The Non-Boolean Logic of Natural Language Negation
Marie La Palme Reyes, John Macnamara, Gonzalo E. Reyes, Houman Zolfaghari · Philosophia Mathematica · 1994
Since antiquity two different negations in natural languages have been noted: predicate negation (not honest) and predicate term negation (dishonest). The extensive literature offers no models. We propose category-theoretic models with two distinct negation operators, neither of them in general Boolean. We study combinations of the two (not dishonest) and sentential counterparts of each. We emphasize the relevance of our work for the theory of cognition.