On Monotone Data Mining Languages
DBPL '01 Revised Papers from the 8th International Workshop on Database Programming Languages
On preservation under homomorphisms and unions of conjunctive queries
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
On preservation under homomorphisms and unions of conjunctive queries
Journal of the ACM (JACM)
Homomorphism preservation theorems
Journal of the ACM (JACM)
When is naive evaluation possible?
Proceedings of the 32nd symposium on Principles of database systems
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A characterization of definability by positive first order formulas in terms of Fraisse-Ehrenfeucht-like games is developed. Using this characterization, an elementary, purely combinatorial, proof of the failure of Lyndon's Lemma (that every monotone first order property is expressible positively) for finite models is given. The proof implies that first order logic is a bad candidate to the role of uniform version of positive Boolean circuits of constant depth and polynomial size. Although Lyndon's Lemma fails for finite models, some similar characterization may be established for finitely monotone properties, and we formulate a particular open problem in this direction.