The Lattice of Super-Belnap Logics
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F23%3A00542368" target="_blank" >RIV/67985807:_____/23:00542368 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S1755020321000204" target="_blank" >http://dx.doi.org/10.1017/S1755020321000204</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S1755020321000204" target="_blank" >10.1017/S1755020321000204</a>
Alternative languages
Result language
angličtina
Original language name
The Lattice of Super-Belnap Logics
Original language description
We study the lattice of extensions of four-valued Belnap-Dunn logic, called super-Belnap logics by analogy with superintuitionistic logics. We describe the global structure of this lattice by splitting it into several subintervals, and prove some new completeness theorems for super-Belnap logics. The crucial technical tool for this purpose will be the so-called antiaxiomatic (or explosive) part operator. The antiaxiomatic (or explosive) extensions of Belnap-Dunn logic turn out to be of particular interest owing to their connection to graph theory: the lattice of finitary antiaxiomatic extensions of Belnap-Dunn logic is isomorphic to the lattice of upsets in the homomorphism order on finite graphs (with loops allowed). In particular, there is a continuum of finitary super Belnap logics. Moreover, a non-finitary super-Belnap logic can be constructed with the help of this isomorphism. As algebraic corollaries we obtain the existence of a continuum of antivarieties of De Morgan algebras and the existence of a prevariety of De Morgan algebras which is not a quasivariety.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Review of Symbolic Logic
ISSN
1755-0203
e-ISSN
1755-0211
Volume of the periodical
16
Issue of the periodical within the volume
1
Country of publishing house
GB - UNITED KINGDOM
Number of pages
50
Pages from-to
114-163
UT code for WoS article
000792356600001
EID of the result in the Scopus database
2-s2.0-85104753444