Bounded Hyperset Theory and Web-like Data Bases
نویسندگان
چکیده
It is demonstrated how a Hyperset Theory (satisfying P.Aczel's Anti-Foundation Axiom) naturally arises from the idea of World-Wide Web (WWW). Alternatively, Web serves as an illustration and possible application of the abstract notion of antifounded sets. A -language of Bounded Hyperset Theory is presented as a query language to the Web or, more generally, to Web-like Data Bases (WDB). It is shown that it describes exactly all abstract (or generic, up to bisimulation) PTIME-computable queries with respect to (possibly cyclic) graph encoding of hypersets. This result is based (i) on reducing of the -language for hypersets to the language FO+LFP ( = First-Order Logic with the Least Fixed-Point operator) over graphs considered up to bisimulation relation and (ii) on de nability in FO+LFP of a linear ordering on any strongly extensional nite graph by a single formula (cf. also DIMACS TR97-05). The case of nitely branching, possibly in nite graphs and corresponding hypersets is also discussed. It corresponds to nitely-branching, but in nite Web. However, it deserves special further investigation.
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