Skip to main content

Natural Logic and Semantics

  • Conference paper
Logic, Language and Meaning

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6042))

Abstract

Two of the main motivations for logic and (model-theoretic) semantics overlap in the sense that both subjects are concerned with representing features of natural language meaning and inference. At the same time, the two subjects have other motivations and so are largely separate enterprises. This paper returns to the topic of language and logic, presenting to semanticists natural logic, the study of logics for reasoning with sentences close to their surface form. My goal is to show that the subject already has some results that natural language semanticists might find interesting. At the same time it leads to problems and perspectives that I hope will interest the community. One leading idea is that the target logics for translations should have a decidable validity problem, ruling out first-order logic. I also will present a fairly new result based on the transitivity of comparative adjective phrases that suggests that in addition to ‘meaning postulates’ in semantics, we will also need to posit ‘proof principles’.

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

  1. Ben-Avi, G., Francez, N.: Proof-theoretic Semantics for a Syllogistic Fragment. In: Dekker, P., Franke, M. (eds.) Fifteenth Amsterdam Colloquium. ILLC/Department of Philosophy, U. Amsterdam, pp. 9–15 (2005)

    Google Scholar 

  2. van Benthem, J.: Essays in Logical Semantics. Reidel, Dordrecht (1986)

    Google Scholar 

  3. van Benthem, J.: A Brief History of Natural Logic. In: Chakraborty, M., Löwe, B., Nath Mitra, M., Sarukkai, S. (eds.) Logic, Navya-Nyaya and Applications, Homage to Bimal Krishna Matilal. College Publications, London (2008)

    Google Scholar 

  4. Englebretsen, G.: Three Logicians. Van Gorcum, Assen (1981)

    Google Scholar 

  5. Fitch, F.B.: Natural Deduction Rules for English. Philosophical Studies 24(2), 89–104 (1973)

    Article  MathSciNet  Google Scholar 

  6. Geurts, B.: Reasoning with Quantifiers. Cognition 86, 223–251 (2003)

    Article  Google Scholar 

  7. Grädel, E., Otto, M., Rosen, E.: Undecidability Results on Two-Variable Logics. Archive for Mathematical Logic 38, 313–354 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Łukasiewicz, J.: Aristotle’s Syllogistic, 2nd edn. Clarendon Press, Oxford (1957)

    Google Scholar 

  9. McAllester, D.A., Givan, R.: Natural Language Syntax and First-Order Inference. Artificial Intelligence 56, 1–20 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  10. Moss, L.S.: Completeness Theorems for Syllogistic Fragments. In: Hamm, F., Kepser, S. (eds.) Logics for Linguistic Structures, pp. 143–173. Mouton de Gruyter, Berlin (2008)

    Chapter  Google Scholar 

  11. Moss, L.S.: Syllogistic Logics with Verbs. J Logic Computat 20, 761–793 (2010)

    Google Scholar 

  12. Moss, L.S.: Logics for Two Fragments Beyond the Syllogistic Boundary. In: Blass, A., Dershowitz, N., Reisig, W. (eds.) Studies in Honor of Yuri Gurevich. LNCS. Springer, Heidelberg (2010)

    Google Scholar 

  13. Nishihara, N., Morita, K., Iwata, S.: An Extended Syllogistic System with Verbs and Proper Nouns, and its Completeness Proof. Systems and Computers in Japan 21(1), 760–771 (1990)

    MathSciNet  Google Scholar 

  14. Pelletier, F.J.: A Brief History of Natural Deduction. History and Philosophy of Logic 20, 1–31 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  15. Pratt-Hartmann, I., Moss, L.S.: Logics for the Relational Syllogistic. Review of Symbolic Logic 2(4), 647–683 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  16. Pratt-Hartmann, I.: A Two-Variable Fragment of English. J. Logic, Language and Information 12(1), 13–45 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  17. Pratt-Hartmann, I.: Fragments of Language. J. Logic, Language and Information 13, 207–223 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  18. Pratt-Hartmann, I., Third, A.: More Fragments of Language. Notre Dame J. Formal Logic 47(2) (2006)

    Google Scholar 

  19. Purdy, W.C.: A Logic for Natural Language. Notre Dame J. Formal Logic 32(3), 409–425 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  20. Saanchez Valencia, V.: Studies on Natural Logic and Categorial Grammar. Ph.D. thesis, Univ. of Amsterdam (1991)

    Google Scholar 

  21. Sommers, F.: The Logic of Natural Language. Clarendon Press, Oxford (1982)

    Google Scholar 

  22. Westerståhl, D.: Aristotelian Syllogisms and Generalized Quantifiers. Studia Logica XLVIII(4), 577–585 (1989)

    Google Scholar 

  23. Zamansky, A., Francez, N., Winter, Y.: A Natural Logic Inference System Using the Lambek Calculus. J. Logic, Language and Information 15(3), 273–295 (2006)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Moss, L.S. (2010). Natural Logic and Semantics. In: Aloni, M., Bastiaanse, H., de Jager, T., Schulz, K. (eds) Logic, Language and Meaning. Lecture Notes in Computer Science(), vol 6042. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14287-1_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14287-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14286-4

  • Online ISBN: 978-3-642-14287-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics