Re: Syntactic Options for Probabilistic Semantics

Dörthe,
All,

With respect to syntactic options for probabilistic logic and semantics, I recently created a GitHub discussion thread: https://github.com/w3c-cg/planning/discussions/26#discussioncomment-4369123 . The most recent comment, there, broaches some syntactic options including some discussion that RDF-star is useful for these scenarios.

For instance:


<< ex:myPredicate calc:holdsFor ( ex:x ex:y ex:z ) >> calc:probability "0.95"^^xsd:double .

and (see also: https://github.com/w3c/rdf-star/issues/276):


<< ex:myPredicate calc:holdsFor ( ex:x ex:y ex:z ) >> calc:probability "0.95"^^xsd:double {| o:accordingTo ex:Alice |} ,
                                                                       "0.96"^^xsd:double {| o:accordingTo ex:Bob   |} .

Considering these intricate RDF-star examples, above, the @-directive approach, broached earlier, might not have been the best syntactic option for probabilistic logic and semantics...

While the N3 design appears to be migrating from @-directives (https://w3c.github.io/N3/spec/#changes-since-team-submission), brainstorming, here is an idea, expressed using a @-directive syntax (other syntaxes possible), which pertains to iterating over statements in one named graph to process a second graph and to assert content from it.

The following example intends to express, for each statement, ?statement, in a named graph, example:graph1, that we desire to process and to assert the contents of example:graph2.

@foreach(?statement in example:graph1 insert example:graph2)
{
    example:graph1
    {
        ### this graph is iterated and not added to the deserialized graph or dataset
        example:x1 example:p1 example:y1 .
        example:x2 example:p2 example:y2 .
        example:x3 example:p3 example:y3 .
    }
    example:graph2
    {
        ### the ?statement iterand variable can be utilized throughout this graph.
        ### there could be a path-related notation utilized to obtain the iterands' subjects, predicates, objects, and so forth.
        ### for each iterated statement, this template graph is to be processed and added to the graph or dataset being deserialized.
    }
}

What do you think of this abstract idea? If such a feature would be useful, is there a better syntax for it?


Best regards,
Adam

________________________________
From: Adam Sobieski <adamsobieski@hotmail.com>
Sent: Thursday, November 24, 2022 10:46 AM
To: Doerthe Arndt <doerthe.arndt@tu-dresden.de>
Cc: semantic-web@w3.org <semantic-web@w3.org>
Subject: Re: Syntactic Options for Probabilistic Semantics

Dörthe,

Thank you. I also like the solution you presented which uses a defined and well-known vocabulary.

Comparing these two options, with a @-directive-based approach underlying storage approaches, implementations, would seemingly be more flexible. With the solution you shared, the underlying storage approach appears to be more rigidly graph-based.

Clarifying, with respect to runtime memory storage approaches, many implementations provide a "Triple" class and an implementation could provide, for probabilistic semantics, a "ProbabilisticTriple" class with a new property or new method: "getProbability()". In theory, such a virtual method could be added to the "Triple" class and implemented there to always return 1.0 (or <1.0, 0.0, 0.0>). "ProbabilisticTriple", extending "Triple", could override this virtual method, e.g., to return varying data.

With respect to backend implementation approaches, in the case of database storage, certain tables could provide an extra column for probability-related data. Were it not for consideration of neutrosophic logics, we could envision such columns to always simply be scalars.

With either of the two options, with some new syntax, e.g., @-directive-based, or a well-known vocabulary for probabilistic semantics, software can readily detect when probability-related content appears in data or queries. That is, software could detect when to deserialize to "Graph" and when to deserialize to "ProbabilisticGraph".

These are some initial thoughts about comparing these two options.


Best regards,
Adam

P.S.: It appears that there is an opportunity to update the Wikipedia article on probabilistic semantics<https://en.wikipedia.org/wiki/Probabilistic_semantics>.

________________________________
From: Doerthe Arndt <doerthe.arndt@tu-dresden.de>
Sent: Thursday, November 24, 2022 7:53 AM
To: Adam Sobieski <adamsobieski@hotmail.com>
Cc: semantic-web@w3.org <semantic-web@w3.org>
Subject: Re: Syntactic Options for Probabilistic Semantics

Dear Adam,

I like your idea to express probabilistic semantics with N3, but I would like to clearly understand why you think that we need the @-based directives for it instead of using the language as it is together with a defined vocabulary. The background here is, that in the N3 group we try to avoid keys and special constructs where possible.  So, why would you need the special construct?



Brainstorming, we could, in a manner resembling other @-based directives in N3, express:

@p(0.95) . { domain:X domain:r domain:Y . }

Instead of writing that, you could also simply add some predicate :probability (of course using a shared vocabulary and not just something made up ad-hoc) and state:


{ domain:X domain:r domain:Y . } :probability 0.95.

The advantage of doing so is, that you would even be able to reason with your probabilities without any extra effort. If you have the probability of a person having black hair and the probability of a person being male

{:person a :Male} :probability 0.49.
{:person :hairColor :black } :probability 0.3.

You could use a rule to calculate the probably of encountering a male with black hair just like:

{
{?s ?p ?o} :probability ?x.
{?s ?p2 ?o2} :probability ?y.
{?s ?p ?o} log:notEqualTo {?s ?p2 ?o2}.
(?x ?y) math:product ?z.
({?s ?p ?o} {?s ?p2 ?o2}) log:conjunction ?c
}=>{
?c :probability ?z
}.

And get that

{:person :hairColor :black. :person a :Male} :probability 0.147 .

You can also directly try the example here: http://ppr.cs.dal.ca:3002/n3/editor/s/RfwLWp8T

I would of course expect, that the rules you would actually need for proper probabilistic semantics are far more complicated, but I also think that the built-ins in N3 would allow you to write some exchangeable rules supporting the theory. So, having these nice implementations at hand, I wonder why you would want to ask for extra syntax? You could stay in the syntax as it is and define a vocabulary (ontology, depending how far you go) for the concept of probability which we would then reuse.


Also, beyond [0, 1] scalars per fuzzy logic, there are multivalued logics, e.g., neutrosophic logics which describe every logical variable x as being described by a triple: x = (t, f, i), where t is the degree of truth, f is the degree of false, and i is the level of indeterminacy. We could express this in a manner resembling:

@p(t: 0.95, f: 0.05, i: 0.0) . { domain:X domain:r domain:Y . }

Would

{ domain:X domain:r domain:Y . } :probability_t 0.95, :probability_f 0.05, probability_i: 0.0.

also do the job? Why would you want to have the special format?



What do you think of these syntactic options for expressing probabilistic semantics in N3-based languages?

Before I form an opinion, I really need to understand, why we would need extra syntax here. I am sure, I am missing something, but so far, it looks to me that the proposal rather complicates the language than bringing extra advantages. Maybe an example could help?

Kind regards,
Dörthe