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)
Logics with aggregate operators
Journal of the ACM (JACM)
Complexity and expressive power of logic programming
ACM Computing Surveys (CSUR)
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
Theoretical Computer Science - Database theory
Foundations of rule-based query answering
RW'07 Proceedings of the Third international summer school conference on Reasoning Web
Model theory makes formulas large
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Proceedings of the 32nd symposium on Principles of database systems
An Optimal Gaifman Normal Form Construction for Structures of Bounded Degree
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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Most proofs showing limitations of expressive power of first-order logic rely on Ehrenfeucht-Fraisse games. Playing the game often involves a nontrivial combinatorial argument, so it was proposed to find easier tools for proving expressivity bounds. Most of those known for first-order logic are based on its "locality'', that is defined in different ways. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences and one with open formulae. We prove that the former implies Hanf's notion of locality, which in turn implies Gaifman's locality for open formulae. Each of these implies the bounded degree property, which is one of the easiest tools for proving expressivity bounds. These results apply beyond the first-order case. We use them to derive expressivity bounds for first-order logic with unary quantifiers and counting. Finally, we apply these results to relational database languages with aggregate functions, and prove that purely relational queries defined in such languages satisfy Gaifman's notion of locality. From this we derive a number of expressivity bounds for languages with aggregates.