Finite Model Theory and Its Applications

Unifying Themes in Finite Model Theory.- On the Expressive Power of Logics on Finite Models.- Finite Model Theory and Descriptive Complexity.- Logic and Random Structures.- Embedded Finite Models and Constraint Databases.- A Logical Approach to Constraint Satisfaction.- Local Variations on a Loose Theme: Modal Logic and Decidability.

[1]  A. Pillay,et al.  Definable sets in ordered structures , 1984 .

[2]  Jörg Flum,et al.  Pseudo-finite homogeneity and saturation , 1999, Journal of Symbolic Logic.

[3]  Jan Van den Bussche,et al.  On Capturing First-Order Topological Properties of Planar Spatial Databases , 1999, ICDT.

[4]  Michael Sipser,et al.  Parity, circuits, and the polynomial-time hierarchy , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[5]  Victor Vianu,et al.  Topological Queries in Spatial Databases , 1999, CSL.

[6]  Olivier Chapuis,et al.  Definability of Geometric Properties in Algebraically Closed Fields , 1999, Math. Log. Q..

[7]  Achim Blumensath,et al.  Automatic structures , 2000, Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332).

[8]  Herbert B. Enderton,et al.  A mathematical introduction to logic , 1972 .

[9]  Michael Benedikt,et al.  Aggregate Operators in Constraint Query Languages , 2002, J. Comput. Syst. Sci..

[10]  Richard Hull,et al.  The Format Model: A Theory of database Organization , 1984, J. ACM.

[11]  Miklós Ajtai,et al.  ∑11-Formulae on finite structures , 1983, Ann. Pure Appl. Log..

[12]  David Harel,et al.  Towards a theory of Recursive Structures , 1998, Computer Science Today.

[13]  Saharon Shelah,et al.  Definability by Constant-Depth Polynomial-Size Circuits , 1986, Inf. Control..

[14]  Jianwen Su,et al.  Queries with Arithmetical Constraints , 1997, Theor. Comput. Sci..

[15]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[16]  J. Risler,et al.  Real algebraic and semi-algebraic sets , 1990 .

[17]  Michael A. Taitslin,et al.  Linear vs. order constraint queries over rational databases (extended abstract) , 1996, PODS.

[18]  B. F. Caviness,et al.  Quantifier Elimination and Cylindrical Algebraic Decomposition , 2004, Texts and Monographs in Symbolic Computation.

[19]  Jan Van den Bussche,et al.  First-Order Queries on Finite Structures Over the Reals , 1998, SIAM J. Comput..

[20]  Michael C. Laskowski,et al.  Vapnik-Chervonenkis classes of definable sets , 1992 .

[21]  Jörg Flum,et al.  Finite model theory , 1995, Perspectives in Mathematical Logic.

[22]  Stephan Kreutzer,et al.  Descriptive Complexity Theory for Constraint Databases , 1999, CSL.

[23]  Gabriel M. Kuper,et al.  Tractable Recursion over Geometric Data , 1997, CP.

[24]  Michael Benedikt,et al.  Relational queries over interpreted structures , 2000, JACM.

[25]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[26]  Theodore Andronikos,et al.  On the Expressiveness of Query Languages with Linear Constraints; Capturing Desirable Spatial Properties , 1997, CDB.

[27]  S. Shelah.  Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory , 1971 .

[28]  Moshe Y. Vardi.  The Decision Problem for Database Dependencies , 1981, Inf. Process. Lett..

[29]  Michael A. Taitslin,et al.  Extended Order-Generic Queries , 1999, Ann. Pure Appl. Log..

[30]  B. Poizat.  A Course in Model Theory , 2000 .

[31]  Jan Van den Bussche,et al.  First-Order Queries on Databases Embedded in an Infinite Structure , 1996, Inf. Process. Lett..

[32]  J. Spencer.  Ramsey Theory , 1990 .

[33]  Michael A. Taitslin,et al.  Finite Queries Do Not Have Effective Syntax , 1999, Inf. Comput..

[34]  Gabriel M. Kuper,et al.  Constraint Databases , 2010, Springer Berlin Heidelberg.

[35]  Gabriel M. Kuper,et al.  Constraint Query Languages , 1995, J. Comput. Syst. Sci..

[36]  Marie-Françoise Roy,et al.  Real algebraic geometry , 1992 .

[37]  Michael Benedikt,et al.  Safe Constraint Queries , 2000, SIAM J. Comput..

[38]  Charles Steinhorn,et al.  Tame Topology and O-Minimal Structures , 2008 .

[39]  Yoram Hirshfeld,et al.  On first order database query languages , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

[40]  Oscar H. Ibarra,et al.  A Technique for Proving Decidability of Containment and Equivalence of Linear Constraint Queries , 1999, J. Comput. Syst. Sci..

[41]  R. Tijdeman,et al.  The Number of Solutions of Diophantine Equations , 2022 .

[42]  Yuri Gurevich,et al.  Metafinite Model Theory , 1994, Inf. Comput..

[43]  N. S. Barnett,et al.  Private communication , 1969 .

[44]  Peter Z. Revesz,et al.  Safe query languages for constraint databases , 1998, TODS.

[45]  David Harel,et al.  Computable Queries for Relational Data Bases , 1980, J. Comput. Syst. Sci..

[46]  A. Wilkie.  Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function , 1996 .

[47]  Martin Grohe,et al.  On first-order topological queries , 2002, TOCL.

[48]  Michael Benedikt,et al.  Reachability and connectivity queries in constraint databases , 2003, J. Comput. Syst. Sci..

[49]  Pascal Koiran,et al.  Approximating the volume of definable sets , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[50]  Marek Karpinski,et al.  Approximating the Volume of General Pfaffian Bodies , 1997, Structures in Logic and Computer Science.

[51]  Victor Vianu,et al.  Querying spatial databases via topological invariants , 1998, J. Comput. Syst. Sci..

[52]  C. Michaux,et al.  LOGIC AND p-RECOGNIZABLE SETS OF INTEGERS , 1994 .

[53]  H. Jerome Keisler,et al.  Definability over Linear Constraints , 2000, CSL.

[54]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[55]  Marc Gyssens,et al.  An expressive language for linear spatial database queries , 1998, J. Comput. Syst. Sci..

[56]  Michael A. Taitslin,et al.  Safe stratified Datalog with integer order does not have syntax , 1998, TODS.

[57]  Marc Gyssens,et al.  On the expressiveness of linear-constraint query languages for spatial databases , 2001, Theor. Comput. Sci..

[58]  Yuri Gurevich,et al.  Toward logic tailored for computational complexity , 1984 .

[59]  L. van den Dries,et al.  Tame Topology and O-minimal Structures , 1998 .

[60]  Anand Pillay,et al.  Model theory of fields , 1996 .

[61]  Jennifer Widom,et al.  A First Course in Database Systems , 1997 .

[62]  Saugata Basu,et al.  New results on quantifier elimination over real closed fields and applications to constraint databases , 1999, JACM.

[63]  Michael Benedikt,et al.  On the structure of queries in constraint query languages , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[64]  Michael Benedikt,et al.  Stability theory, permutations of indiscernibles, and embedded finite models , 2000 .

[65]  Neil Immerman,et al.  Descriptive Complexity , 1999, Graduate Texts in Computer Science.

[66]  Martin Anthony,et al.  Computational Learning Theory , 1992 .

[67]  L. Dries.  Remarks on Tarski's problem concerning (R, +, *, exp) , 1984 .

[68]  Richard Hull,et al.  Safety and translation of calculus queries with scalar functions , 1993, PODS.

[69]  David Haussler,et al.  Learnability and the Vapnik-Chervonenkis dimension , 1989, JACM.

[70]  A. K. Ailamazyan,et al.  Reduction of a relational model with infinite domains to the finite-domain case , 1986 .

[71]  Robert Blackett,et al.  Section 1 , 2007, Developing Self and Self-Concepts in Early Childhood Education and Beyond.

[72]  Thomas Schwentick,et al.  String operations in query languages , 2001, PODS '01.

[73]  Jianwen Su,et al.  Domain independence and the relational calculus , 1994, Acta Informatica.

[74]  Marc Gyssens,et al.  On the decidability of semi-linearity for semi-algebraic sets and its implications for spatial databases (extended abstract) , 1997, PODS '97.

[75]  Anil Nerode,et al.  Automatic Presentations of Structures , 1994, LCC.

[76]  Jan Van den Bussche,et al.  Topological elementary equivalence of closed semi-algebraic sets in the real plane , 2000, Journal of Symbolic Logic.

[77]  Thomas Schwentick,et al.  A model-theoretic approach to regular string relations , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[78]  Leonid Libkin,et al.  Elements of Finite Model Theory , 2004, Texts in Theoretical Computer Science.