[seqfan] Re: Linked Open Data (LOD) and the OEIS
Antti Karttunen
antti.karttunen at gmail.com
Fri Mar 16 20:00:47 CET 2012
Interesting suggestion below by Marc.
Just a couple of questions:
I guess it is possible to have also ternary relations between sequences, e.g.
Axxxxxx --is_a_convolution_of--> Ayyyyyy, Azzzzzz
or:
Axxxxxx --is_a_composition_of--> Ayyyyyy, Azzzzzz
(this latter meaning something like Axxxxxx(n) = Ayyyyyy(Azzzzzz(n)) )
or:
Axxxxxx --is_a_conjugate_of_conjugated_by_a_sequence--> Ayyyyyy, Azzzzzz
(meaning: Axxxxxx = Azzzzzz^-1(Ayyyyyy(Azzzzzz(n))),
where Azzzzzz^-1 is found via --is_inverse_of--> link,
and of course, Azzzzzz doesn't necessarily need to be unique)
?
Another questions: How to record conjectural information? With
separate keywords, e.g. as:
Axxxxxx --is_conjectured_to_be_Moebius_transform_of--> Ayyyyyy
Axxxxxx --is_conjectured_to_be_a_conjugate_of_Y_conjugated_by_some_unknown_sequence--
Ayyyyyy
(meaning: Axxxxxx = Azzzzzz^-1(Ayyyyyy(Azzzzzz(n))) for some Azzzzzz,
but where no Azzzzzz
is currently known. Also, I guess there might be cases where this can
be proved (existentially),
but still not a single Azzzzzz can be easily found.)
and how is this piece of information to be replaced, when the conjecture
is either refuted or proved?
With another such an item, like
Axxxxxx --is_proved_to_be_Moebius_transform_of--> Ayyyyyy
or
Axxxxxx --is_refuted_to_be_Moebius_transform_of--> Ayyyyyy
which will have a priority over --is_conjectured_to_be...--> type
keyword?
That is, how the system is specified/expected to manage knowledge
whose veracity status might change in the future?
(Also, because of say, a changing starting offset, e.g.:
Axxxxxx --is_Moebius_transform_of--> Ayyyyyy
which then has to be changed to:
Axxxxxx --is_Moebius_transform_of_left_shifted--> Ayyyyyy
if Ayyyyyy's starting offset grows by one, and what is
then the inverse of this relation?)
But, if done well, then there could be a possibility for
automatic generation of code, starting from simple definitions
with machine-readable formulae (e.g. some non-proprietary
mathematical or declarative programming language/notation),
together with an extensive web of such relations.
Just my two cents,
Antti Karttunen
On Thu, Mar 1, 2012 at 11:31 PM, <seqfan-request at list.seqfan.eu> wrote:
>
> Message: 6
> Date: Thu, 01 Mar 2012 10:08:02 -0800
> From: Marc LeBrun <mlb at well.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Linked Open Data (LOD) and the OEIS
> Message-ID: <CB74FB02.A6C9%mlb at well.com>
> Content-Type: text/plain; charset="US-ASCII"
>
> I was reminded again recently that the OEIS would be an ideal database to
> contribute to the world's knowledge in the form of "Linked Open Data" (LOD).
>
> You can easily find more about LOD by searching the web; an introduction is
> here: http://en.wikipedia.org/wiki/Linked_data
>
> Briefly, LOD is a foundation for the "semantic web", and is actively being
> advocated by Tim Berners-Lee, the W3C and others.
>
> Wikipedia notes the LOD available on the web grew from 2 billion triples in
> 2009 to 31 billion in 2011. There are many domains represented, including
> medicine, law, media, science and others. The OEIS would be a natural fit.
>
> There are powerful technologies available for using LOD and more will be
> coming. These would complement the OEIS "native" mathematical strengths
> (such as lookup and superseeker) to help address all the OTHER valuable
> "metadata" that is included in each entry.
>
> Some amazing applications have already been built federating data from
> different domains. For example crossing pharmaceutical info and medical
> research. The OEIS would naturally federate with things like publication
> citation databases, and so on.
>
> LOD is a hot topic these days, and I believe the OEISF could perhaps even
> get some support to help it join the semantic web community.
>
> Of course many of us are very busy, but I think this is an exciting idea, so
> if you are personally interested in pursuing LOD for the OEIS further please
> let me know (off list) and maybe we can figure out a good way to collaborate
> on it somehow...
>
> --MLB
>
>
> ========
>
> To make this more concrete and relevant here's a brief description of what
> LOD would be like from the perspective of the OEIS:
>
> The basis of LOD is to reference everything with HTTP URIs. Of course all
> the OEIS entries are already identified in this way. For example A007317,
> "Binomial transform of Catalan numbers", has the URL
> http://oeis.org/A007317 and so forth.
>
> Building on that URI foundation, all other knowledge is represented as
> triples (implemented in RDF) that describe relationships between entities.
>
> For example some (informal) triples related to A007317 would include:
>
> A007317 --hasName--> "Binomial transform of Catalan numbers"
>
> A007317 --binomialTransform--> A000108
>
> A000108 --isCalled--> "Catalan numbers"
>
> A000108 --isCalled--> "Segner numbers"
>
> Similarly other entities can be ID'd, say http://oeis.org/user/Marc+LeBrun
> and used (eg in "hasAuthor" triples), related to eachother and so on.
>
> The triple "schema" is itself also represented as triples, and thus is used
> to provide an ontology of the domain:
>
> binomialTransform --hasInverse--> inverseBinomialTransform
>
> This allows automatic reasoners to make useful deductions like
>
> A000108 --inverseBinomialTransform--> A007317
>
> and many more complicated inferences, removing the need to explicitly
> represent them in the database itself.
>
> By use of namespaces any number of ontologies can be used together, which
> enables sharing existing standard ontologies. Only truly OEIS-oriented
> relationships would need to be modeled.
>
> This work seems like it could qualify as fundable research that would
> produce a valuable public resource.
>
>
>
>
> ------------------------------
>
> Message: 7
> Date: Thu, 01 Mar 2012 10:17:29 -0800
> From: Marc LeBrun <mlb at well.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Linked Open Data (LOD) and the OEIS -- DBpedia
> Message-ID: <CB74FD39.A6CE%mlb at well.com>
> Content-Type: text/plain; charset="US-ASCII"
>
> I forgot to mention that Wikipedia itself is being represented as an LOD
> knowledge base called DBpedia. There are thus many interesting potential
> collaborators that could help the OEIS.
>
>
>
>
> ------------------------------
>
> Message: 8
> Date: Thu, 1 Mar 2012 13:18:32 -0500
> From: Neil Sloane <njasloane at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: Linked Open Data (LOD) and the OEIS
> Message-ID:
> <CAAOnSgT31PgXdPk5Q3NaYwUVkP_YsNMKtTrHt=q3gxb9H7_GZQ at mail.gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1
>
> Marc, That's an interesting suggestion.
>
> The obvious questions are,
> how much would it cost to hire someone to do this,
> and
> who would we pay to do it?
>
> I think if we can answer these two questions then we might well
> be able to find the money.
>
> Neil
>
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