From: Harold Boley (boley@informatik.uni-kl.de)
Date: 08/09/03
Hi Benjamin and All, > issue: restrict to Datalog? [Benj] > - binary Horn FOL with possibly further restrictions Binary Datalog is certainly a (modest) possibility. It's also one of the RuleML sublanguages: http://www.ruleml.org/dtd/0.8/ruleml-bindatalog.dtd We defined it as a restriction of N-ary Datalog: http://www.ruleml.org/dtd/0.8/ruleml-datalog.dtd Bindatalog is currently prefix or postfix: <!ELEMENT atom ((_opr, (ind | var), (ind | var)) | ((ind | var), (ind | var), _opr))> This could be extended to infix: <!ELEMENT atom ((_opr, (ind | var), (ind | var)) | ((ind | var), (ind | var), _opr)) | ((ind | var), _opr, (ind | var))> > Harold: possible issue of essential expressive limitation arising from > combination of finite lists with binary relations > - may not be able to show the general case of the usual reduction of > n-ary to binary I actually meant the following: N-ary Datalog is closed w.r.t. bounded lists, since any argument aI containing a list of fixed length L can be 'flattened' to a subsequence of L arguments (N=M+L-1): aI /----^----\ r(a1,...,[e1,...,eL],...,aM) --> r(a1,...,e1,...,eL,...,aM) This can be continued recursively, for any eJ that is again a bounded list, etc., down to a fixed depth D. The result of such flattening of a given KB utilizing "Datalog with bounded lists" still gives us an N-ary Datalog KB. (In practice 'bounded' means rest variables, like X in [e1,...,eL|X], are forbidden on all list levels.) A given binary Datalog KB, however, will not normally be N=2 after flattening. (I had exemplified a binary-to-ternary leap at the end of http://www.daml.org/listarchive/joint-committee/1420.html.) Best, Harold
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