negation
Abstract:
3. Stratified DATALOG Queries with choice 4. Stratified DATALOG Queries with ordering 5. Stratified DATALOG Queries with choice and inflationary fixpoint 6. Extending the expressive power of DATALOG Queries 3 Database Concepts and Notation • U: a universe of constant symbols • d: a database scheme 〈r1, · · · , rm〉 • ri: a relation scheme, say with arity ki • Ri: a relation on ri. i.e., a finite set of tuples on U ki • inst(ri): the set of all relations on ri • D = 〈R1,..., Rm〉: a database on d — the active domain consists of all constants occurring in D • inst(d): the set of all databases on d. 4 Database Search Queries • Q =< d, g>: a partial multivalued function inst(d) → inst(g), computable and generic • generic: ∀D ∈ d and ∀ρ, isomorphism on U, Q(ρ(D)) = ρ(Q(D)) • ∀D ∈ inst(d), Q(D) is the set of answers • dom(Q) = {D ∈ d | ∃G ∈ g (G ∈ Q(D))} • graph(Q) = {〈D, G 〉 | D ∈ dom(Q), G ∈ Q(D)}. • because of genericity, graph(Q) is polynomially balanced. i.e. ∀D ∈ d, Q(D) is polynomially bounded on the size of D. • NQ: the set of all database queries 5
Citations
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| 1 | Some Complexity Results on Multivalued Functions, unpublished manuscript – Saccà, Scarcello - 2001 |
