[1] Alon, N. 1995. Tools from Higher Algebra. Pages 1749–1783 of: Graham, R., Grötschel, M., and Lovasz, L. (eds), Handbook of Combinatorics, vol. II. North-Holland.Google Scholar

[2] Andréka, H., van Benthem, J., and Németi, I. 1998. Modal Languages and Bounded Fragments of Predicate Logic. Journal of Philosophical Logic, 27, 217–274.CrossRefGoogle Scholar

[3] Atserias, A., Dawar, A., and Grohe, M. 2005. Preservation under extensions on well-behaved finite structures. Pages 1437–1449 of: Proceedings of 32nd International Colloquium on Automata, Languages and Programming ICALP'05. LNCS, vol. 3580.CrossRefGoogle Scholar

[4] Atserias, A., Dawar, A., and Kolaitis, P. 2006. On preservation under homomorphisms and unions of conjunctive queries. Journal of the ACM, 53, 208–237.CrossRefGoogle Scholar

[5] Barany, V., Gottlob, G., and Otto, M. 2010. Querying the guarded fragment. Pages 2–11 of: Proceedings of 25th Annual IEEE Symposium on Logic in Computer Science LICS'10.Google Scholar

[6] Beeri, C., Fagin, R., Maier, D., and Yannakakis, M. 1983. On the desirability of acyclic database schemes. Journal of the ACM, 30, 497–513.CrossRefGoogle Scholar

[7] Berge, C. 1973. Graphs and Hypergraphs. North-Holland.Google Scholar

[8] Berwanger, D., and Grädel, E. 2001. Games and Model Checking for Guarded Logics. Pages 70–84 of: Proceedings of the 8th International Conference on Logic for Programming and Automated Reasoning LPAR'01. LNCS, vol. 2250.Google Scholar

[9] Blackburn, P., de Rijke, M., and Venema, Y. 2001. Modal Logic. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press.CrossRefGoogle Scholar

[10] Blackburn, P., van Benthem, J., and Wolter, F. (eds). 2007. Handbook of Modal Logic. Elsevier.Google Scholar

[11] Chang, C. C., and Keisler, H. J. 1990. Model Theory. North-Holland.Google Scholar

[12] Courcelle, B. 1990. Graph rewriting: An algebraic and logic approach. Pages 194–242 of: van Leeuwen, J. (ed), Handbok of Theoretical Computer Science, volume B. Elsevier.Google Scholar

[13] Dalmau, V., Kolaitis, P., and Vardi, M. 2002. Constraint satisfaction, bounded treewidth, and finite-varaible logics. Pages 310–326 of: Proceedings of 8th International Conference on Constraint Programming. LNCS, vol. 2470.Google Scholar

[14] Dawar, A., and Otto, M. 2009. Modal characterisation theorems over special classes of frames. Annals of Pure and Applied Logic, 161, 1–42. Extended journal version of LICS'05 paper.CrossRefGoogle Scholar

[15] Ebbinghaus, H.-D., and Flum, J. 1999. Finite Model Theory. 2nd edn. Springer.Google Scholar

[16] Frick, M., and Grohe, M. 2001. Deciding first-order properties of locally tree-decomposable structures. Journal of the ACM, 48, 1184–1206.CrossRefGoogle Scholar

[17] Goranko, V., and Otto, M. 2007. Model Theory of Modal Logic. Pages 249–329 of: Blackburn, P., van Benthem, J., and Wolter, F. (eds), Handbook of Modal Logic. Elsevier.CrossRefGoogle Scholar

[18] Gottlob, G., Leone, N., and Scarcello, F. 2001. The complexity of acyclic conjunctive queries. Journal of the ACM, 43, 431–498.CrossRefGoogle Scholar

[19] Gottlob, G., Grädel, E., and Veith, H. 2002a. Datalog LITE: A deductive query language with linear time model checking. ACM Transactions on Computational Logic, 3, 1–35.CrossRefGoogle Scholar

[20] Gottlob, G., Leone, N., and Scarcello, F. 2002b. Hypertree decompositions and tractable queries. Journal of Computer and System Sciences, 64, 579–627.CrossRefGoogle Scholar

[21] Grädel, E. 1999. On the restraining power of guards. Journal of Symbolic Logic, 64, 1719–1742.CrossRefGoogle Scholar

[22] Grädel, E. 2007. Finite model theory and descriptive complexity. Pages 125–230 of: Finite Model Theory and Its Applications. Springer.CrossRefGoogle Scholar

[23] Grädel, E., and Otto, M. 1999. On Logics with Two Variables. Theoretical Computer Science, 224, 73–113.CrossRefGoogle Scholar

[24] Grädel, E., and Walukiewicz, I. 1999. Guarded fixed point logic. Pages 45–54 of: Proceedings of 14th Annual IEEE Symposium on Logic in Computer Science LICS'99.Google Scholar

[25] Grädel, E., Hirsch, C., and Otto, M. 2002. Back and forth between guarded and modal logics. ACM Transactions on Computational Logics, 3, 418–463.CrossRefGoogle Scholar

[26] Grohe, M. 2008. Logic, graphs, and algorithms. Pages 357–422 of: Flum, J., Grädel, E., and Wilke, T. (eds), Logic and Automata, History and Perspectives. Amsterdam University Press.Google Scholar

[27] Herwig, B. 1995. Extending partial isomorphisms on finite structures. Combinatorica, 15, 365–371.CrossRefGoogle Scholar

[28] Herwig, B. 1998. Extending partial isomorphisms for the small index property of many omega-categorical structures. Israel Journal of Mathematics, 107, 93–124.CrossRefGoogle Scholar

[29] Herwig, B., and Lascar, D. 2000. Extending partial isomorphisms and the profinite topology on free groups. Transactions of the AMS, 352, 1985–2021.CrossRefGoogle Scholar

[30] Hodges, W. 1993. Model Theory. Cambridge University Press.CrossRefGoogle Scholar

[31] Hodkinson, I., and Otto, M. 2003. Finite conformal hypergraph covers and Gaifman cliques in finite structures. Bulletin of Symbolic Logic, 9, 387–405.CrossRefGoogle Scholar

[32] Hoogland, E., Marx, M., and Otto, M. 1999. Beth definability for the guarded fragment. In: Gebrandy, J., Marx, M., de Rijke, M., and Venema, Y. (eds), JFAK – Essays Dedicated to Johan van Benthem on the Occasion of his 50th Birthday. Amsterdam University Press. CD-ROM.Google Scholar

[33] Immerman, N. 1998. Decsriptive Complexity. Graduate Texts in Computer Science. Springer.Google Scholar

[34] Janin, D., and Walukiewicz, I. 1996. On the Expressive Completeness of the Propositional mu-Calculus with Respect to Monadic Second Order Logic. Pages 263–277 of: Proceedings of 7th International Conference on Concurrency Theory CONCUR'96. LNCS, vol. 1119.CrossRefGoogle Scholar

[35] Kolaitis, P. 2007. On the expressive power of logics on finite models. Pages 27–123 of: Finite Model Theory and Its Applications. Springer.CrossRefGoogle Scholar

[36] Kolaitis, P., and Vardi, M. 2000a. Conjunctive-query containment and constraint satisfaction. Journal of Computer and System Sciences, 61, 302–332.CrossRefGoogle Scholar

[37] Kolaitis, P., and Vardi, M. 2000b. A game-theoretic approach to constraint satisfaction. Pages 175–181 of: Proceedings of Of 17th Conference on Artificial Intelligence AAAI'00.Google Scholar

[38] Kolaitis, P., and Vardi, M. 2007. A logical approach to constraint satisfaction. Pages 339–370 of: Finite Model Theory and Its Applications. Springer.CrossRefGoogle Scholar

[39] Kreutzer, S. 2008. Algorithmic Meta-Theorems. In: Esparza, J., Michaux, C., and Steinhorn, C. (eds), Finite and Algorithmic Model Theory. CUP. (this volume).Google Scholar

[40] Lorenz, K. 1968. Dialogspiele als semantische Grundlage von Logikkalkülen. Archiv für Mathematische Logik und Grundlagenforschung, 11, 32–55 and 73–100.CrossRefGoogle Scholar

[41] Lorenzen, P. 1961. Ein dialogisches Konstruktivitätskriterium. Pages 193–200 of: Infinitistic Methods, Proceedings of the Symposium on Foundations of Mathematics, Warsaw 1959. Oxford University Press.Google Scholar

[42] Otto, M. 2004. Modal and guarded characterisation theorems over finite transition systems. Annals of Pure and Applied Logic, 130, 173–205.CrossRefGoogle Scholar

[43] Otto, M. 2010a. Highly acyclic groups, hypergraph covers and the guarded fragment. Pages 12–21 of: Proceedings of 25th Annual IEEE Symposium on Logic in Computer Science LICS'10.Google Scholar

[44] Otto, M. 2010b. Highly acyclic groups, hypergraph covers and the guarded fragment. Draft of extended version of LICS 2010 paper.

[45] Rabin, M. 1969. Decidability of second order theories and automata on infinite trees. Transactions of the AMS, 141, 1–35.Google Scholar

[46] Rosen, E. 1997. Modal logic over finite structures. Journal of Logic, Language and Information, 6, 427–439.CrossRefGoogle Scholar

[47] Rossman, B. 2008. Homomorphism preservation theorems. Journal of the ACM, 55.CrossRefGoogle Scholar

[48] Vardi, M. 1995. On the complexity of bounded-variable queries. Pages 266–276 of: Proceedings of 14th Annual ACM Symposium on Principles of Database Systems PODS'95.Google Scholar

[49] Vardi, M. 1997. Why is modal logic so robustly decidable? Pages 149–184 of: Immerman, N., and Kolaitis, P. (eds), Descriptive Complexity and Finite Models. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 31. AMS.CrossRefGoogle Scholar

[50] Vardi, M. 2006. Games as an algorithmic construct. Tutorial, Isaac Newton Institute workshop on Games and Verification (Logic and Algorithms programme).Google Scholar

[51] Weinstein, S. 2007. Unifying themes in finite model theory. Pages 1–25 of: Finite Model Theory and Its Applications. Springer.Google Scholar