Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Infinitary logics and 0–1 laws
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Computing with first-order logic
Selected papers of the 23rd annual ACM symposium on Theory of computing
On a monadic NP vs monadic co-NP
Information and Computation
On the expressive power of counting
ICDT '92 Selected papers of the fourth international conference on Database theory
Information and Computation
Counting quantifiers, successor relations, and logarithmic space
Journal of Computer and System Sciences - special issue on complexity theory
Query languages for bags and aggregate functions
Journal of Computer and System Sciences - Special issue on principles of database systems
Information and Computation - Special issue: logic and computational complexity
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Local Properties of Query Languages
ICDT '97 Proceedings of the 6th International Conference on Database Theory
Inductive Definability with Counting on Finite Structures
CSL '92 Selected Papers from the Workshop on Computer Science Logic
First Order Logic, Fixed Point Logic and Linear Order
CSL '95 Selected Papers from the9th International Workshop on Computer Science Logic
Expressive Power of Unary Counters
ICDT '97 Proceedings of the 6th International Conference on Database Theory
On the Forms of Locality over Finite Models
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Logics with Aggregate Operators
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Locality of order-invariant first-order formulas
ACM Transactions on Computational Logic (TOCL)
Logics capturing local properties
ACM Transactions on Computational Logic (TOCL)
Logics with aggregate operators
Journal of the ACM (JACM)
ICDT '01 Proceedings of the 8th International Conference on Database Theory
An Existential Locality Theorem
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Theoretical Computer Science - Database theory
The description logic handbook
Locally consistent transformations and query answering in data exchange
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The finite model theory toolbox of a database theoretician
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Locality of Queries and Transformations
Electronic Notes in Theoretical Computer Science (ENTCS)
Database theory: query languages
Algorithms and theory of computation handbook
Model theory makes formulas large
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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The expressive power of first-order logic over finite structures is limited in two ways: it lacks a recursion mechanism, and it cannot count. Overcoming the first limitation has been a subject of extensive study. A number of fixpoint logics have been introduced. and shown to be subsumed by an infinitary logic Lw∞w. This logic is easier to analyze than fixpoint logics, and it still lacks counting power, as it has a 0-1 law. On the counting side, there is no analog of Lw∞w . There are a number of logics with counting power, usually introduced via generalized quantifiers. Most known expressivityy bounds are based on the fact that counting extensions of first-order logic preserve the locality properties. This article has three main goals. First, we introduce a new logic L*∞w (C) that plays the same role for counting asLw∞w does for recursion—it subsumes a number of extensions of first-order logic with counting, and has nice properties that make it easy to study. Second, we give simple direct proof thatLw∞w (C) expresses only local properties: those that depend on the properties of small neighborhoods, but cannot grasp a structure as a whole. This is a general way of saying that a logic lacks a recursion mechanism. Third, we consider a finer analysis of locality of counting logics. In particular, we address the question of how local a logic is, that is, how big are those neighborhoods that local properties depend on. We get a uniform answer for a variety of logics between first-order and L*∞w (C). This is done by introducing a new form of locality that captures the tightest condition that the duplicator needs to maintain in order to win a game. We also use this technique to give bounds on outputs of L*∞w (C)-definable queries.