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Re: [ontolog-forum] Requesting Opinions on the Benefits of Predicates as

To: Jack Park <jackpark@xxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Wed, 11 Jun 2014 18:09:02 -0500
Message-id: <01F3E8D9-F389-4C84-8B1E-D3E5D07E5856@xxxxxxx>

On Jun 11, 2014, at 11:20 AM, Jack Park <jackpark@xxxxxxxxx> wrote:    (01)

> I see an additional benefit, but not necessarily affiliated with the
> way you describe an 'implicit node' -- where a predicate appears,
> still, to be a second-class citizen in the graph.
> 
> Let me explain.
> 
> Mostly, it would seem that a predicate in a triple performs the task
> of linking subject and object; it has no other reason for being there
> other than to complete the assertion, e.g. A relates to B.    (02)

Its role is to specify the nature of the relationship.     (03)

> 
> But, consider this: if a specific *instance* of a predicate exists as
> a connective between two objects, then it can be said to carry the
> full semantics of the assertion itself.    (04)

It could be said to, but that would be a mistake. (It is also incorrect to 
describe an instance of a relation as a 'connective', by the way.) There are 
several things that need to be distinguished, if we are not to fall into 
complete confusion. Fortunately, the necessary distinctions are already 
formalized in the IKL extension to ISO Common Logic, and which RDF can be 
trivially embedded into (preserving the RDF semantics exactly.)    (05)

A triple S P O . is written in CL and IKL as the atomic sentence     (06)

(P S O)     (07)

Just as in RDF, all three components are 'first-class' entities, so the 
predicate P can be the argument of some other assertion:    (08)

(nicerPredicate P Q)    (09)

and can be quantified over    (010)

(exists (x)(and (x S O)(nicerPredicate x Q)))    (011)

However, in IKL, we can also refer to the proposition expressed by the triple:    (012)

(that (P S O))    (013)

as a first-class object. This is not the same as P, or even as an instance of P 
(whatever that is), because it inherently involves S and O, in that order as 
specified. (In the IKL semantics, a proposition is in fact a zero-ary relation, 
ie one with no arguments.)    (014)

> The instance is not an
> 'implicit' node: it is a vertex like any other in a graph.
> 
> If I say: A cause B, then the node which is the 'cause' predicate can
> carry the full semantics of the triple itself.    (015)

No, it can't. The 'cause' predicate name used on an RDF node or arc denotes the 
actual relation. Yes that is a first-class citizen in RDF and CL/IKL (though 
not in OWL-DL), but it cannot carry the semantics of the triple, because it is 
the same relation even when used in a different triple:    (016)

T P R .    (017)

that 'P' in there still denotes the same thing it did when it was between S and 
O. In IKL syntax, the propositions 
(that (P T R))
(that (P S O))
are different things, each of which can be said to "carry the semantics" of 
their containing triples, but the name 'P' denotes the same relation in each 
case.     (018)

> It's not just your
> father's predicate anymore; it's a first class citizen.
> 
> Why do I care?
> 
> Consider that said predicate has entails a possibly complex biography.
> Who discovered it? What evidence supports it? What debates are in play
> about it?    (019)

Questions which can be asked about the relation/predicate, and also about a 
proposition formed using that predicate. But might have different answers when 
asked about those different things.     (020)

> 
> I can't assign or otherwise link that biography to either A or B, but
> only to the specific predicate that ties them together.
> 
> If I might add, I will assert that predicates as first class citizens
> is perhaps the only difference between an RDF graph and a topic map.    (021)

The main difference is that topic maps don't have any precise normative 
semantics, so all discussions about what they mean or don't mean are inherently 
vague and indecisive, in contrast with RDF.    (022)

Pat     (023)

> I've built topic maps with RDF using the BigData RDF store; they work
> just fine, can import and export from, e.g. OWL documents, but with a
> loss of information when the topic map becomes OWL.
> 
> 
> On Wed, Jun 11, 2014 at 8:59 AM, Frank Guerino <Frank.Guerino@xxxxxxxxx> 
>wrote:
>> Hi All,
>> 
>> For a number of years, we've been working with Data Driven Synthesis as a
>> means of rapidly generating Data Networks/Graphs and the Knowledge
>> Constructs (e.g. Library Catalogs, Indexes, Taxonomies, Visualizations,
>> etc.) that help humans make easier & better sense of them  (If interested,
>> see NOUNZ).  Like many other Graph representations, we use "triples" or
>> "triplets" to help represent Semantic Relationships, where descriptive
>> Predicates are used as the binding between Subject Nodes and Object Nodes.
>> 
>> To date, we've only treated Subjects and Objects as "Nodes" but we've always
>> known that we can (and have planned to) implement and treat Predicates as a
>> special type of "implicit" Node, as well.  (Time didnít' allow us to get to
>> doing so, until now.)  We believe that doing so grants users of Graphs
>> certain benefits.  We've identified three (3)Ö
>> 
>> #1: The first and obvious advantage is that users can now enter a Graph from
>> any Edge/Predicate as easily as they can enter from any Node, and start to
>> traverse the Graph based on that point of entry.
>> 
>> #2: The second advantage of treating Predicates as Nodes is that a Predicate
>> can now be used as an "Index" or "Pointer" that allows users to quickly find
>> all Nodes which are tied to said Predicate (or any Predicates that match
>> certain traits).  In other words, it's a way of asking the Graph to quickly
>> identify all Nodes that are connected to a specific Edge/Link/Predicate (or
>> any of a common set of Predicate traits).  This means that, in addition to
>> being able to ask "Node-oriented" questions of the Graph, you can now also
>> ask "Predicate/Edge-oriented" questions of the Graph, as well.  This leads
>> to even more complex scenarios of being able to ask questions of, both,
>> Nodes and Edges.
>> 
>> #3: The third advantage (based on the second) is that traversal of a Graph
>> can be even quicker, leading to even shorter paths, because instead of only
>> traversing a Graph from Node-to-Node-to-Node, through Nodes, users can now
>> traverse from any Edge/Predicate to any other Edge/Predicate, through
>> Edges/Predicates.
>> 
>> My question to the Community:  Aside from the above three, do you see any
>> other benefits that we're missing?
>> 
>> Thanks for your help.
>> 
>> My Best,
>> 
>> Frank
>> --
>> Frank Guerino, Chairman
>> The International Foundation for Information Technology (IF4IT)
>> http://www.if4it.com
>> 1.908.294.5191 (M)
>> 
>> 
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