Skip to main content

The MSO Logic-Automaton Connection in Linguistics

  • Conference paper
  • First Online:
Logical Aspects of Computational Linguistics (LACL 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1582))

Abstract

In this paper we discuss possible applications of a system which uses automata-based theorem-proving techniques drawing on the decidability proof forweak monadic second-order (MSO) logic on trees to implement linguistic processing and theory verification. Despite a staggering complexity bound, the success of and the continuing work on these techniques in computer science promises a usable tool to test formalizations of grammars. The advantages are readily apparent. The direct use of a succinct and flexible description language together with an environment to test the formalizations with the resulting finite, deterministic tree automata offers a way of combining the needs of both formalization and processing. The aim of this paper is threefold. Firstly we show how to use this technique for the verification of separate modules of a Principles-and-Parameters (P&P) grammar and secondly for the approximation of an entire P&P theory. And thirdly, we extend the language of the MSO tree logic to overcome remaining engineering problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ayari, A., Basin, D. and Podelski, A. (1998). LISA: A specification language based on WS2S, in M. Nielsen and W. Thomas (eds), Computer Science Logic, 11th International Workshop, CSL'97, LNCS 1414, Springer.

    Google Scholar 

  • Basin, D. and Klarlund, N. (To Appear). Automata based symbolic reasoning in hardware verification, The Journal of Formal Methods in Systems Design.

    Google Scholar 

  • Bryant, R. E. (1992). Symbolic boolean manipulation with ordered binary-decision diagrams, ACM Computing Surveys24(3): 293–318.

    Article  MathSciNet  Google Scholar 

  • Büchi, J. R. (1960). Weak second-order arithmetic and finite automata, Zeitschrift für mathematische Logik und Grundlagen der Mathematik6: 66–92.

    Article  MathSciNet  Google Scholar 

  • Doner, J. (1970). Tree acceptors and some of their applications, Journal of Computer and System Sciences4: 406–451.

    Article  MathSciNet  Google Scholar 

  • Frank, R. and Vijay-Shanker, K. (1998). TAG Derivation as Monotonic C-Command, Proceedings of the Fourth Workshop on Tree-Adjoining Grammars and Related Frameworks TAG+98, Philadelphia, PA. (Extended abstract)

    Google Scholar 

  • Gécseg, F. and Steinby, M. (1997). Tree languages, in G. Rozenberg and A. Salomaa (eds), Handbook of Formal Languages: Beyond Words, Vol. 3, Springer, Berlin.

    Google Scholar 

  • Gurevich, Y. (1985). Monadic second-order theories, in J. Barwise and S. Feferman (eds), Model-Theoretic Logics, Springer, Heidelberg, pp. 479–506.

    Google Scholar 

  • Henriksen, J. G., Jensen, J., Jørgensen, M., Klarlund, N., Paige, R., Rauhe, T. and Sandhol, A. (1995). MONA: Monadic second-order logic in practice, in Brinksma et al. (eds), International Workshop TACAS '95, LNCS 1019, Springer, pp. 89–110.

    Google Scholar 

  • Höhfeld, M. and Smolka, G. (1988). Definite relations over constraint languages, LILOG Report 53, IBM Deutschland, Stuttgart, Germany.

    Google Scholar 

  • Johnson, M. (1995). Constraint-based natural language parsing, European Summer School of Logic, Language and Information (ESSLLI '95), Barcelona, Course notes.

    Google Scholar 

  • Kayne, R. S. (1994). The Antisymmetry of Syntax, Vol. 25 of Linguistic Inquiry Monographs, MIT Press, Cambridge, Mass. and London, England.

    Google Scholar 

  • Kelb, P., Margaria, T., Mendler, M. and Gsottberger, C. (1997). Mosel: A flexible toolset for monadic second-order logic, in E. Brinksma (ed), International Workshop TACAS '97, LNCS 1019, Springer, pp. 183–202.

    Google Scholar 

  • Klarlund, N. and Møller, A. (1998). MONA Version 1.2 User Manual, BRICS Notes Series NS-98-3, Department of Computer Science, University of Aarhus.

    Google Scholar 

  • Klarlund, N. and Schwartzbach, M. I. (1997). A domain-specific language for regular sets of strings and trees, Proceedings of the Conference on Domain-Specific Languages, USENIX, Santa Barbara, Ca.

    Google Scholar 

  • Morawietz, F. (To appear). Monadic second order logic, tree automata and constraint logic programming, in H.-P. Kolb and U. Mönnich (eds), The Mathematics of Syntactic Structure, Mouton de Gruyter.

    Google Scholar 

  • Morawietz, F. and Cornell, T. L. (1997). Representing constraints with automata, Proceedings of the 35th Annual Meeting of the ACL andt he 8th Conference of the EACL, Madrid, Spain, pp. 468–475.

    Google Scholar 

  • Niehren, J. and Podelski, A. (1992). Feature automata and recognizable sets of feature trees, in M.-C. Gaudel and J.-P. Jouannaud (eds), Proceedings of the 4th International Joint Conference on Theory and Practice of Software Development, Springer, LNCS 668, Orsay, France, pp. 356–375.

    Google Scholar 

  • Rabin, M. O. (1969). Decidability of second-order theories and automata on infinite trees, Transactions of the American Mathematical Society 141: 1–35.

    MathSciNet  MATH  Google Scholar 

  • Rizzi, L. (1990). Relativized Minimality, MIT Press.

    Google Scholar 

  • Roche, E. and Schabes, Y. (1997). Introduction to finite-state devices in natural language processing, in E. Roche and Y. Schabes (eds), Finite-State Language Processing, Language, Speech, and Communication Series, MIT Press.

    Google Scholar 

  • Rogers, J. (To appear). A Descriptive Approach to Language-Theoretic Complexity, Studies in Logic, Language and Information, CSLI Publications.

    Google Scholar 

  • Stabler, E. (1994). The finite connectivity of linguistic structure, in C. Clifton et al. (eds), Perspectives on Sentence Processing, Lawrence Erlbaum, New Jersey.

    Google Scholar 

  • Thatcher, J. W. and Wright, J. B. (1968). Generalized finite automata theory with an application to a decision problem of second-order logic, Mathematical Systems Theory2(1): 57–81.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Morawietz, F., Cornell, T. (1999). The MSO Logic-Automaton Connection in Linguistics. In: Lecomte, A., Lamarche, F., Perrier, G. (eds) Logical Aspects of Computational Linguistics. LACL 1997. Lecture Notes in Computer Science(), vol 1582. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48975-4_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-48975-4_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65751-4

  • Online ISBN: 978-3-540-48975-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics