Ed, Kingsley, Tom, (01)
EJB
> It seems you and I are in violent agreement. (02)
Sometimes it takes a while, but I'm glad that we converged. (03)
EJB
> In your list of contributors to the 'possible world' concept,
> I am a bit surprised that you don't mention Plantinga... (04)
I have a high regard for his work, but in that article, I was talking
about issues developed by Jaako Hintikka, Saul Kripke, and Michael Dunn: (05)
1. Hintikka introduced "model sets", each of which is a set of
propositions that completely describe a possible world. This
view is close to what is implemented in any AI or DB systems. (06)
2. Around the same time, Saul Kripke developed the most popular
version of modal semantics based on possible worlds as undefined
primitives. For any world w, you can define the Hintikka model
set as the set of propositions: {p | p true in w}. He also
defined an "accessibility relation" R(w1,w2) that is equivalent
to Hintikka's alternativity relation. (07)
3. Dunn (1973) combined Hintikka's version and Kripke's version.
For any world w, he defined the set of facts as {p | p true in w}.
Then he also defined the laws of w as the subset of facts that
are necessarily true: {p | p is necessarily true in w}. Then
he defined the accessibility relation: World w2 is accessible
from world w1 iff every law in w1 is true in w2 (but it might
be demoted from a law in w1 to a mere fact in w2). (08)
EJB
> I am not convinced that Kripke's 'possible world' semantics is adequate
> for deontic logics. A customary semantics for deontic logics is more
> often based on an 'acceptable world' notion, which would be a strange
> interpretation of 'possible world'. (09)
Kripke did cover deontic logics in his second paper on semantics
for modal logic. He called the alethic version *normal* and the
deontic version *non-normal*. His non-normal worlds are indeed
strange because a world in which there are sinners (people who
violate some laws) is not "accessible" from itself. Despite the
"strangeness", the axioms for deontic logics hold for those worlds. (010)
Dunn's semantics is equivalent to Kripke's, but the terminology sounds
more natural. You can just say that some laws may be violated -- i.e.,
the set of laws might not be a subset of the facts. (011)
KI
> In Figure 23 of http://www.jfsowa.com/pubs/eg2cg.pdf , shouldn't it
> be: [Cat: #Yojo] rather than [Cat: Yojo] in one situation and then
> [Entity: Yojo] in another? (012)
The general question of how to handle proper names in English is
by no means trivial. But in that story (top of page 21), the first
sentence introduces the context: "At 10:17 pm, Yojo the cat and
a mouse were in the basement of a house." Then it's safe to treat
the name Yojo as a constant -- at least for the duration of the story.
Therefore, it's not necessary to mark it as an indexical. (013)
But in the book "Moby Dick", 'Yojo' is the name of Queequeg's
ebony idol. If both the cat and the idol were mentioned in the
same context, then you could write (014)
[Cat]->(HasName)->[Word: 'Yojo']
[Idol]->(HasName)->[Word: 'Yojo'] (015)
In English, you could say "A cat named Yojo and an idol named Yojo." (016)
TJ
> I note also that by reifying statements themselves (and not just their
> inscriptions, as is done everywhere else), it becomes possible to track
> both inscription (statement token) provenance, and also statement
> (type) provenance. (017)
That is an important point. In fact, that is exactly what IKL does: (018)
TJ
> I confess to total ignorance of IKL. I don't even know what the
> acronym stands for. (019)
Very few people have heard of it. IKL stands for IKRIS Knowledge
Language. It's an extension of Common Logic that was developed by
the IKRIS project. See Section 2 of http://www.jfsowa.com/ikl (020)
The principal innovation beyond Common Logic is the "that" operator,
which reifies a proposition and enables references to it. For example,
the sentence "Sue believes that 2+2=4" could be represented (021)
(believes Sue (that (= 4 (plus 2 2)))) (022)
Another example, "Bob believes everything that Sue believes": (023)
(forall (p)
(if (believes Sue p) (believes Bob p)) ) (024)
The above two sentences imply (025)
(believes Bob (that (= 4 (plus 2 2)))) (026)
TJ
> But by summarizing bits and pieces of it (another piece is my notion
> of an upper-level ontology common to all relational databases, a
> notion that Matthew West seems skeptical of), I hope to garner
> valuable criticism. (027)
There's a huge number of critical issues. See the 100+ documents
listed and linked by that web page http://www.jfsowa.com/ikl .
For a summary, look at Figures 1 to 6 and the associated documents. (028)
John (029)
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