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  3. Finite and Algorithmic Model Theory
Publisher:
Cambridge University Press
Online publication date:
June 2011
Print publication year:
2011
Online ISBN:
9780511974960
DOI:
https://doi.org/10.1017/CBO9780511974960
Subjects:
Mathematics (general), Mathematics, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
Series:
London Mathematical Society Lecture Note Series (379)
Information

Book description

Intended for researchers and graduate students in theoretical computer science and mathematical logic, this volume contains accessible surveys by leading researchers from areas of current work in logical aspects of computer science, where both finite and infinite model-theoretic methods play an important role. Notably, the articles in this collection emphasize points of contact and connections between finite and infinite model theory in computer science that may suggest new directions for interaction. Among the topics discussed are: algorithmic model theory, descriptive complexity theory, finite model theory, finite variable logic, model checking, model theory for restricted classes of finite structures, and spatial databases. The chapters all include extensive bibliographies facilitating deeper exploration of the literature and further research.

Reviews

"Researchers will find the book useful for referring to theorems on finite model theory. For building models of complicated problems, the book provides a good foundation."
Maulik A. Dave, Computing Reviews

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Contents

Contents
References
Bibliography
Bibliography
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[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.
[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.
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[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.
[15] Ebbinghaus, H.-D., and Flum, J. 1999. Finite Model Theory. 2nd edn. Springer.
[16] Frick, M., and Grohe, M. 2001. Deciding first-order properties of locally tree-decomposable structures. Journal of the ACM, 48, 1184–1206.
[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.
[18] Gottlob, G., Leone, N., and Scarcello, F. 2001. The complexity of acyclic conjunctive queries. Journal of the ACM, 43, 431–498.
[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.
[20] Gottlob, G., Leone, N., and Scarcello, F. 2002b. Hypertree decompositions and tractable queries. Journal of Computer and System Sciences, 64, 579–627.
[21] Grädel, E. 1999. On the restraining power of guards. Journal of Symbolic Logic, 64, 1719–1742.
[22] Grädel, E. 2007. Finite model theory and descriptive complexity. Pages 125–230 of: Finite Model Theory and Its Applications. Springer.
[23] Grädel, E., and Otto, M. 1999. On Logics with Two Variables. Theoretical Computer Science, 224, 73–113.
[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.
[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.
[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.
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[30] Hodges, W. 1993. Model Theory. Cambridge University Press.
[31] Hodkinson, I., and Otto, M. 2003. Finite conformal hypergraph covers and Gaifman cliques in finite structures. Bulletin of Symbolic Logic, 9, 387–405.
[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.
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[35] Kolaitis, P. 2007. On the expressive power of logics on finite models. Pages 27–123 of: Finite Model Theory and Its Applications. Springer.
[36] Kolaitis, P., and Vardi, M. 2000a. Conjunctive-query containment and constraint satisfaction. Journal of Computer and System Sciences, 61, 302–332.
[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.
[38] Kolaitis, P., and Vardi, M. 2007. A logical approach to constraint satisfaction. Pages 339–370 of: Finite Model Theory and Its Applications. Springer.
[39] Kreutzer, S. 2008. Algorithmic Meta-Theorems. In: Esparza, J., Michaux, C., and Steinhorn, C. (eds), Finite and Algorithmic Model Theory. CUP. (this volume).
[40] Lorenz, K. 1968. Dialogspiele als semantische Grundlage von Logikkalkülen. Archiv für Mathematische Logik und Grundlagenforschung, 11, 32–55 and 73–100.
[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.
[42] Otto, M. 2004. Modal and guarded characterisation theorems over finite transition systems. Annals of Pure and Applied Logic, 130, 173–205.
[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.
[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.
[46] Rosen, E. 1997. Modal logic over finite structures. Journal of Logic, Language and Information, 6, 427–439.
[47] Rossman, B. 2008. Homomorphism preservation theorems. Journal of the ACM, 55.
[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.
[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.
[50] Vardi, M. 2006. Games as an algorithmic construct. Tutorial, Isaac Newton Institute workshop on Games and Verification (Logic and Algorithms programme).
[51] Weinstein, S. 2007. Unifying themes in finite model theory. Pages 1–25 of: Finite Model Theory and Its Applications. Springer.

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