Logic Reduced To Bare (Proof-Theoretical) Bones

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F15%3A00444109" target="_blank" >RIV/67985955:_____/15:00444109 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10849-015-9214-7" target="_blank" >http://dx.doi.org/10.1007/s10849-015-9214-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10849-015-9214-7" target="_blank" >10.1007/s10849-015-9214-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Logic Reduced To Bare (Proof-Theoretical) Bones

Popis výsledku v původním jazyce

What is a minimal proof?theoretical foundation of logic? Two different ways to answer this question may appear to offer themselves: reduce the whole of logic either to the relation of inference, or else to the property of incompatibility. The first way would involve defining logical operators in terms of the algebraic properties of the relation of inference?with conjunction A&B as the infimum of A and B, negation A as the minimal incompatible of A, etc. The second way involves introducing logical operators in terms of the relation of incompatibility, such that X is incompatible with {A} iff every Y incompatible with X is incompatible with {A}; and X is incompatible with {A&B} iff X is incompatible with {A,B}; etc. Whereas the first route leads us naturally to intuitionistic logic, the second leads us to classical logic. The aim of this paper is threefold: to investigate the relationship of the two approaches within a very general framework, to discuss the viability of erecting logic on

Název v anglickém jazyce

Logic Reduced To Bare (Proof-Theoretical) Bones

Popis výsledku anglicky

What is a minimal proof?theoretical foundation of logic? Two different ways to answer this question may appear to offer themselves: reduce the whole of logic either to the relation of inference, or else to the property of incompatibility. The first way would involve defining logical operators in terms of the algebraic properties of the relation of inference?with conjunction A&B as the infimum of A and B, negation A as the minimal incompatible of A, etc. The second way involves introducing logical operators in terms of the relation of incompatibility, such that X is incompatible with {A} iff every Y incompatible with X is incompatible with {A}; and X is incompatible with {A&B} iff X is incompatible with {A,B}; etc. Whereas the first route leads us naturally to intuitionistic logic, the second leads us to classical logic. The aim of this paper is threefold: to investigate the relationship of the two approaches within a very general framework, to discuss the viability of erecting logic on

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

AA - Filosofie a náboženství

OECD FORD obor

—

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Journal of Logic, Language, and Information

ISSN

0925-8531

e-ISSN

—

Svazek periodika

24

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

17

Strana od-do

193-209

Kód UT WoS článku

000355693100004

EID výsledku v databázi Scopus

2-s2.0-84939969396