Logics with counting and local properties
ACM Transactions on Computational Logic (TOCL)
Locality of order-invariant first-order formulas
ACM Transactions on Computational Logic (TOCL)
Equivalences among aggregate queries with negation
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Pushing extrema aggregates to optimize logic queries
Information Systems
Lower bounds for invariant queries in logics with counting
Theoretical Computer Science - Complexity and logic
ICDT '01 Proceedings of the 8th International Conference on Database Theory
Counting and Locality over Finite Structures: A Survey
ESSLLI '97 Revised Lectures from the 9th European Summer School on Logic, Language, and Information: Generalized Quantifiers and Computation
On the Power of Incremental Evaluation in SQL-Like Languages
DBPL '99 Revised Papers from the 7th International Workshop on Database Programming Languages: Research Issues in Structured and Semistructured Database Programming
Logics Capturing Local Properties
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
An Existential Locality Theorem
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Equivalences among aggregate queries with negation
ACM Transactions on Computational Logic (TOCL)
Deciding equivalences among conjunctive aggregate queries
Journal of the ACM (JACM)
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We study adding aggregate operators, such as summing up elements of a column of a relation, to logics with counting mechanisms. The primary motivation comes from database applications, where aggregate operators are present in all real life query languages. Unlike other features of query languages, aggregates are not adequately captured by the existing logical formalisms. Consequently, all previous approaches to analyzing the expressive power of aggregation were only capable of producing partial results, depending on the allowed class of aggregate and arithmetic operations.We consider a powerful counting logic, and extend it with the set of all aggregate operators. We show that the resulting logic satisfies analogs of Hanf's and Gaifman's theorems, meaning that it can only express local properties. We consider a database query language that expresses all the standard aggregates found in commercial query languages, and show how it can be translated into the aggregate logic, thereby providing a number of expressivity bounds, that do not depend on a particular class of arithmetic functions, and that subsume all those previously known. We consider a restricted aggregate logic that gives us a tighter capture of database languages, and also use it to show that some questions on expressivity of aggregation cannot be answered without resolving some deep problems in complexity theory.