## On Measures and Messages

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• Hello Vaughan, the task of defining a measure for rationals still keeps me busy, because the meaning is getting more general than I had initially thought of.
Message 1 of 4 , Feb 14, 2009
Hello Vaughan,
the task of defining a measure for rationals still keeps me busy,
because the meaning is getting more general than I had initially
thought of. Have you, has anyone on this list, ever thought/read of a
measure for (scientific) knowledge? I wonder, how such a space could
look like and if we are/would be able to measure it ...
Jens

--- in December Vaughan Pratt wrote:
> ...
> For any vector space V over any extension K
> of Q, just give V the weakest topology for which addition (in each
> argument separately) and multiplication by the scalars of K are
> continuous. V can then be reduced to a vector space V' over any
> subfield K' of K by forgetting those scalar multipliers in K'\K.
>...
• On Saturday 14 February 2009 21:31:28 Jens Doll wrote: the task of defining a measure for rationals still keeps me busy, because the meaning is getting
Message 2 of 4 , Feb 16, 2009
On Saturday 14 February 2009 21:31:28 Jens Doll wrote:
> the task of defining a measure for rationals still keeps me busy,
> because the meaning is getting more general than I had initially
> thought of. Have you, has anyone on this list, ever thought/read of a
> measure for (scientific) knowledge? I wonder, how such a space could
> look like and if we are/would be able to measure it ...

If you can describe the context in more detail, then I can try to suggest
something. The subject is quite big and it is usually a good idea to study
enough philosophy.

Many approaches will start from modal logic. That is almost compulsory if you
want to deal with knowledge representation. Again you will need to pay
attention to the philosophical motivations behind modal logic. If you are good
in duality or canonical models, then you can always use them.

Rough sets can be used for defining relative measures of scientific knowledge.
See Pawlak's book or other tutorials/books for the basics. There are
connections with concept lattices.
But what is your concept of scientific knowledge?

Belief revision is closely connected with non-monotonic reasoning and logics.
It can be used for decision making, but I do not know of any good application
to 'measure scientific knowledge'.

Best

A. Mani

--
A. Mani
Member, Cal. Math. Soc

Send instant messages to your online friends http://in.messenger.yahoo.com
• Thank you for this firework of imaginations. I am now aware of the different types of logic, which scientific disciplines use. There seems to be only one
Message 3 of 4 , Feb 17, 2009
Thank you for this firework of imaginations. I am now aware of the
different types of logic, which scientific disciplines use. There
seems to be only one widely used measure : lop=lines of publication.
Maybe a different and generally accepted one can be found by search
engines.
Jens
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