languages, in other words,
a category whose objects are formal languages
and whose arrows are morphisms between them.
I think that this probably puts us outside
the the ballpark of the Boys of FOL.
Set Theory
I have opened an information booth on basic set theory.
There is nothing really here yet, but I am hopeful that
if I build it, y'all will come.
01. http://suo.ieee.org/ontology/msg04082.html
02. http://suo.ieee.org/ontology/msg04083.html
03. http://suo.ieee.org/ontology/msg04084.html
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