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Epsilon-logic is more expressive than first-order logic over finite structures

Published online by Cambridge University Press:  12 March 2014

Martin Otto
Martin Otto*
Affiliation:
Department of Computer Science, University of Wales, Swansea, Swansea SA2 8PP, UK, E-mail:m.otto@swan.ac.uk
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Abstract

There are properties of finite structures that are expressible with the use of Hilbert's ∈-operator in a manner that does not depend on the actual interpretation for ∈-terms. but not expressible in plain first-order. This observation strengthens a corresponding result of Gurevich, concerning the invariant use of an auxiliary ordering in first-order logic over finite structures. The present result also implies that certain non-deterministic choice constructs, which have been considered in database theory, properly enhance the expressive power of first-order logic even as far as deterministic queries are concerned, thereby answering a question raised by Abiteboul and Vianu.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 4 , December 2000 , pp. 1749 - 1757
Copyright
Copyright © Association for Symbolic Logic 2000

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References

REFERENCES

[1]Abiteboul, S., Hull, R., and Vianu, V., Foundations of databases, Addison-Wesley, 1995.Google Scholar
[2]Abiteboul, S., Simon, E., and Vianu, V., Non-deterministic languages to express deterministic transformations, Proceedings ofthe 9th ACMsymposium on principles of database systems, 1990, pp. 218–229.Google Scholar
[3]Abiteboul, S. and Vianu, V., Non-determinism in logic-based languages, Annals of Mathematics and Artificial Intelligence, vol. 3 (1991), pp. 151–186.CrossRefGoogle Scholar
[4]Benedikt, M. and Keisler, H., Expressive power of unary counters, Proceedings of the 6th international conference on database theory ICDT 97 (Afrati, F. and Kolaitis, P., editors), LNCS, vol. 1186, Springer-Verlag, 1997, pp. 291–305.CrossRefGoogle Scholar
[5]Blass, A. and Gurevich, Y., Fixed-choice and independent-choice logics, in preparation, 1998.Google Scholar
[6]Cai, J., Fürer, M., and Immerman, N., An optimal lower bound on the number of variables for graph identification, Combinatorica, vol. 12 (1992), pp. 389–410.CrossRefGoogle Scholar
[7]Caicedo, X., Hubert's epsilon-symbol in the presence of generalized quantifiers, Apuntes Matematicos, no. 15, Universidad de los Andes, 1991, also in: Quantifiers: Logics, Models and Computation, vol. 2, (Krynicki, M.et al., editors), Kluwer, 1995, pp. 469–585.Google Scholar
[8]Caicedo, X., Finite model theory and computational complexity, Apuntes Matematicos, no. 32, Universidad de los Andes, 1995.Google Scholar
[9]Chang, C. and Keisler, H., Model theory, North-Holland, 1973.Google Scholar
[10]Ebbinghaus, H.-D. and Flum, J., Finite model theory, Perspectives in Mathematical Logic, Springer Verlag, 1996.Google Scholar
[11]Hella, L., Logical hierarchies in PTIME, Information and Computation, vol. 129 (1996), pp. 1–19.CrossRefGoogle Scholar
[12]Immerman, N., Descriptive complexity, Graduate Texts in Computer Science, Springer Verlag, 1998.Google Scholar
[13]Libkin, L. and Wong, L., Unary quantifiers, transitive closure, and relations of large degree, Proceedings of the symposium on theoretical aspects of computer science STACS 98, LNCS, vol. 1373, Springer, 1998, pp. 183–193.Google Scholar