bblfishJan 24, 2023
"Putting logic on the web changes logic itself"
Pat Hayes, 2009, in his Blog-IC talk.
BLOGIC a.k.a. #RDF surfaces, has recently garnered interest of reasoning engine specialists like @josd.
With Surfaces we move from #RDF graphs to (evolving) hyper graphs.
http://videolectures.net/iswc09_hayes_blogic/
Why did this *now* lead to the creation of a @w3c comunity group? https://www.w3.org/community/rdfsurfaces/
We should bring #CategoryTheory here to clarify what is going on #Peirce #logic #WorldWideWeb
Slides: https://bblfish.net/tmp/2023/2009-Hayes-BLogic.pdf
BLOGIC or Now What's in a Link?

Viidea
Show threadbblfishJan 24, 2023
@w3c @josd
When Pat emphasises the importance of names in Blog-ic (as opposed to traditional interpretations of logic where names are arbitrary) one should see a connection to Symmetric Monoidal Categories as introduced by @johncarlosbaez and their relation to the open world, which is fundamental to #RDF
https://www.youtube.com/watch?v=DAGJw7YBy8E
See further discussion:
https://twitter.com/bblfish/status/1397962748429062145
John Baez: "Symmetric Monoidal Categories A Rosetta Stone"

YouTube
Show threadbblfishJan 25, 2023

@josd @johncarlosbaez
On slide 19 Pat Hayes talks about blank nodes (existential quantifiers) in #RDF. He suggests that by thinking of nodes as marks on a surface, tying bnodes to what we would call a named graph, would have made things a lot easier.

In his 2009 PhD thesis modelling #RDF with #CategoryTheory @[email protected] tied bnodes to graphs too...
"Formal Modelling and Applicationof Graph Transformations in the Resource Description Framework" https://core.ac.uk/reader/57704480

Formal Modelling and Application of Graph Transformations in the Resource Description Framework - CORE Reader

Show threadbblfishJan 25, 2023
@josd In November 2020 I gave a 10 min intro talk @semwebpro on #RDF and #CategoryTheory, which I then started writing up in "Functorial RDF" . I was intrigued by how basic the move is from CT graphs as functors from the small category \( s, t: A \to N\) to Set, and RDF graphs as \(s, r, t: A \to N\) to what are I think surfaces \(s, r, t, g: A \to N\) known as hyper graphs... Those are very close to simplical sets somehow I was told.
https://co-operating.systems/2020/11/FunctorialRDF.pdf @semwebpro
Show threadbblfishJan 26, 2023
@josd @semwebpro
Oh, there already is a Primer for #RDF Surfaces that one can look at here:
https://w3c-cg.github.io/rdfsurfaces/
RDF Surfaces Primer

Show threadbblfishJan 26, 2023

@josd @semwebpro
@hochstenbach

Here is an interesting talk from 2020 that links #Peirce's logic of surfaces and #CategoryTheory.

https://www.youtube.com/watch?v=j7Bp6_uiFaQ

Now that we know that #RDF Surfaces help us think about the #SemanticWeb this talk takes on a whole new practical dimension. See the newly published RDF Surfaces spec:

https://w3c-cg.github.io/rdfsurfaces/

The talk starts simple and ends being too difficult (for me), but there are links to 3 papers that should help make things clearer.

Rocco Gangle: A Generic Figures Reconstruction of Peirce's Existential Graphs (Alpha)

YouTube
Show threadbblfishJan 26, 2023

@josd @semwebpro @hochstenbach

Some of the Papers on Peirce and Category Theory are:
"Compositional Diagrammatic First-Order Logic"
(also available online for free)
https://link.springer.com/chapter/10.1007/978-3-030-54249-8_32

Compositional Diagrammatic First-Order Logic

Peirce’s $$\beta $$ variant of Existential Graphs (EGs) is a diagrammatic formalism, equivalent in expressive power to classical first-order logic. We show that the syntax of EGs can be presented as the arrows of a free symmetric monoidal category. The...

SpringerLink
Show threadbblfishJan 26, 2023
@josd @semwebpro @hochstenbach
The other paper on Peirce and Category Theory is
"A categorical interpretation of C.S. Peirce's propositional logic Alpha"
https://www.sciencedirect.com/science/article/pii/S0022404998001790
and "Towards a Complex Variable Interpretation of Peirce’s Existential Graphs"
https://www.nordprag.org/nsp/1/IdeasInAction.pdf#page=288
Show threadJon AwbreyJan 26, 2023

@bblfish @josd @semwebpro @hochstenbach

Chillin' watchin' TV right now (#Chuck, it's #Nerdstalgic) but I should explain at this point I started working on #Peirce's #LogicalGraphs in a computational context sometime in the late '60s and it led me down a different fork from a lot of what you'll read in the current mainstream.

Show threadJon AwbreyJan 26, 2023

@bblfish @josd @semwebpro @hochstenbach

One thing I found out early on is how critical it is to get #AlphaGraphs (#BooleanFunctions, #PropositionalCalculus, #ZerothOrderLogic) down tight. If you do that it changes how you view #FOL (#PredicateCalculus, #QuantificationalLogic). That tends to rub people who view FOL as #GOL (#GodsOwnLogic) the wrong way so you have watch out for that if you go down this road.

Here's a primer on \(\alpha\) #LogicalGraphs as I see them —
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no

Logical Graphs - OeisWiki

Show threadbblfishJan 27, 2023

@Inquiry @hochstenbach

Pat Hayes started his talk with the sentence "Putting logic on the web changes logic itself". So there is not an aim here to stick to #FOL at any price. I guess the proposal for #RDF Surfaces should at an instant in time be equivalent to FOL when only two types of surfaces are allowed: True and False ones. But of course there could be the set of surfaces published by one individual only, fictional, obligatory, ... ones. Without counting that surfaces change over time.

Show threadbblfishJan 30, 2023
@Inquiry @hochstenbach
I used to have trouble understanding what is new because I very quickly learned about N3, which is evoling a spec too https://w3c.github.io/N3/spec/
Notation3 Builtin Functions

Show threadPatrick HochstenbachFeb 3, 2023
@bblfish @Inquiry @josd I understand there is a large body of research already in Peirce's graphs and extentions to Sowa's conceptual graphs and work on common logic. What we are trying to find out why this hasn't been taken up in semantic web community more? And can we change that and bring it back to the agenda. Would you be interested in a conference call about the context of all this?
Show threadJon AwbreyFeb 3, 2023

@hochstenbach @bblfish @josd

Sure. I've been thinking a lot about that lately. Who would be involved?

Show threadPatrick HochstenbachFeb 3, 2023
@Inquiry @bblfish @josd Well if there is interest, then I send out a doodle on our mailing list and we set a date for a discussion.
Patrick HochstenbachFeb 4, 2023
Show threadjosd
@hochstenbach @Inquiry @bblfish as we are on the syntactic/semantic/pragmatic web the main point for me is to have independent implementations that run the examples and test cases in https://github.com/w3c-cg/rdfsurfaces/blob/main/etc.md
rdfsurfaces/etc.md at main · w3c-cg/rdfsurfaces

RDF Surfaces is classical first-order logic with negation in RDF - rdfsurfaces/etc.md at main · w3c-cg/rdfsurfaces

GitHub
Feb 3, 2023 at 11:04pmWeb
Show threadJon AwbreyFeb 4, 2023

@bblfish @hochstenbach @josd

Here's the skinny on #MinimalNegationOperators —

• https://mathstodon.xyz/@Inquiry/109806663808536523

Minimal negation operators are a family of logical operators or #BooleanFunctions \(\nu(),\ \nu(x),\ \nu(x,y),\ \nu(x,y,z),\) etc.

In the so-called #ExistentialInterpretation of the brand of #LogicalGraphs I'll be using, \(\nu(x_1, \ldots, x_k)\) says exactly one of the \(x_i\) is equal to \(0\), that is, false.

Jon Awbrey (@[email protected])

#MinimalNegationOperators • https://oeis.org/wiki/Minimal_negation_operator #Peirce #LogicalGraphs #MinimalNegations #BooleanFunctions #PropositionalCalculus #CactusGraphs #CactusLanguage #CactusSyntax

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