About self-referential syntactic constructs

In Web Ontology Language (OWL) Abstract Syntax and Semantics 
[2. Abstract Syntax
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The abstract syntax here is less general than the exchange syntax for OWL. In particular, it does not permit the construction of self-referential syntactic constructs. It is also intended for use in cases where classes, properties, and individuals form disjoint collections. These are roughly the limitations required to make reasoning in OWL be decidable, and thus this abstract syntax should be thought of a syntax for OWL DL. 

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What are self-referential syntactic constructs?

Does it mean the following situation?
If an axiom uses a class or property to (partially) define itself, then this axiom is using a self-referential syntactic construct.


How about the following situation?

An axiom uses a class or property (say B) to (partially) define another class or property (say A), and the another axiom uses A to (partially) define B. 

May I use "cross-referential syntactic constructs" to mean the above situation?

Further more, what's the constraint on OWL Lite/DL about this issue? How does the Description Logic deal with this issue (self-reference/cross reference)? 


Best regards,

Yuhzong Qu

Received on Friday, 28 March 2003 21:43:05 UTC