Undecidability results on two-variable logics

Archive for Mathematical Logic

Volumn 38, Issue 4-5, 1999, Pages 313-354

  Grädel, Erich ^a   Otto, Martin ^a   Rosen, Eric ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040714484     PISSN: 09335846     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001530050130     Document Type: Article

References (39)

1. F. Baader, H. Bürckert, B. Hollunder, A. Laux, W. Nutt, Terminologische Logiken, KI, 3/92 (1992), pp. 23-33.
2. R. Berger, The undecidability of the domino problem, Mem. AMS 66 (1966).
3. E. Börger, E. Grädel, Y. Gurevich, The Classical Decision Problem, Springer, 1997.
4. A. Borgida, On the relative expressiveness of description logics and predicate logics, Artificial Intelligence 82 (1996), 353-367.
5. H.-D. Ebbinghaus, Extended logics: The general framework, in: Model-Theoretic Logics, J. Barwise, S. Feferman, eds., Springer, 1985, pp. 25-76.
6. H.-D. Ebbinghaus, J. Flum, Finite Model Theory, Springer, 1995.
7. A. Ehrenfeucht, Decidability of the theory of one function, Notices of the AMS 6 (1959), 268.
8. E. Emerson, J. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, Journal of Computer and System Sciences 30 (1985), 1-24.
9. M. Fürer, The computational complexity of the unconstrained limited domino problem (with implications for logical decision problems), in Logic and Machines: Decision Problems and Complexity, Lecture Notes in Computer Science No. 171, Springer, 1984, pp. 312-319.
10. E. Grädel, Dominoes and the complexity of subclasses of logical theories, Annals of Pure and Applied Logic 43 (1989), 1-30.
11. E. Grädel, On transitive closure logic, in Proceedings of 5th Workshop on Computer Science Logic CSL '91, Bern 1991, Lecture Notes in Computer Science No. 626, Springer, 1991, pp. 149-163.
12. E. Grädel, P. Kolaitis, M. Vardi, On the decision problem for two-variable first-order logic, Bulletin of Symbolic Logic 3 (1997), 53-69.
13. E. Grädel, G. McColm, On the power of deterministic transitive closures, Information and Computation 119 (1995), 129-135.
14. E. Grädel, M. Otto, Inductive definability with counting on finite structures, in Proceedings of 6th Workshop on Computer Science Logic CSL '92, San Miniato 1992, Selected Papers, Lecture Notes in Computer Science No. 702, Springer, 1993, pp. 231-247.
15. E. Grädel, M. Otto, E. Rosen, Two-variable logic with counting is decidable, in Proceedings of 12th IEEE Symposium on Logic in Computer Science LICS '97, Warsaw 1997, pp. 306-317.
16. Y. Gurevich, The decision problem for standard classes, Journal of Symbolic Logic41 (1976), 460-464.
17. Y. Gurevich, I. Koryakov, Remarks on Berger's paper on the domino problem, Siberian Math. Journal 13 (1972), 319-321.
18. Y. Gurevich, S. Shelah, Fixed-point extensions of first-order logic, Annals of Pure and Applied Logic 32 (1986), 265-280.
19. D. Harel, Recurring dominoes: Making the highly undecidable highly understandable, Annals of Discrete Mathematics 24 (1985), 51-72.
20. D. Harel, Effective transformations on infinite trees, with applications to high undecidability, dominoes and fairness, Journal of the ACM 33 (1986), 224-248.
21. K. Härtig, Über einen Quantifikator mit zwei Wirkungsbereichen, in Colloquium on the foundations of mathematics, mathematical machines and their applications, L. Kalmár, ed., Akadémiai Kiadó, Budapest, 1962, pp. 31-36.
22. K. Heidler, Untersuchungen zur Reduktionstheorie des Entscheidungsproblems in der Prädikaten- und Termlogik, PhD thesis, Universität Freiburg, 1973.
23. H. Hermes, Term logic with choice operator, Springer Lecture Notes in Mathematics No. 6 (2nd ed.), 1970.
24. H. Herre, M. Krynicki, A. Pinus, J. Väänänen, The Härtig quantifier: a survey, Journal of Symbolic Logic 56 (1991), 1153-1183.
25. N. Immerman, Relational queries computable in polynomial time, Information and Control 68 (1986), 86-104.
26. N. Immerman, Languages that capture complexity classes, SIAM Journal of Computing 16 (1987), 760-778.
27. N. Immerman, M. Vardi, Model Checking and Transitive Closure Logic, in Proc. 9th Conf. on Computer-Aided Verification CAV '97, Lecture Notes in Computer Science No. 1254, Springer, 1997, pp. 258-272.
28. A. Kahr, E. Moore, H. Wang, Entscheidungsproblem reduced to the ∀∃∀ case, Proc. Nat. Acad. Sci. USA 48 (1962), 365-377.
29. D. Kozen, A finite model theorem for the propositional μ-calculus, Studia Logica 47 (1987), 233-241.
30. D. Kozen, R. Parikh, A decision procedure for the prepositional μ-calculus, in Logics of Programs, E. Clarke, D. Kozen, eds., Lecture Notes in Computer Science No. 164, Springer, 1984, pp. 313-325.
31. A. Leisenring, Mathematical logic and Hilbert's ε-symbol, Gordon & Breach, New York, 1969.
32. H. Lewis, Complexity Results for Classes of Quantificational Formulas, Journal of Computer and System Sciences 21 (1980), 317-353.
33. E. López-Escobar, On denning well-orderings, Fund. Math. 59 (1966), 13-21.
34. M. Mortimer, On languages with two variables, Zeitschr. f. math. Logik u. Grundlagen d. Math. 21 (1975), 135-140.
35. M. Otto, Bounded variable logics and counting - a study in finite models, Lecture Notes in Logic No. 9, Springer, 1997.
36. M. Rabin, Decidability of second-order theories and automata on infinite trees, Trans. Amer. Math. Soc. 141 (1969), 1-35.
37. B. Trakhtenbrot, On recursive separability, Dokl. Akad. Nauk SSSR 88 (1953), 953-955. In Russian.
38. M. Vardi, The complexity of relational query languages, in Proc. 14th ACM Symp. on Theory of Computing, 1982, pp. 137-146.
39. M. Vardi, Why is modal logic so robustly decidable, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 31, American Math. Society, 1997, 149-184.