Chris (01)
I don't have all the answers at this point, but I want to discuss
a few things, to try and establish some understanding between
us. (02)
Starting with (b), just because it's easier. mKR has
if-then-else-fi iff implies
and or not
quantifiers: no a any the some all every
for quantifier loops similar to many logic languages
I don't know why you say mKR is completely lacking
the apparatus of propositional and first-order logic. (03)
In regard to (a), primitives such as "action", "context", "part",
"attribute", "relation", "time" are axiomatic concepts upon
which all other concepts depend. They are dependent upon
each other. I have given terse genus-differentia definitions of
each. For example
attribute is characteristic with single entity, non-separable;
action is characteristic with single entity, non-separable, space, time.
part is characteristic with single entity, separable;
relation is characteristic with multiple entity;
My model of an action is something that takes place in an interval of
(real number) space, time, but I allow space, time measurements
to be real or discrete. (04)
mKR is English-like, but it is formal, precise and unambiguous.
The simplest mKR proposition has the form
at space=s, time=t, view=v { sentence };
v names a list of propositions (the context) which disambiguates
the sentence. s,t name the sub-context associated with the changes
of an action. Genus-differentia definitions are used to make terms
precise. Sentence structure is governed by a formal grammar. (05)
In effect, mKR starts with a "Simple English" language -- no word
variations for number, tense, etc. -- and prefixes every sentence with
the context which disambiguates it. (06)
Dick McCullough
Ayn Rand do speak od mKR done;
mKE do enhance od Real Intelligence done;
knowledge := man do identify od existent done;
knowledge haspart proposition list;
http://mKRmKE.org/ (07)
----- Original Message -----
From: "Christopher Menzel" <cmenzel@xxxxxxxx>
To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Friday, September 12, 2008 4:53 PM
Subject: Re: [ontolog-forum] mKR (was Thing and Class) (08)
> On Sep 12, 2008, at 6:04 PM, Richard H. McCullough wrote:
>> Chris
>>
>> I would appreciate some pointers on how to do that. The things that
>> I have read say that a formal semantics maps the "meaningless"
>> symbols of formal logic to the "meaningful" symbols of English.
>
> No, that is nothing like a formal semantics; that is at best an
> informal semantics, which is generally pretty useless for the central
> purposes of KR. The point of a formal semantics is (a) to provide
> interpretations of the non-logical primitives of a language and (b)
> to provide a *systematic* account of how the meanings of complex
> expressions in a language are determined by the meanings assigned to
> their component parts. This, in particular, is what is missing from
> mKR.
>
> (b) has to do primarily with the interpreting the logical components
> of your language -- boolean operators, modal operators, quantifiers,
> etc. You can learn about this in any good text on mathematical
> logic. (And just note: It appears to me that your language is
> completely lacking the apparatus of propositional and first-order
> logic. These are essential to any modern KR language.)
>
> In regard to (a), many of your important non-logical primitives --
> e.g., "action", "context", "part", "attribute", "relation", "time",
> etc -- are left utterly uninterpreted. Try replacing them with "foo,
> bar, baz, etc" and you get an idea of how useful your language is for
> KR. The notions above are ambiguous and difficult. They need to be
> nailed down by a semantics that fixes (as far as possible) their
> properties and the logical connections. For instance, what is the
> relation between "action" and "time"? Intuitively, the two are
> *intimately* connected. A good formal semantics will do that: for
> example, it might represent time as the real line and will map each
> action to an interval. Alternatively, if one has ≠ discrete
> processes in mind, a semantics might represent time by the integers
> and assign to each action a start point and a (later) endpoint.
> Again, what is an attribute? Can you combine different attributes
> like "red" and "smooth" into a single attribute? A good semantics
> will represent attributes as functions of some ilk, or as objects with
> extensions, or perhaps extensions at possible worlds, or whatever.
> But however, it is done, it will be perfectly clear what you do and do
> not mean by "attribute". See the idea? You might have a look at the
> NIST Process Specification Language for a good example of a language
> whose non-logical primitives are rigorously interpreted in a formal
> semantics, and how those interpretations are reflected in the PSL
> axioms. Or, for that matter, have a look at the model theory for RDF
> and OWL on the W3C web site.
>
>> But mKR propositions are paraphrases of English. mKR is composed of
>> English words and phrases, not "meaningless" symbols of formal logic.
>
> But the symbols of formal logic are not meaningless *at all*. They
> are given very rigorous interpretations in any standard semantics
> (a.k.a model theory) for a given formal language -- of which any
> useful KR language is a species.
>
>> I haven't seen any formal semantics for English.
>
> Sure thing, but neither is English anything like a KR language; indeed
> it is the very opposite of a KR language. It is informal, imprecise,
> fraught with ambiguity, and impossible for computers to process
> (without severe restrictions). It is WHY we have KR languages; it is
> WHY we build ontologies. KR exists precisely because you can't rely
> on informal, intuitive understandings of English when you want to
> share and process information, and use computers to aid significantly
> in the process.
>
> -chris
>
>
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