Journal of the ACM (JACM)
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Proceedings of the 30th IEEE symposium on Foundations of computer science
Finite model theory and finite variable logics
Finite model theory and finite variable logics
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
A relational model of data for large shared data banks
Communications of the ACM
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Syntax vs. Semantics on Finite Structures
Structures in Logic and Computer Science, A Selection of Essays in Honor of Andrzej Ehrenfeucht
On Vertex Ranking for Permutations and Other Graphs
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Preservation Theorems in Finite Model Theory
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Homomorphism Closed vs. Existential Positive
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
On the order of countable graphs
European Journal of Combinatorics
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
On Digraph Coloring Problems and Treewidth Duality
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Existential Positive Types and Preservation under Homomorphisisms
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
On preservation under homomorphisms and unions of conjunctive queries
Journal of the ACM (JACM)
Tree-depth, subgraph coloring and homomorphism bounds
European Journal of Combinatorics
Grad and classes with bounded expansion I. Decompositions
European Journal of Combinatorics
From Hilbert's program to a logic tool box
Annals of Mathematics and Artificial Intelligence
Homomorphism preservation on quasi-wide classes
Journal of Computer and System Sciences
European Journal of Combinatorics
Incomplete information and certain answers in general data models
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Extension Preservation Theorems on Classes of Acyclic Finite Structures
SIAM Journal on Computing
Local transformations and conjunctive-query equivalence
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Datalog and constraint satisfaction with infinite templates
Journal of Computer and System Sciences
Datalog: a perspective and the potential
Datalog 2.0'12 Proceedings of the Second international conference on Datalog in Academia and Industry
Ontology-based access to probabilistic data with OWL QL
ISWC'12 Proceedings of the 11th international conference on The Semantic Web - Volume Part I
When is naive evaluation possible?
Proceedings of the 32nd symposium on Principles of database systems
Ontology-based data access: a study through disjunctive datalog, CSP, and MMSNP
Proceedings of the 32nd symposium on Principles of database systems
Graph partitions with prescribed patterns
European Journal of Combinatorics
First-order rewritability of atomic queries in horn description logics
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
On the complexity of existential positive queries
ACM Transactions on Computational Logic (TOCL)
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The homomorphism preservation theorem (h.p.t.), a result in classical model theory, states that a first-order formula is preserved under homomorphisms on all structures (finite and infinite) if and only if it is equivalent to an existential-positive formula. Answering a long-standing question in finite model theory, we prove that the h.p.t. remains valid when restricted to finite structures (unlike many other classical preservation theorems, including the Łoś--Tarski theorem and Lyndon's positivity theorem). Applications of this result extend to constraint satisfaction problems and to database theory via a correspondence between existential-positive formulas and unions of conjunctive queries. A further result of this article strengthens the classical h.p.t.: we show that a first-order formula is preserved under homomorphisms on all structures if and only if it is equivalent to an existential-positive formula of equal quantifier-rank.