[RuleML-all] Non-moniticity and model theory

[Bart Orriens]

Hello everyone,

the issue I'm bringing to your attention is not directly related to RuleML, but is relevant i think, as it deals with the interpretation of non-monotic statements.

In my research I need to use non-monotonic rules to define business collaboration requirements. These rules are then used to drive design of business collaborations, i.e. to create models. In order to give semantics to the rules, it is necessary to emply some semantics of logic. As I work with models I made the choice to utilize the popular model theoretic semantics upon which model theory is based. My question now is this:

Has there been formal proof of some sort with which model theory can be applied to interpret the truth of non-monotonic rules? I would be much obliged if someone could point me towards literature in this direction, as I am not native to the domain of logic.
A related question concerns the usage of negation as failure. On this matter I did find a reference in SWSL, which states with regard to their rule semantics:

"Any rule set that does not use the features of the NAF layer and its extensions is known to have a unique minimal model, which is also its canonical model. This is an extension of the well-known
fact for Horn clauses in classical logic programming. With NAF, a rule set may have multiple incomparable minimal models, and it is well-known that not all of these models appropriately capture the intended meaning of rules. However, it turns out that one such model can be distinguished, and it is called the well-founded model. A formula is considered to be true according to the SWSL-Rules semantics if and
only if it is true in that one single model, and the formula is false if and only if it is false in that model."

Any help, as said, would be much obliged.

Cheers,
Bart
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Drs. Bart Orriens          
B704, Tilburg University 	
PO Box 90153, 5000 LE Tilburg, 	 
The Netherlands
Phone : +31 13 4662779 
Fax   : +31 13 4663069                 
Email : b.orriens at uvt.nl
Web   : http://infolab.uvt.nl/~borriens   
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