Natural Logic and Semantics

  • Lawrence S. Moss
Part of the Lecture Notes in Computer Science book series (LNCS, 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’.

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References

  1. 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. 2.
    van Benthem, J.: Essays in Logical Semantics. Reidel, Dordrecht (1986)Google Scholar
  3. 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. 4.
    Englebretsen, G.: Three Logicians. Van Gorcum, Assen (1981)Google Scholar
  5. 5.
    Fitch, F.B.: Natural Deduction Rules for English. Philosophical Studies 24(2), 89–104 (1973)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Geurts, B.: Reasoning with Quantifiers. Cognition 86, 223–251 (2003)CrossRefGoogle Scholar
  7. 7.
    Grädel, E., Otto, M., Rosen, E.: Undecidability Results on Two-Variable Logics. Archive for Mathematical Logic 38, 313–354 (1999)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Łukasiewicz, J.: Aristotle’s Syllogistic, 2nd edn. Clarendon Press, Oxford (1957)Google Scholar
  9. 9.
    McAllester, D.A., Givan, R.: Natural Language Syntax and First-Order Inference. Artificial Intelligence 56, 1–20 (1992)MATHCrossRefMathSciNetGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 11.
    Moss, L.S.: Syllogistic Logics with Verbs. J Logic Computat 20, 761–793 (2010)Google Scholar
  12. 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. 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)MathSciNetGoogle Scholar
  14. 14.
    Pelletier, F.J.: A Brief History of Natural Deduction. History and Philosophy of Logic 20, 1–31 (1999)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Pratt-Hartmann, I., Moss, L.S.: Logics for the Relational Syllogistic. Review of Symbolic Logic 2(4), 647–683 (2009)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Pratt-Hartmann, I.: A Two-Variable Fragment of English. J. Logic, Language and Information 12(1), 13–45 (2003)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Pratt-Hartmann, I.: Fragments of Language. J. Logic, Language and Information 13, 207–223 (2004)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Pratt-Hartmann, I., Third, A.: More Fragments of Language. Notre Dame J. Formal Logic 47(2) (2006)Google Scholar
  19. 19.
    Purdy, W.C.: A Logic for Natural Language. Notre Dame J. Formal Logic 32(3), 409–425 (1991)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Saanchez Valencia, V.: Studies on Natural Logic and Categorial Grammar. Ph.D. thesis, Univ. of Amsterdam (1991)Google Scholar
  21. 21.
    Sommers, F.: The Logic of Natural Language. Clarendon Press, Oxford (1982)Google Scholar
  22. 22.
    Westerståhl, D.: Aristotelian Syllogisms and Generalized Quantifiers. Studia Logica XLVIII(4), 577–585 (1989)Google Scholar
  23. 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)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Lawrence S. Moss
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

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