One can describe hypertext documents as families of interlinked texts. One
can take each text and decompose (parse) it into sub-texts. I presume context
to have provided meaning for various forms of sub-text (ultimately depending on
the syntax and semantics of the language of the text, in the present case
English; but potentially layering some more precise terminology on it); I
presume that meaning to provide a framework for discussing values
(entities potentially external to the text) and statements (a.k.a. assertions)
about values
; I presume that one can thereby formalise discussion of
relations among values; the context of my own mathematical web pages takes
relations themselves as a flavour of value, only indirectly discussing any other
kind of value, and my plaintext denotations provide means of expression for
relations and tools to manipulate them and, via them, any other values a
discourse, using these denotations, may chose to introduce.
Two parts of the semantics of a text are particularly pertinent: the text
may make an assertion; the text may stand for
a value. I do not define
any denotations which do neither; and see no reason why a given text need not do
both. Assertions add directly to what the text means. Values are generally
anything context choses to describe as such, in so far as context provides a
means for a text to stand for
(a.k.a. denote) the value. An
expression
or denotation
is a text which stands for a value,
optionally also making some assertions.
A denotation's value may be ambiguous (though its semantics won't be, other
than via its value): a square root of 4
may stand for either 2
or
-2
, as indeed may either 2 or -2
.
Assertions made by the denotations (subject to consistent binding of each name
to the same value throughout each sub-text whose context does not provide it
with a value for the given name)
will concern themselves
with
Substituting values for their denotations thus
(potentially) leads to a family of meanings for each text, parameterised by the
values of the various ambiguous sub-texts. Indeed, a simple name, used to
denote a value, denotes an arbitrary value; its appearance as a sub-text may
involve it being the subject of some assertions, so that the text in which it
appears only sees those values for the name as are consistent with its context.