Reductio ad Contradictionem: An Algebraic Perspective
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F16%3A00454996" target="_blank" >RIV/67985807:_____/16:00454996 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11225-015-9645-9" target="_blank" >http://dx.doi.org/10.1007/s11225-015-9645-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11225-015-9645-9" target="_blank" >10.1007/s11225-015-9645-9</a>
Alternative languages
Result language
angličtina
Original language name
Reductio ad Contradictionem: An Algebraic Perspective
Original language description
We introduce a novel expansion of the four-valued Belnap–Dunn logic by a unary operator representing reductio ad contradictionem and study its algebraic semantics. This expansion thus contains both the direct, non-inferential negation of the Belnap–Dunn logic and an inferential negation akin to the negation of Johansson’s minimal logic. We formulate a sequent calculus for this logic and introduce the variety of reductio algebras as an algebraic semantics for this calculus. We then investigate some basic algebraic properties of this variety, in particular we show that it is locally finite and has EDPC. We identify the subdirectly irreducible algebras in this variety and describe the lattice of varieties of reductio algebras. In particular, we prove that this lattice contains an interval isomorphic to the lattice of classes of finite non-empty graphs with loops closed under surjective graph homomorphisms.
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
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP202%2F10%2F1826" target="_blank" >GAP202/10/1826: Mathematical Fuzzy Logic in Computer Science</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Studia Logica
ISSN
0039-3215
e-ISSN
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Volume of the periodical
104
Issue of the periodical within the volume
3
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
27
Pages from-to
389-415
UT code for WoS article
000376278900002
EID of the result in the Scopus database
2-s2.0-84953431875