Term negation in first-order logic

Igor Sedlár, Karel Šebela

Abstract


We provide a formalization of Aristotelian term negation within an extension of classical first-order logic by two predicate operators. The operators represent the range of application of a predicate and the term negation of a predicate, respectively. We discuss several classes of models for the language characterised by various assumptions concerning the interaction between range of application, term negation and Boolean complementation. We show that the discussed classes can be defined by sets of formulas. In our intended class of models, term negation of $P$ corresponds to the complement of $P$ relative to the range of application of $P$. It is an established fact about term negation that it does not satisfy the the principle of Conversion by Contraposition. This seems to be in conflict with the thesis, put forward by Lenzen and Berto, that contraposition is a minimal requirement for an operator to be a proper negation. We show that the arguments put forward in support of this thesis do not apply to term negation.

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