Term Negation in First Order logic

0505127 - ÚI 2020 RIV BE eng J - Článek v odborném periodiku
Sedlár, Igor - Šebela, K.
Term Negation in First Order logic.
Logique et Analyse. Roč. 62, č. 247 (2019), s. 265-284. ISSN 0024-5836
GRANT EU: European Commission(XE) 689176 - SYSMICS
Grant ostatní: AV ČR(CZ) JSPS-16-08
Program: Bilaterální spolupráce
Institucionální podpora: RVO:67985807
Klíčová slova: Aristotle * Contraries * Contraposition * Law of Excluded Middle * Negation * Term negation
Obor OECD: Pure mathematics
Způsob publikování: Omezený přístup
http://dx.doi.org/10.2143/LEA.247.0.3287264

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.
Trvalý link: http://hdl.handle.net/11104/0296650