Pat, (01)
I have no complaints about the IKL model theory, which I
have found sufficient to support what I want to do. (02)
Re contexts: I agree that the word has been used in many
confusing ways. My definition is very simple and formal:
in CGs, a context is a concept box that contains a nested
conceptual graph. (03)
Since concept nodes have type labels (the absence of a type
label defaults to an untyped node that can accommodate any
referent of any type), the type label of the context serves
to "coerce" the interpretation of the nested CG: (04)
1. If the type label is CG, the nested graph is a literal,
which is effectively quoted by an ordinary quote. (05)
2. If the type label is Proposition, the nested CG states
the proposition (which I map to an IKL proposition). (06)
3. If the type label is anything else, the nested CG
states a proposition that describes some entity
of the given type. (07)
So far, I have not found any common use of the word 'context'
that cannot be mapped to one of these three options. If the
context is some linguistic expression, it maps to a proposition.
If it is some nonlinguistic situation or whatever, it maps to
a concept of the appropriate type that is described by a CG. (08)
Some comments on selections from your note: (09)
PH> I too [like Quine] find modal logics essentially meaningless,
> I don't believe in possibilia (how many possible men are standing
> in an empty doorway?) (010)
I don't blame you (or Quine) for not believing in possibilia, but
we constantly use modal talk in ordinary language, and I believe
it is a legitimate object for further analysis and clarification. (011)
One reason why I prefer Dunn's semantics to Kripke's semantics
is that Dunn makes the laws that define any modality explicit.
Whenever people say "you must ...", they implicitly intend
some law(s) that determine why you must. Those laws could be
laws of logic, physics, economics (i.e., financial limitations),
engineering (i.e., practical limitations), governments, or even
your mommy (as in "because I told you to"). Anything implied
by the laws is necessary (or obligatory, according to the mode),
and anything consistent with the laws is possible. (012)
This provides a very clear explanation of modality, which is
completely formal and compatible with ordinary language. (013)
PH> I think that natural language - *real* natural language, not
> the prissified academic stuff that philosophers write and read
> to one another - is beyond the pale of any attempt to formalize
> its actual meanings. About half the stuff we say to one another
> isn't even intended to convey meaning: its more like a kind of
> verbal grooming. But in any case, I also think, purely now as
> a matter of engineering, that to confuse natural language with
> ontological formalisms is a serious methodological blunder. (014)
I agree. I blame Montague for some of the worst excesses, which
followed from his claim "I reject the contention that an important
theoretical difference exists between formal and natural languages"
(published in "English as a Formal Language", 1970). (015)
In the early 1970s, when I read Montague's papers, I was impressed
by the technical virtuosity, but I couldn't believe that anything
remotely similar to that could serve as the foundation for NLs. (016)
JFS>> ... the semantics of NLs, for which many people would like
>> to use IKL. (017)
PH> Hmm. News to me. It wasn't designed with that purpose in mind,
> for sure. (018)
But that was one of the requirements laid down by people like
Jerry Hobbs, etc. Lenat had always said that he wanted to use CycL
to represent NL semantics (or whatever he extracted from NL), and
he said that the CG contexts were more suitable for that purpose
than CL. But he (and the other CycLers) agreed that they could
use IKL to represent CycL. (019)
PH> I really don't think we need to be this fussy about terminology.
> IKL is a formal logic, and without the proposition names it really
> is just common logic, which is FOL written in an unusually slack
> syntax. (020)
I agree, but that point about propositions is the thin opening wedge
that pries open the floodgates to an enormous range of options. When
I had been working with Genesereth to develop ANSI standards for KIF
and CGs, I mapped CG contexts to KIF statements in "backquotes". I
regard IKL propositions as a nicer notation for KIF backquotes (which
very few people ever understood or used). (021)
PH> So any discussion of propositions in English is really beside
> the point for IKL: it does not set out to capture all propositions
> expressible in English (a tensed, modal, indexical, elliptical
> language which evolved to convey speech acts in a social context)... (022)
You can ignore them if you like, but IKL gives me the mechanisms to
define the kinds of things I was doing in the following two papers: (023)
http://www.jfsowa.com/pubs/laws.htm
Laws, Facts, and Contexts (024)
http://www.jfsowa.com/pubs/worlds.pdf
Worlds, Models, and Descriptions (025)
PH> And strictly speaking, there is no notion in IKL of a proposition
> being 'inside' a context, or of contexts being 'nested'. (026)
As I said, I use the word 'context' for CG boxes that contain other
CGs -- and I map those boxes to IKL that-clauses. The CG boxes
can be nested in the same way as IKL that-clauses. That is all I
need to define the structures I want to define. (027)
John (028)
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