No. No. No. You should design your argumentation system to have the
semantics you want. Just because it is based on classical logic and
probability theory doesn't mean that everything is well founded and well
understood.
For example, the Independent Choice Logic (and it's predecessor
probabilistic Horn abduction) is based on logic and probability, and
corresponds to Bayesian networks (extended to a first-order language,
but with the ability to express context-specific independence in the
form of rules, and also choices by other agents). It could be described
as an argumentation system or as a form of abductive logic programming.
What is important is the design decisions that go into the combination.
What do you want to be able to express? For what purpose?
The independent choice logic is based on the idea that people are quite
happy to write all of the conditions under which some predicate is true
(this justifies the negation as failure in logic programming, for
example). Also that we want the user to be able to express independence
assumptions. It was based on assumption-based reasoning (as in ATMSs and
first-order extensions) with probabilities over assumptions. As a
design decision I wanted *all* uncertainty to be handled by probability.
I didn't set out to design first-order language for Bayesian networks,
but that was the result. I could argue that when you combine
argumentation systems (that give arguments from assumptions) and
probability (in the form of probabilities over assumptions) that
Bayesian networks arise. But this depends on the details of the
combination and the design decisions that went into building it.
You can't justify something like D-S by saying that when you mix logic
and probability you get D-S, particularly when you don't state your
design decisions. It's not surprising that you get D-S as you seem to
have the same design decisions that went in to design D-S theory.
David
A Couple of References (These, and many others, are available from my
web page. See also http://www.cs.ubc.ca/spider/poole/ongoing.html ).
D. Poole, ``Probabilistic Horn abduction and Bayesian networks'',
Artificial Intelligence, 64(1), 81-129, 1993.
D. Poole, ``The Independent Choice Logic for modelling multiple agents
under uncertainty'', Artificial Intelligence, 94(1-2), special issue on
economic principles of multi-agent systems, pages 7-56, 1997.
D. Poole, ``Decision Theory, the Situation Calculus and Conditional
Plans'', Linköping Electronic Articles in Computer and Information
Science, Vol 3 (1998):nr 8. http://www.ep.liu.se/ea/cis/1998/008/ June
15, 1998. Under discussion, The Electronic Transactions on Artificial
Intelligence.
-- David Poole, Office: +1 (604) 822-6254 Professor, Fax: +1 (604) 822-5485 Department of Computer Science, poole@cs.ubc.ca University of British Columbia, http://www.cs.ubc.ca/spider/poole Vancouver, B.C., Canada V6T 1Z4 ftp://ftp.cs.ubc.ca/ftp/local/poole