Re: [ontolog-forum] The Open world assumption shoe does not always fit -

["Adrian Walker" <adriandwalker@xxxxxxxxx>]

Pat, John, Chimeze and all --

Illuminating discussion.

Two points: 

1. If you move to from SQL-like NAF reasoning, to full FOL with closure statements at the meta level, you may also be moving from low order polynomial computational complexity to exponential, or even into the undecidable region.  A succinct paper on this issue would be good to have.

2.  Some of the worry about SQL-NAF possibly leading to wrong conclusions appears to come from the assumption that the intended real world meaning of things like p133(?X,?Y) is nowhere documented.  However, if you attach English sentences to  predicates [1], and hide the predicates themselves, then answers from your deductions can be sentences like

 "Assuming that we have all the relevant data, as of 20080627, Pat does not work for IBM".  

Then, there's no way for the English documentation to get separated from the logic, because authors and users deal only with the executable English.  English explanations can also help to document how the answers are arrived at.

These two points may also be relevant for RDF [2].

Thanks for your further thoughts.

                                         -- Adrian

[1]  Internet Business Logic
A Wiki and SOA Endpoint for Executable Open Vocabulary English over SQL and RDF
Online at www.reengineeringllc.com    Shared use is free

[2]  www.reengineeringllc.com/demo_agents/RDFQueryLangComparison1.agent

Adrian Walker
Reengineering

On Fri, Jun 27, 2008 at 1:34 AM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:

Folks,

I'd just like to summarize a few points, which reinforce the claim I
made earlier:  There is an open-ended number of different variations of
nonmonotonic logic, and it's impossible to adopt a one-size-fits-all
solution for nonmonotonic logic.

To paraphrase Tolstoy, every happy logic (i.e., classical) is happy
in the same way, but every unhappy logic (nonmonotonic) is unhappy
in its own way.

The solution I recommend is to treat all nonmonotonic operators
as metalevel predicates about some proposition or some proof.
In IKL (or any other logic that supports metalevel statements),
predicates such as is-provable(p), is-not-provable(p), is-default(p),
has-fuzzy-value(p,x), or probability-of(p,x), are metalevel
statements about some proposition p.

If you assume a closed world (such as a database of all airline
reservations or all employees), you can write metalevel axioms
saying that anything not provable is false.  If you have an open
world with incomplete information, you can write metalevel axioms
that say what to do about such cases.  If you have a mixed DB
with complete info about some things and incomplete info about
other things, you can write axioms to say what to do in each case.

Professional database administrators and authors who have studied
the issue for a long time (such as Chris Date), know how to
design and use DB systems in order to achieve predictable
results.  Many casual users manage to avoid trouble by using
a database as a convenient way of storing and accessing positive
data, and they assume that the "not" operator is shorthand for
"not found".

In short, a logic with a classical semantics, such as CL or IKL,
is an ideal foundation for defining the semantics of any and every
version of nonmonotonic logic that has ever been invented.

John

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