>>>>>For example, you may have two contexts c1 and c2 such that (= (tnb
>>>>>'name') name) evaluates to true in both of them
>>>>
>>>>That is meaningless in IKL. Contexts are objects in the domain,
>>>>not entities in which sentences are evaluated. You are talking
>>>>'context logic' style. IMO context logic is a dead end. One of
>>>>John McCarthy's rare blunders.
>>>
>>>I was thinking about syntactic contexts, syntactic closures, as
>>>first-class objects.
>>
>>Well, Im not sure what you mean by this terminology. The word
>>"context" is, unfortunately, very dependent on the context for its
>>meaning. It sounds as though you mean the scope of a syntactic
>>binder such as a quantifier, is that correct?
>
>Not necessarily a quantifier. Perhaps mislead by the syntactic
>similarity of IKL (and KIF, for that matter), I was thinking in
>terms of LISP (Scheme, for that matter). Then, a syntactic binder
>is not necessarily a quantifier, as in a do-loop, it can be a lambda
>expression, or the syntactic sugar let:
>
>(let ((x 1))
> (= (tnb 'x') x))
>(let ((x 2))
> (= (tnb 'x') x))
>
>=> true
>=> true
>
>though 'x' does not denote the same object in the whole scope. (01)
That is what I meant, yes. But in normal assertional logic, the
quantifiers are the only such name-binding operators. Of course all
these languages can be rendered down into functors applied to a
single binder, usually lambda. (02)
BUt contexts in context logic play a rather different role: in
particular, there is no explicit name binding syntax, only the notion
that a name may (or may not) denote differently when asserted
relative to a context. Contextual assertion is more like inclusion
inside a modal operator than being in a syntactic binding scope.
>
>I am not quite familiar with IKL, and it seems that you do not have
>such syntactic scoping there. (03)
Only the usual quantifiers, yes. (04)
>>> Within each closure, clearly, 'x' (a name) means x (the
>>>denotation of 'x' in that context).
>>
>>In IKL, every *use* of a name, anywhere in the language, means the
>>same thing. There is no idea of a use of a name 'within' anything.
>>Hence the entire language is referentially transparent.
>
>You can have referential transparence with lexical scoping. The
>point is not to have dynamic scoping. A purely functional language
>is referentially transparent, though names have meanings dependent
>on the context (the environment). (05)
Free names do not, though. In context logic, even free names may
change their contextual referents. (06)
>
>'Referential transparence' may be an ambiguous term.
>
>>
>>> Across closures, though, the meaning of 'x' may be different.
>>>
>>>In this sense, your (tnb name context) is equivalent to looking up
>>>the specified closure for the name's entry, and (tnb name) is
>>>implicitly using the closest closure
>>
>>Hmm, I have no idea what 'closest' could mean.
>
>Another import from lisp. Inessential here.
>
>>
>>>(do you allow hierarchically nested contexts?)
>>
>>Contexts have whatever structure ones axioms describe them to have.
>>They are simply entities in the domain of discourse, and have no
>>particular logical role.
>
>Since we were talking about an artificial language which has to have
>some means for binding identifiers with semantic objects, I was
>thinking of a context as of an environment, which provides bindings
>for identifiers. In lisp (scheme, at least), environments are
>hierarchical, and the referent of an identifier is looked up in the
>current environment of the computation, if not found there, there in
>the next enclosing environment, and so on, until the global one, if
>needed.
>
>Apparently in IKL contexts are whatever one wishes them to be. I
>guess my dog might be a context in IKL, it seems. Do you have any
>definition of context there? (07)
No definition, no. Following McCarthy, we say that context is
whatever satisfies ones axioms which purport to describe contexts.
Yes, your dog could be a context, for example for a learned
discussion between two veterinary surgeons, where one says "the liver
appears to be inflamed" , meaning (but without explicitly saying) the
liver *of this dog we are looking at*. McCarthys example is a surgeon
saying to his assistant, "scalpel", with the contextual meaning,
"Pass me the scalpel that I need at this point, by putting it, handle
first, into my outstretched hand." (08)
>>>Whatever the relation to McCarthy's dead idea, let it be.
>>
>>McCarthy is widely credited with the idea of introducing contexts to logic.
>>
>>>
>>>>
>>>>>, 'name' as in c1 =
>>>>>'name' as in c2 (trivially), yet name as in c1 != name as in c2.
>>>>
>>>>In IKL:
>>>>(not (= (tnb s context1) (tnb s context2)))
>>>>
>>>>where s is 'name'. Indeed, this situation can arise. But there
>>>>are types of 'context', such as times and locations - parts of
>>>>the 'real world' - which do not affect the meanings of names. In
>>>>IKL these can be defined axiomatically:
>>>>
>>>>(forall (x) (iff (transparentContext x)
>>>> (forall ((s charseq))(= (tnb s)(tnb s x)))
>>>>))
>>>
>>>Yes, if (tnb s) is equivalent to (tnb s the-global-context), with
>>>the-global-context being the global context
>>
>>Well, there is no global context as such in IKL, any more than
>>there is in, say, first-order logic.
>
>OK. Then what does (tnb s) actually mean? (09)
Remember s is a character string. It means, whatever that string
would denote, if you were to use it as a name. In fact, the 'tnb' is
unnecessary: it is sufficient to simply call the string as a function
with no arguments: (s) (010)
> And what does (tnb s x) actually mean? (011)
That has no predefined logical meaning, but you can use the form to
assign a meaning to it by writing appropriate axioms. You have to do
this for contextual meanings anyway: there is no *logical* reason why
they should mean anything in particular or that it should be related
in any systematic way to their simple (non-contextual) meaning. (012)
> (I guess I'd better consult the documentation.) (013)
http://www.ihmc.us:16080/users/phayes/IKL/GUIDE/guide.html (014)
Pat
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