Abstract
I introduce a formal language called the language of informational independence (IL-language, for short) that extends an ordinary first-order language in a natural way. This language is interpreted in terms of semantical games of imperfect information. In this language, one can define two negations: (i) strong or dual negation, and (ii) weak or contradictory negation. The latter negation, unlike the former, can occur only sentence-initially. Then I argue that, to a certain extent, the two negations match the distinction existing in natural languages between sentential and constituent negation. As a corollary, I derive the fact that there are no mechanical rules for forming the contradictory negation of an English sentence.
Similar content being viewed by others
References
Barwise, J.: 1976, ‘Some Applications of the Henkin Quantifiers’,Israel J. of Mathematics 25, 47–63.
Barwise, J.: 1979, ‘On Branching Quantifiers in English’,Journal of Philosophical Logic 8, 47–80.
Hand, M.: 1988, ‘How Game-Theoretical Semantics Works: Classical First-Order Logic’,Erkenntnis 29, 77–93.
Hintikka, J.: 1974, ‘Quantifiers vs. Quantification Theory’,Linguistic Theory 5, 153–77.
Hintikka, J., and J. Kulas: 1983,The Game of Language, Studies in Game Theoretical Semantics and its Applications, D. Reidel, Dordrecht.
Hintikka, J., and J. Kulas: 1985,Anaphora and Definite Descriptions, Two Applications of Game-Theoretical Semantics, D. Reidel, Dordrecht.
Jackendoff, R. S.: 1969, ‘An Interpretative Theory of Negation’,Foundations of Language 5, 214–41.
Klima, E.: 1964, ‘Negation in English’, in J. Fodor and J. Katz (eds.),The Structure of Language, Prentice Hall, Englewood Cliffs, pp. 246–323.
Lakoff, G.: 1969,On Derivational Constraints, Chicago Linguistic Society,5, 117–39.
McCawley, J. D.: 1972, ‘A Program for Logic’, in D. Davidson and G. Harman (eds.),Semantics of Natural Languages, D. Reidel, Dordrecht, pp. 498–544.
Sandu, G.: 1993, ‘On the Logic of Informational Independence and its Applications’,Journal of Philosophical Logic 22, 29–60.
Seuren, P. A. M.: 1984, ‘Operator Lowering’,Linguistics 22, 573–627.
Westerståhl, D.: 1989, ‘Quantifiers in Formal and Natural Languages’, in D. Gabbay and F. Guenthner (eds.),Handbook of Philosophical Logic, Vol. IV, D. Reidel, Dordrecht, pp. 1–131.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sandu, G. Some aspects of negation in English. Synthese 99, 345–360 (1994). https://doi.org/10.1007/BF01063993
Issue Date:
DOI: https://doi.org/10.1007/BF01063993