Logic Reduced To Bare (Proof-Theoretical) Bones
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Logic Reduced To Bare (Proof-Theoretical) Bones
Original language description
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
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
AA - Philosophy and religion
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Logic, Language, and Information
ISSN
0925-8531
e-ISSN
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Volume of the periodical
24
Issue of the periodical within the volume
2
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
17
Pages from-to
193-209
UT code for WoS article
000355693100004
EID of the result in the Scopus database
2-s2.0-84939969396