Term Negation in First Order logic

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F19%3A00505127" target="_blank" >RIV/67985807:_____/19:00505127 - isvavai.cz</a>

Alternative codes found

RIV/61989592:15210/19:73600912

Result on the web

<a href="http://dx.doi.org/10.2143/LEA.247.0.3287264" target="_blank" >http://dx.doi.org/10.2143/LEA.247.0.3287264</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2143/LEA.247.0.3287264" target="_blank" >10.2143/LEA.247.0.3287264</a>

Result language

angličtina

Original language name

Term Negation in First Order logic

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Logique et Analyse

ISSN

0024-5836

e-ISSN

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Volume of the periodical

62

Issue of the periodical within the volume

247

Country of publishing house

BE - BELGIUM

Number of pages

20

Pages from-to

265-284

UT code for WoS article

000518710900003

EID of the result in the Scopus database

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