Journal of Philosophical Logic

, Volume 46, Issue 1, pp 65–95 | Cite as

Same Same But Different: An Alphabetically Innocent Compositional Predicate Logic

  • Udo Klein
  • Wolfgang Sternefeld



Compositionality is at the heart of model theoretical semantics and its application to the semantics of natural language. As has become standard practice, linguists translate a fragment of English into an intensional extension of classical predicate logic (PL). Yet, somewhat ironically and strangely, PL itself is not compositional, because the standard truth conditions for quantificational statements are not a function of the denotations of its parts but depend on value assignments for variables. This kind of dependence on value assignments leads to non-compositionality as will be demonstrated explicitly in Section 1.2. One could, as is well-known, remedy this awkwardness by considering not truth values as denotations of formulas but sets of value assignments for variables. As we will show in Section 1.3, such a semantics is compositional but not “alphabetically invariant” (or “innocent”). In this article we will formulate a compositional extension of PL that...


Free Variable Semantic Feature Predicate Logic Semantic Role Assignment Function 
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  1. 1.
    de Bruijn, N.G. (1972). Lambda Calculus notation with nameless dummies, a tool for automatic formula manipulation with application to the Church-Rosser theorem. Indagationes Mathematicae, 34, 381–392.CrossRefGoogle Scholar
  2. 2.
    Fine, K. (2007). Semantic relationism. Oxford: Blackwell.CrossRefGoogle Scholar
  3. 3.
    Heim, I., & Kratzer, A. (1998). Semantics in generative grammar. Oxford: Blackwell.Google Scholar
  4. 4.
    Henkin, L., & Tarski, A. (1961). Cylindric algebras. In Dilworth, R. (Ed.) Lattice theory, proceedings symposium in pure mathematics, (Vol. 2 p. 83113). Providence: American Mathematical Society.Google Scholar
  5. 5.
    Jacobson, P. (1999). Towards a variable free semantics. Linguistics and Philosophy, 22, 117–185.CrossRefGoogle Scholar
  6. 6.
    Jacobson, P. (2007). Direct compositionality and variable-free semantics. In Barker, C., & Jacobson, P. (Eds.) Direct compositionality (pp. 191–236). Oxford: Oxford University Press.Google Scholar
  7. 7.
    Kracht, M. (2007). The emergence of syntactic structure. Linguistics and Philosophy, 30, 47–95.CrossRefGoogle Scholar
  8. 8.
    Kracht, M. (2011). Lectures on interpreted languages and compositionality. Berlin: Springer.CrossRefGoogle Scholar
  9. 9.
    Mahler, T. (1993). Morphogrammatik. Eine Einführung in die Theorie der logischen Form.
  10. 10.
    Mendelson, E. (1963). Introduction to mathematical logic. Princeton: Van Nostrand.Google Scholar
  11. 11.
    Montague, R. (1973). The proper treatment of quantification in ordinary english. In Hintikka, J., & Suppes, P. (Eds.) Approaches to natural language (pp. 221–242). Dordrecht: Reidel.CrossRefGoogle Scholar
  12. 12.
    Montague, R. (1974). Formal philosophy. Selected papers of Richard Montague. In Thomason, R.H. (Ed.) New Haven/London: Yale University Press.Google Scholar
  13. 13.
    Quine, W.V.O. (1960). Variables explained away. Proceedings of the American Philosophical Association, 140, 343–347.Google Scholar
  14. 14.
    Zimmermann, T.E., & Sternefeld, W. (2013). Introduction to semantics an essential guide to the composition of meaning. Berlin: De Gruyter Mouton.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.PITSS GmbHBielefeldGermany
  2. 2.Uni TübingenSeminar für Allgemeine SprachwissenschaftTübingenGermany

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