Operational and abstract semantics of the query language G-Log
Theoretical Computer Science
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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 $\Delta$-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 $\Delta$-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 definability in FO+LFP of a linear ordering on any strongly extensional finite graph by a single formula (cf.\ also DIMACS TR-97-05). The case of finitely branching, possibly infinite graphs and corresponding hypersets is also discussed. It corresponds to finitely-branching, but infinite Web. However, it deserves special further investigation.