Generalized quantifiers in logic programs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1754, Issue , 1999, Pages 72-98

  Eiter, Thomas ^a   Gottlob, Georg ^a   Veith, Helmut ^a,b  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b Carnegie Mellon University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL LINGUISTICS; LOGIC PROGRAMMING; PHILOSOPHICAL ASPECTS; POLYNOMIALS; RECONFIGURABLE HARDWARE;

EXPRESSIVE POWER; FINITE STRUCTURES; GENERALIZED QUANTIFIERS; LOGICAL FUNCTIONS; NOVEL APPLICATIONS; POLYNOMIAL HIERARCHIES; PROGRAM COMPLEXITY; SECOND-ORDER LOGIC;

COMPUTER CIRCUITS;

EID: 84958974654     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-46583-9_4     Document Type: Conference Paper

References (65)

1. A. Aho and J. Ullman. Universality of Data Retrieval Languages. In Proceedings ACM Symposium on Principles of Programming Languages, pages 110-117, 1979.
2. K. Apt and N. Bol. Logic Programming and Negation: A Survey. Journal of Logic Programming, 19/20:9-71, 1994.
3. A. Badia, M. Gyssens, and D. V. Gucht. Query languages with generalized quantifiers. In R.Ramakrishnan, editor, Applications of Logic Databases, pages 235-258. Kluwer Academic Publishers, 1995.
4. C. Baral and M. Gelfond. Logic Programming and Knowledge Representation. Journal of Logic Programming, 19/20:73-148, 1994.
5. J. Barwise. Some Applications of Henkin Quantifiers. Israel Journal of Mathematics, 25:47-63, 1976.
6. J. Barwise and R. Cooper. Generalized Quantifiers and Natural Language. Linguistic and Philosophy, 4:159-219, 1981.
7. J. Barwise and S. Feferman. Model-Theoretic Logics. Springer, 1985.
8. N. Bidoit. Negation in rule-based database systems: a survey. Theoretical Computer Science, 78:3-83, 1991.
9. A. Blass and Y. Gurevich. Henkin Quantifiers and Complete Problems. Annals of Pure and Applied Logic, 32:1-16, 1986.
10. M. Bugliesi, E. Lamma, and P. Mello. Modularity in Logic Programming. Journal of Logic Programming, 19/20:443-502, 1994
11. E. Dantsin, T. Eiter, G. Gottlob, and A. Voronkov. Complexity and Expressive Power of Logic Programming. In Proceedings of the Twelth IEEE International Conference on Computational Complexity (CCC '97), pages 82-101, 1997.
12. A. Dawar, G. Gottlob, and L. Hella. Capturing Relativized Complexity Classes without Order. Mathematical Logic Quarterly, 15:109-122, 1998.
13. H.-D. Ebbinghaus and J. Flum. Finite Model Theory. Perspectives in Mathematical Logic. Springer, 1995.
14. T. Eiter and G. Gottlob. Expressiveness of Stable Model Semantics for Disjunctive Logic Programs with Functions. Journal of Logic Programming, 33(2):167-178, 1997.
15. T. Eiter, G. Gottlob, and H. Mannila. Disjunctive Datalog. ACM Transactions on Database Systems, 22(3):364-417, September 1997.
16. T. Eiter, G. Gottlob, and H. Veith. Modular Logic Programming and Generalized Quantifiers. In J. Dix, U. Furbach, and A. Nerode, editors, Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-97), number 1265 in LNCS, pages 290-309. Springer, 1997.
17. T. Eiter, G. Gottlob, and H. Veith. Modular Logic Programming and Generalized Quantifiers. Technical Report CD-TR 97/111, Christian Doppler Laboratory for Expert Systems, TU Vienna, January 1997. Preliminary Report.
18. H. Enderton. Finite Partially-Ordered Quantifiers. Zeitschrift f¨ur Mathematische Logik und Grundlagen der Mathematik, 16:393-397, 1970.
19. M. Fitting. Enumeration Operators and Modular Logic Programming. Journal of Logic Programming, 4:11-21, 1987.
20. M. Garey and D. S. Johnson. Computers and Intractability - A Guide to the Theory of NP-Completeness. W. H. Freeman, New York, 1979.
21. M. Gelfond and V. Lifschitz. The Stable Model Semantics for Logic Programming. In Logic Programming: Proceedings Fifth Intl Conference and Symposium, pages 1070-1080, Cambridge, Mass., 1988. MIT Press.
22. G. Gottlob. Relativized Logspace and Generalized Quantifiers over Ordered Finite Structures. Journal of Symbolic Logic, 62(2):545-574, 1997.
23. G. Gottlob, N. Leone, and H. Veith. Second-Order Logic and the Weak Exponential Hierarchies. In J. Wiedermann and P. Hajek, editors, Proceedings of the 20th Conference on Mathematical Foundations of Computer Science (MFCS '95), number 969 in Lecture Notes in Computer Science, pages 66-81, Prague, 1995.
24. G. Gottlob, N. Leone, and H. Veith. Succinctness as a Source of Complexity in Logical Formalisms. Annals of Pure and Applied Logic, 97:231-260, 1999.
25. E. Grädel. Capturing Complexity Classes with Fragments of Second Order Logic. Theoretical Computer Science, 101:35-57, 1992.
26. P. Hfiajek. Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, 1998.
27. L. Henkin. Some Remarks on Infinitely Long Formulas. In Infinitistic Methods, Proc. Symp. on Foundations of Mathematics, pages 167-183. Warsaw, Panstwowe Wydawnictwo Naukowe and Pergamon Press, 1961.
28. J. Hintikka. Quantifiers vs. Quantification Theory. Linguistic Inquiry, 5:153-177, 1974.
29. J. Hintikka. Quantifiers in Logic and Quantifiers in Natural Languages. In S. Körner, editor, Philosophy of Logic, chapter V. Univ. of California Press, Berkeley et al, 1976.
30. N. Immerman. Languages that Capture Complexity Classes. SIAM Journal of Computing, 16:760-778, 1987.
31. N. Immerman. Descriptive Complexity. Springer, 1997.
32. D. S. Johnson. A Catalog of Complexity Classes. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A, chapter 2. Elsevier Science Publishers B.V. (North-Holland), 1990.
33. M. Krynicky and J. Väänänen. Henkin and Function Quantifiers. Annals of Pure and Applied Logic, 43:273-292, 1989.
34. P. Lindström. First Order Predicate Logic with Generalized Quantifiers. Theoria, 32:186-195, 1966.
35. J. Lloyd. Foundations of Logic Programming. Springer, Berlin, 1984, 1987.
36. J. Makowsky. Model Theory and Computer Science: An Appetizer. In S. Abramsky, D. Gabbay, and T. Maibaum, editors, Handbook of Logic in Computer Science, volume 1, chapter 6. Oxford University Press, 1992.
37. J. Makowsky. Capturing Relativized Complexity Classes with Lindström Quantifiers. In W. D. Pauli-Schimanovich, editor, The Foundational Debate, pages 133-140. Kluwer Academic Publishers, 1995.
38. J. Makowsky and Y. Pnueli. Oracles and Quantifiers. In Computer Science Logic 1993 (CSL'93), number 832 in LNCS, pages 189-222. Springer, 1994.
39. J. Makowsky and Y. Pnueli. Computable Quantifiers and Logics over Finite Structures. In M. Krynicki, M. Mostowski, and L. Szczerba, editors, Quantifiers: Logics, Models and Computation, Volume 1, pages 313-357. Kluwer Academic Publishers, 1995.
40. J. Makowsky and Y. Pnueli. Logics Capturing Relativized Complexity Classes Uniformly. In D. Leivant, editor, Proceedings LCC'94, Logic and Computational Complexity, number 960 in LNCS, pages 463-479. Springer, 1995.
41. J. Makowsky and Y. Pnueli. Arity and Alternation in Second-Order Logic. Annals of Pure and Applied Logic, 78:189-202, 1996.
42. D. Miller. A Theory of Modules in Logic Programming. In Proceedings of the International Logic Programming Symposium (ILPS '86), pages 106-114. MIT Press, 1986.
43. R. Montague. In R. Thomasson, editor, Formal Philosophy: Selected Papers. Yale University Press, New Haven, Conn, 1974.
44. A. Mostowski. On a Generalization of Quantifiers. Fundamenta Mathematicae, 44:12-36, 1957.
45. R. O'Keefe. Towards an Algebra for Constructing Logic Programs. In Proceedings of the IEEE Symposium on Logic Programming, pages 152-160. IEEE CS Press, 1985.
46. C. H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.
47. S. Rao, A. Badia, and D. Van Gucht. Processing Queries Containing Generalized Quantifiers. Technical Report TR 428, Computer Science Department, Indiana University, 1996.
48. B. Russell. The Principles of Mathematics. George Allen and Unwin, London, 1903.
49. D. Saccfia. Deterministic and Nondeterministic Stable Model Semantics for Unbound DATALOG Queries. In Proceedings 5th Intl. Conference on Database Theory (ICDT-95), LNCS 893, pages 353-367, January 1995.
50. G. Sandu and J. Väänänen. Partially Ordered Connectives. Zeitschrift f¨ur Mathematische Logik und Grundlagen der Mathematik, 38:361-372, 1992.
51. J. Schlipf. The Expressive Powers of Logic Programming Semantics. Journal of Computer and System Sciences, 51(1):64-86, 1995. Abstract in Proc. PODS 90, pp. 196-204.
52. J. Spivey. The Z Notation: A Reference Manual. Addison Wesley, Harlow, 1992.
53. I. Stewart. Logical Characterizations of Bounded Query Classes I: Logspace Oracle Machines. Fundamenta Informaticae, 18:65-92, 1993.
54. I. Stewart. Logical Characterizations of Bounded Query Classes II: Polynomial-Time Oracle Machines. Fundamenta Informaticae, 18:93-105, 1993.
55. I. Stewart. Incorporating generalized quantifiers and the least fixed point operator. In Proc. Computer Science Logic, number 832 in LNCS, pages 318-333, 1994.
56. I. Stewart. Complete problems for monotone NP. Theoretical Computer Science, 145:147-157, 1995.
57. I. Stewart. Logical Descriptions of monotone NP problems. Journal of Logic and Computation, 4:337-357, 1995.
58. L. J. Stockmeyer. The Polynomial-Time Hierarchy. Theoretical Computer Science, 3:1-22, 1977.
59. J. Väänänen. Generalized Quantifiers, an Introduction. This volume.
60. M. Vardi. Complexity of Relational Query Languages. In Proceedings 14th STOC, pages 137-146, San Francisco, 1982.
61. H. Veith. Succinct Representation, Leaf Languages, and Projection Reductions. Information and Computation, 142(2):207-236, 1998.
62. H. Vollmer. A General Quantifier Concept in Computational Complexity Theory. This volume.
63. K. Wagner. Bounded Query Classes. SIAM Journal of Computing, 19(5):833-846, 1990.
64. W. Walkoe. Finite Partially-Ordered Quantification. Journal of Symbolic Logic, 35:535-555, 1970.
65. J. Wordsworth. Software Engineering with B. Addison Wesley, 1996.