Term Negation in First Order logic

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/61989592:15210/19:73600912

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Term Negation in First Order logic

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Term Negation in First Order logic

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Logique et Analyse

ISSN

0024-5836

e-ISSN

—

Svazek periodika

62

Číslo periodika v rámci svazku

247

Stát vydavatele periodika

BE - Belgické království

Počet stran výsledku

20

Strana od-do

265-284

Kód UT WoS článku

000518710900003

EID výsledku v databázi Scopus

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