The non-Boolean logic of natural language negation
Philosophia Mathematica 2 (1):45-68 (1994)
| Abstract | 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. | |||||||||
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Marco Hollenberg (1997). An Equational Axiomatization of Dynamic Negation and Relational Composition. Journal of Logic, Language and Information 6 (4):381-401.
John N. Martin (2003). All Brutes Are Subhuman: Aristotle and Ockham on Private Negation. Synthese 134 (3):429 - 461.
John N. Martin (1995). Existence, Negation, and Abstraction in the Neoplatonic Hierarchy1. History and Philosophy of Logic 16 (2):169-196.
Jaakko Hintikka (2002). Negation in Logic and in Natural Language. Linguistics and Philosophy 25 (5-6):585-600.
Ernesto Napoli (2006). Negation. Grazer Philosophische Studien 72 (1):233-252.
Gabriel Sandu (1994). Some Aspects of Negation in English. Synthese 99 (3):345 - 360.
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