Re: New avenues for research - integrating CT, HoTT, RDF, SQL, SPARQL, Scala, ... was: The Joy of NULLs

Hi. Not being a mathematician, nor even having the logics and category
theory background deserved to the level of this discussions (I'm just a
developer), I dare to ask here if a problem: ontology matching and systems
integration could be addressed using RDF and (my bare notion) of Monads. My
"intuition" tell me yes.

This is part of a series of statements from a fuzzy scrapbook of ideas I'm
working on with spare toughts regarding the serialization in SW RDF Quads
of a hierarchical / functional layered meta model of knowledge.

Please you, having stronger theoretical foundations, be patient if you'd
like to skim through this lines. My attempt is, if you find with your
knowledge something remotely familiar or coherent, to know if implementing
something like this is something remotely viable:

Inputs: RDF Statements, aggregated into a series of layers (category
contexts) from aligned / matched resources (URIs) to a Dimensional
knowledge layer.

Context hierarchies: categories of wrapped subject occurrences. Statement
Context monad (category) for Subject occurrences (layers).

Context category instance identity: Employee Kind, Work Behavior, etc.
Context statement attribute / value aggregation. Key / value abstraction
scoped in category type / instance.

Functors: Layers (Context categories) aggregation / transforms. Navigation
/ CRUD between layers. Augmentations.

Augmentations: Categories Aggregation (types), Alignment (contexts),
Activation (roles in interactions).


(I'd like to have "generic" algorithms for what I call "augmentations"
transforms: type / layer aggregation, attribute / values alignment /
inferences and context occurrence activation roles)

Locators (keys): (metaclass, class, instance, occurrence);

Metaclass: Transform OntResource

Class: Message Augmentation

Instance: Statement Role

Occurrence: Flow Kind

Locators (keys): local / remote keys. Navigation. Paths. Legends.
Signatures (streams).

Monadic  (locators / signature streams based) category wrappers Functors:

M<T>::flatMap(functor(T) : U) : M<U>;

T: layers nested categories (T<V>, etc.).

Dado rango y alcance, universo: U de una relación R, inferir dominio y
codominio, campo: C.

From Object (O) extension /instances to Context (C) intension / class.

Aggregation (types) functor signatures: stream.

Alignment (contexts) functor signatures: stream.

Activation (roles / matching in interactions) functor signatures: stream.

Encoding. RDF Quads. Model layers:

URIResource context: CSPO form. RESTful / HAL monad: HTTP category functors..

OntResource context: Resource, Occurrence, Attribute, Value form. Aligned
(matched) URIResource(s).

Resource context: OntResource (aligned / matched URIResources) occurrences
in reified Role in Statement.


Meta Model Quads layers:

(URIResource, URIResource, URIResource, URIResource);

(OntResource, URIResource, URIResource, URIResource);

Aggregated URIResource OntResource attributes / values (recursion to
attributes / values OntResource).

(Transform, OntResource, URIResource, URIResource);

(Mapping, Transform, OntResource, URIResource);

(Template, Mapping, Transform, OntResource);

(Augmentation, Template, Mapping, Transform);

Functor "applications".

(Message, Augmentation, Template, Mapping);

Functor "declarations".

(Context, Message, Augmentation, Template);

Model.

(Resource, Context, Message, Augmentation);

(Role, Resource, Context, Message);

Reified CSPO / Resource, Occurrence, Attribute, Value Resource role types
in Resource occurrence / context.

(Statement, Role, Resource, Context);

(Entity, Statement, Role, Resource);

Aggregated "subject" occurrences of Resource in Role in Statement(s).

(Class, Entity, Statement, Role);

Aggregated Entity Class occurrences type (attributes).

(Kind, Class, Entity, Statement);

Aggregated kinds / roles ("interfaces") of Class occurrences.

(Flow, Kind, Class, Entity);

Action "instance". Entity of Class performs role (Kind) of Behavior Flow.

(Behavior, Flow, Class, Kind);

Action "class". Statements: propositions, prescriptions, rules,
productions. DCI / Link Grammar. Context satisfaction (rules).

(Measure, Behavior, Flow, Class);

(Unit, Measure, Behavior, Flow);

(Dimension, Unit, Measure, Behavior);

Order.


I apologize but I lack the ability to express this more formally. Although
my only "scope" is to enable databases and services to interact with each
other, the scope of this meta model is to enable translation between
ontologies. Later I'll try to find how build "Adapters" for whichever
plugged backend "Context" (models) will be necessary.


Regards,

Sebastián.

http://snxama.blogspot.com



On Sat, Aug 31, 2019, 6:51 AM Henry Story <henry.story@bblfish.net> wrote:

> This thread which started on the topic of NULL, has grown to touch
> a large  number of fields of contemporary mathematics, database theory
> and programming languages. As Ryan below is looking for people interested
> in integrating these with semweb, and as it is likely that some who
> may be interested won’t have noticed, I have changed the title.
>
> > On 29 Aug 2019, at 18:47, Ryan Wisnesky <ryan@conexus.ai> wrote:
> >
> > Hi all,
> >
> > QINL is simply the name we gave to a common phenomenon in dependent type
> theories, which is that you can usefully represent sets as dependent types,
> instead of as terms.  That has both positive and negative implications.
> It's possible that Dotty's (upcoming Scala's) type system may support QINL,
> and similarly for Dependent Haskell.  Once you represent sets as dependent
> types, you can e.g. manipulate them using Coq tactics:
> https://www.wisnesky.net/dbpl15.pdf ("Using Dependent Types and Tactics
> to Enable Semantic Optimization of Language-Integrated Queries") and
> https://homes.cs.washington.edu/~chushumo/files/cosette_pldi17.pdf
> ("Homotopy Type Theory SQL: Proving Query Rewrites with Univalent SQL
> Semantics").  Although both QINL and LINQ are most naturally described
> using category theory, conceptually they are about how collections are
> represented in type theory.
> >
> > In our work on the categorical query language CQL (
> http://categoricaldata.net), our notion of schema includes
> equationally-defined constraints, sufficient to encode arbitrary behavior
> as functional programs (e.g., there is a CQL schema for SK combinatory
> logic).  This is enabled by CQL's underlying categorical semantics and can
> be implemented in QINL style, although there's no need to do so.
> >
> > Henry alluded to the status of blank nodes in RDF, a question answered
> using the language of category theory in the Ph.D. thesis of Braatz :
> https://pdfs.semanticscholar.org/b8c8/5a3e7a04020259ec9a58c7e5563033f52844.pdf
> , presumably in a way equivalent to their intended set-theoretic
> semantics.  That thesis also contains a variety of constructions on RDF
> graphs such as "pushouts" that may or may not be known or useful to the RDF
> community, but whose analogs in other data models are known to be useful
> for data integration.  So I wanted to take this opportunity to ask around
> to see if anyone was interested in further investigating categorical
> constructions for RDF.
>
> I am! :-)
>
> One very intriguing thing about Category Theory is how clearly it
> articulates dualities.
>
> For example the above work is algebraic: algebraic databases, RDF
> described algebraically
> by Braatz as inference morphisms between graphs, etc…
>
> Coalgebras - the dual of algebras - are the mathematics of state and
> observation
> (e.g. OO programming),  of processes (eg: web servers that stay on all the
> time).
>
> It is quite intriguing that the categorical difference between algebras
> and coalgebras seems
> to mirror a difference between the Semantic Web community, and the linked
> data community.
> Doing an HTTP GET is an observation of the state of a resource, which
> returns
> a representation encoded in some format defined algebraically….
>
>
>
> >
> > Ryan
> >
> >> On Aug 29, 2019, at 6:37 AM, Henry Story <henry.story@bblfish.net>
> wrote:
> >>
> >>
> >>
> >>> On 26 Aug 2019, at 16:26, Steffen Staab <staab@uni-koblenz.de> wrote:
> >>>
> >>> Dear Henry,
> >>>
> >>> the pointers below seem to be really useful to us.
> >>> The work on CQL and QINL seems to be very related to our papers
> >>>
> >>> ISWC2019: https://arxiv.org/abs/1907.00855
> >>> Programming 2019: https://arxiv.org/abs/1902.00545
> >>>
> >>> where we use ontology concepts as well as queries as types in
> >>> programming languages.
> >>
> >> That last one is a very interesting article linking Scala
> >> and SPARQL. I completely agree with the described
> >> limitations of banana-rdf.
> >>
> >> This problem of how RDF and Scala fit together has been
> >> something that has bugged me for a while. Because of the
> >> strong presence of Functional Programmers in the Scala
> >> community I have been lead to look at Category Theory
> >> to look for an answer.
> >>
> >> Your work is also very enlightening. I feel we are at the
> >> cusp of an interesting answer here.
> >>
> >>>
> >>> QINL seems to go one step in this direction
> >>> taking schemata (not so different from ontology concepts / ER
> Entities)
> >>> and extending them with behavior.
> >>>
> >>> Still, I do not quite understand where the two approaches should meet..
> >>> Any idea?
> >>
> >> That is a very good question. I do get the feeling that by answering
> >> this question we can make some very good progress. Perhaps
> >> Ryan Wisnesky, can point to an answer here. I will try, but
> >> it may take me some time to integrate both sides :-)
> >>
> >> Ryan pointed me to an article from 2001 ”A Model Theory for Generic
> >> Schema Management” [1] that is actually an application of Institution
> Theory (IT)
> >> to Schema management with some very simple Java examples, that make
> >> IT accessible. The advantage of looking towards IT - the logic of the
> structure
> >> of all logics [2] - is that it can help one integrate many different
> points of views.
> >> The advantage of moving up the abstraction layer, is that some questions
> >> that within a domain seem arbitrary - eg the status of blank nodes in
> >> RDF - can be answered at the higher level by showing how it ties in
> >> to many other areas of mathematics and engineering in a structured
> >> way - eg. blank nodes appear as NULLs in a coherent formalization of
> >> database theory. In mathematics one can ground a problem by
> >> moving up the abstraction layers, it seems.
> >>
> >> Henry
> >>
> >> [1]
> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.481.7519&rep=rep1&type=pdf
> >> [2] https://www.iep.utm.edu/insti-th/
> >> [3] a page with many links to Categorical Query Language
> >>   https://www.categoricaldata.net/papers
> >>
> >> PS. Sorry for taking so long to answer. 1. It is taking time to
> integrate
> >> all these papers, and 2. I keep having to do Scala programming tests for
> >> job interviews to prove I can code!
> >> If anyone has a need for a Scala dev who understands RDF and
> >> some CT, please let me know :-)
> >>
> >>>
> >>> Cheers
> >>> Steffen
> >>>
> >>>
> >>>> Am 25.08.2019 um 07:19 schrieb Henry Story <henry.story@bblfish.net>:
> >>>>
> >>>> Continuing this thread that started with the funny story on the NULL
> >>>> vanity licence plate reported here:
> >>>>
> https://mashable.com/article/dmv-vanity-license-plate-def-con-backfire/
> >>>>
> >>>> I just came across work by Ryan Wisnesky on Algebraic Databases, where
> >>>> the authors formalizes DBs in terms of Category Theory, in order to
> build provably
> >>>> correct ways to transform data.
> >>>>
> >>>> In that formalization, for which they have software tools, they give
> an clear
> >>>> explanation of NULLs in SQL databases that make each
> >>>> NULL different.  In the talk linked to below Ryan Wisnesky actually
> gives them
> >>>> different  subscripts.
> >>>>
> >>>> In that way nulls  in DBs are very different from nulls in
> >>>> Java - which can be compared for equality  and for which there exists
> only one
> >>>> instance -  and very similar to blank nodes on the semantic web.
> >>>>
> >>>> See the presentation ”Algebraic Databases” on his web site
> >>>>    https://www.wisnesky.net/
> >>>> Or other content I found on this work
> >>>>    https://twitter.com/bblfish/status/1165195822625153024
> >>>>
> >>>> Henry Story
> >>>>
> >>>>
> >>>>> On 13 Aug 2019, at 15:53, Daniel Hernandez <daniel@degu.cl> wrote:
> >>>>>
> >>>>> SQL nulls are similar in some aspects to Codd nulls. A difference is
> that SQL nulls do no provide guaranty that the value exists. Blank nodes,
> on the other hand, are similar to marked nulls. We study the application to
> SPARQL of SQL techniques to approximate certain answers in: "Certain
> Answers for SPARQL with Blank Nodes." However, we founded a unique dataset
> using blank nodes as unknown values (Wikidata). I am curious if you know
> another.
> >>>>>
> >>>>> On Tue, Aug 13, 2019 at 3:53 AM, Franconi Enrico <
> franconi@inf.unibz.it> wrote:
> >>>>>> The situation is slightly more complex than that.
> >>>>>> NULL values in standard SQL are exactly defined as letting any
> equality involving a NULL value fail.
> >>>>>> Note that the string 'NULL' represents a NULL value, namely if you
> type the string NULL into a cell of type STRING then it is understood to be
> a NULL value.
> >>>>>> This is where the implementors failed: a NULL value is never equal
> to itself.
> >>>>>> This can be understood with the following standard SQL example (try
> it!).
> >>>>>>
> >>>>>> With the database:
> >>>>>>
> >>>>>> TABLE: col1 | col2
> >>>>>>      -----+-----
> >>>>>>        a  |  b
> >>>>>>        b  | NULL
> >>>>>>
> >>>>>> the query (meant to be the identity query, namely returning the
> input table itself):
> >>>>>>
> >>>>>> SELECT * FROM TABLE
> >>>>>> WHERE TABLE.col1 = TABLE.col1 AND TABLE.col2 = TABLE.col2 ;
> >>>>>>
> >>>>>> gives the result:
> >>>>>>
> >>>>>> col1 | col2
> >>>>>> -----+-----
> >>>>>> a  |  b
> >>>>>>
> >>>>>> In SQL, the query above returns the table TABLE if and only if the
> table TABLE does not have any NULL value, otherwise it returns just the
> tuples not containing a NULL value, i.e., in this case only the first tuple
> <a,b>. Informally this is due to the fact that a SQL NULL value is never
> equal (or not equal) to anything, including itself. This is because a SQL
> NULL value represents the absence of a value.
> >>>>>>
> >>>>>> Note that this is where SQL NULL values are radically different
> from RDF bnodes. Indeed a bnode is EQUAL to itself but different from any
> other bnode. This is because a RDF bnode represents the existence of an
> unknown value.
> >>>>>>
> >>>>>> --e.
> >>>>>>
> >>>>>>> Il giorno 12 ago 2019, alle ore 16:41, Diogo FC Patrao <
> djogopatrao@gmail.com> ha scritto:
> >>>>>>>
> >>>>>>>
> >>>>>>> Vanity license plates in USA are strings, right? Then this problem
> would only happen if NULL='NULL', which is not.
> >>>>>>>
> >>>>>>> It could be that the private company stored 'NULL' instead of NULL
> to the unassigned tickets, but that's really bad coding/design (and easy to
> fix, I guess).
> >>>>>>>
> >>>>>>> Or maybe the DAO wrongly translate NULL to 'NULL' at some point.
> >>>>>>>
> >>>>>>> Cheers
> >>>>>>>
> >>>>>>> dfcp
> >>>>>>>
> >>>>>>> --
> >>>>>>> diogo patrão
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>> On Mon, Aug 12, 2019 at 11:11 AM Young,Jeff (OR) <jyoung@oclc.org>
> wrote:
> >>>>>>> Here’s an example showing blank nodes being used to declare the
> place of birth is unknown in Wikidata:
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>> https://w.wiki/6$y
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>> In the UI, it is rendered like this:
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>> <image001.png>
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>> Jeff
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>> From: Daniel Hernandez <daniel@degu.cl>
> >>>>>>> Date: Monday, August 12, 2019 at 9:42 AM
> >>>>>>> To: "semantic-web@w3.org" <semantic-web@w3.org>
> >>>>>>> Subject: [External] Re: The Joy of NULLs (not)
> >>>>>>> Resent-From: <semantic-web@w3.org>
> >>>>>>> Resent-Date: Monday, August 12, 2019 at 9:37 AM
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>> As Enrico pointed, blank nodes can be used to represent unknown
> values.
> >>>>>>> An example of this use is Wikidata. I don't know another example.
> >>>>>>>
> >>>>>>> --
> >>>>>>> Daniel
> >>>>>>>
> >>>>>>> On Mon, 12 Aug 2019 07:36:41 +0000
> >>>>>>> Franconi Enrico <franconi@inf.unibz.it> wrote:
> >>>>>>>
> >>>>>>>> Mike, this could easily happen in an RDF world if you register a
> >>>>>>>> vanity licence plate with anything starting with "_". Indeed,
> bnodes
> >>>>>>>> would be the right way to represent unknown but existing plates.
> --e.
> >>>>>>>>
> >>>>>>>> Il giorno 11 ago 2019, alle ore 23:10, Michael F Uschold
> >>>>>>>> <uschold@gmail.com<mailto:uschold@gmail.com>> ha scritto:
> >>>>>>>>
> >>>>>>>>> This is hilarious. It could never happen in an RDF world! No
> value,
> >>>>>>>>> no triple.
> >>>>>>>>>
> >>>>>>>>> He tried to prank the DMV. Then his vanity license plate
> backfired
> >>>>>>>>> big time.
> >>>>>>>>>
> https://mashable.com/article/dmv-vanity-license-plate-def-con-backfire/<
> http://flip.it/NIk7FD>
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>
> >>>>
> >>>
> >>
> >
>
>
>