In Istvan Kenesei & Peter Siptar (eds.), Approaches to Hungarian, Vol. 8. Univ. of Szeged (2002)

Anna Szabolcsi
New York University
The de Morgan laws characterize how negation, conjunction, and disjunction interact with each other. They are fundamental in any semantics that bases itself on the propositional calculus/Boolean algebra. This paper is primarily concerned with the second law. In English, its validity is easy to demonstrate using linguistic examples. Consider the following: (3) Why is it so cold in here? We didn’t close the door or the window. The second sentence is ambiguous. It may mean that I suppose we did not close the door or did not close the window, but I am not sure which. This `I am not sure which’ reading is irrelevant to us because it has disjunction scoping over negation. But the sentence may equally well mean (and indeed this is the preferred reading) that we didn’t close the door and did not close the window. This `neither’ reading bears out de Morgan law (2).
Keywords de Morgan  positive polarity  disjunction
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Positive Polarity - Negative Polarity.Anna Szabolcsi - 2004 - Natural Language and Linguistic Theory 22 (2):409-452..
Varieties of Sobel sequences.Michela Ippolito - 2020 - Linguistics and Philosophy 43 (6):633-671.
Disjunction.Ray Jennings - 2008 - Stanford Encyclopedia of Philosophy.

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