John, (01)
We have apparently switched from what the logic is to what the notation is.
Yes, of course, you can create syntactic sugar for "context", instead of
creating the n-ary predicates outright. But the logic is then based on n-ary
predicates that incorporate the characteristics of the event AND the
characteristics of the context. And I think there should then be relationships
between the contextualized axioms that arise from properties of the "context".
For example:
John was standing on street X throughout time interval T1;
vehicle V came down street X within time interval T2; and
T2 is within T1.
We can thus conclude that V passed by John. But to draw that conclusion we
have to know that there is a relationship between 'throughout T1' and 'within
T2' that has nothing to do with vehicles and streets. And we have to know that
that relationship affects (stands_on_place_over_time John X T1). So the
addition of "temporal context" is *not* purely syntactic. Any formal model of
temporal context in that style will contain CLIF statements with variables
ranging over predicates and will probably require sequence variables as well.
And yes, OK, it is still first-order, but it is a long way from Tarski. (02)
I agree that the Davidsonian approach requires us to produce additional
temporal relations, and additional relations for other "contextual" concepts.
But I could use your syntactic "context" notation and translate it to a
Davidsonian form instead. The point of the Davidsonian approach is that it
allows us to formally axiomatize the relationships among the contextual
concepts as axioms involving the temporal relations, and to explicitly relate
"fundamental" event classes to time in multiple ways. The (neo-)Davidsonian
approach is widely used precisely because it is first-order and can have a
Tarski-style model theory with no bizarre requirements. (03)
Mark and I apparently disagree on the need for the IKL 'that' operator. The
SBVR gang sees many classes that represent states and events as the images of
propositions using an equivalent of the 'that' operator. But a temporal
relation, such as 'occurrence occurs throughout time interval', has the same
semantics regardless of how the 'occurrence' itself is identified. So, the
occurrence can be can be an instance of 'occurrence' that 'is described by' a
proposition:
(occurrence s)
(is_described_by s (that (flies_to John Tucson)))
or an instance of the class 'flies_to' (a subclass of 'occurrence'):
(flies_to s)
(agent s John)
(destination s Tucson)
In either case it is possible to write:
(occurs_within s "14 June 2014")
And you can parse the NL statement "John flew to Tucson on 14 June 2014" as a
statement involving a temporal context and generate either one of those,
instead of
(flies_to John Tucson "14 June 2014"). (04)
The important thing from my perspective is that 'occurrence occurs within time
interval' is a well-defined relation and can be axiomatically related to other
such temporal relationships in a theory of 'time' that is independent of any
more complex notion of events than 'occurrence'. I would argue that your
"syntactic context" approach still requires that theory of time, and that
creating ternary or quaternary relations with time arguments makes that theory
harder to use. (05)
-Ed (06)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
> Sent: Saturday, June 28, 2014 7:53 AM
> To: ontolog-forum@xxxxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] Requesting Opinions on the Benefits of
> Predicates as Nodes
>
> Ed and Mark,
>
> EJB
> > The ternary predicate approach that John describes is viable, but
> > clumsy. The ternary predicate approach requires a different ternary
> > predicate if you want to specify location instead of time, or a
> > quaternary predicate to specify both, etc.
>
> MLH
> > This is why I claimed that IKL "that" (or Sowa "describes") is
> > necessary. It is just plain unrealistic to expect every predicate
> > to have variants for time and location - not to mention other
> > modifiers that English would express using adverbs.
>
> I agree that adding an extra argument to every relation is clumsy.
> And I was *not* recommending it. The points I wanted to emphasize are
> theoretical, but with practical implications:
>
> 1. Quantifying over time can be done in a purely FOL semantics.
> There is no need to introduce the 'that' operator and all
> the semantic issues it entails. (I cited a book that uses
> a sorted FOL with time as one of the sorts.)
>
> 2. If you want to factor out those references (to time, location,
> or whatever), you can introduce a purely-syntactic notion of
> context.
>
> 3. That syntactic notion does not affect the semantics in any way,
> since every use of a context box (or other grouping markers)
> can be eliminated by a syntactic translation that adds an
> extra argument to every relation.
>
> 4. After the translation in #3, you can use an ordinary Tarski-style
> model theory for the semantics. There is no need to go to the
> more complex semantics of IKL in the model theory.
>
> 5. But as a practical KR notation, you don't have to translate
> the context boxes (or other grouping markers) to the form
> with extra relations or arguments.
>
> For the details of how to represent a kind of context, attach time and place
> references to that context, and then eliminate the contexts by a translation
> as above, see the following article:
>
> http://www.jfsowa.com/pubs/laws.htm
> Laws, facts, and contexts
>
> To represent a Tarski-style model, I use *nested graph models* (NGMs),
> which have "context boxes" that allow graphs nested within graphs.
> For the logic, I use conceptual graph notation, but you could use just as well
> use CLIF notation. (The article was published in 2003 while the CL standard
> project was in its early days.)
>
> To see the differences between the three kinds of notations, Figure 9 shows
> a conceptual graph in its nested form with type labels. Fig. 10 shows a
>nested
> graph model for which the denotation of Fig. 9 is true.
>
> Then Fig. 11 shows the translation of the NGM in Fig. 10 to a "flat"
> form with no nesting. An 'isin' relation links a node for each relation to a
> node that represents the context in which the relation occurs.
> This flattened graph could be represented as an ordinary Tarski model.
>
> Figures 9 to 11 have proposition nodes. They raise issues that IKL dealt with
> in more detail about 3 years later. If you're not using verbs like
>'believe', you
> don't need proposition nodes. Those boxes could represent situations at
> particular times and places.
>
> John
>
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