Linguistics and Philosophy

, Volume 36, Issue 1, pp 1–29

Constraints on the lexicalization of logical operators

Research Article

DOI: 10.1007/s10988-013-9130-8

Cite this article as:
Katzir, R. & Singh, R. Linguist and Philos (2013) 36: 1. doi:10.1007/s10988-013-9130-8


We revisit a typological puzzle due to Horn (Doctoral Dissertation, UCLA, 1972) regarding the lexicalization of logical operators: in instantiations of the traditional square of opposition across categories and languages, the O corner, corresponding to ‘nand’ (= not and), ‘nevery’ (= not every), etc., is never lexicalized. We discuss Horn’s proposal, which involves the interaction of two economy conditions, one that relies on scalar implicatures and one that relies on markedness. We observe that in order to express markedness and to account for a bigger typological puzzle, namely the absence of lexicalizations of ‘XOR’ (= exclusive or), ‘all-or-none’, and many other imaginable logical operators, one must restrict the basic lexicalizable elements to a small set of primitives. We suggest that an ordering based perspective, following Keenan and Faltz (Boolean semantics for natural language, 1985), makes the stipulated primitives that we arrive at more natural. We also propose a modification to Horn’s proposal, based on recent work on implicatures, in which only the implicature condition is operative and in which markedness is part of the definition of the alternatives for scalar implicatures rather than an independent condition.


Logical operators Negation Lexicalization Ordering Scalar implicature Contradiction Markedness 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Linguistics and Sagol School of NeuroscienceTel Aviv UniversityTel AvivIsrael
  2. 2.Institute of Cognitive ScienceCarleton UniversityOttawaCanada

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