How Much Propositional Logic Suffices for Rosser's Undecidability Theorem?
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00523434" target="_blank" >RIV/67985807:_____/22:00523434 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S175502032000012X" target="_blank" >http://dx.doi.org/10.1017/S175502032000012X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S175502032000012X" target="_blank" >10.1017/S175502032000012X</a>
Alternative languages
Result language
angličtina
Original language name
How Much Propositional Logic Suffices for Rosser's Undecidability Theorem?
Original language description
In this paper we explore the following question: how weak can a logic be for Rosser’s essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson’s Q is essentially undecidable in intuitionistic logic, and P. Hájek proved it in the fuzzy logic BL for Grzegorczyk’s variant of Q which interprets the arithmetic operations as nontotal nonfunctional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much weaker arithmetic theory, a version of Robinson’s R (with arithmetic operations also interpreted as mere relations). Our result is based on a structural version of the undecidability argument introduced by Kleene and we show that it goes well beyond the scope of the Boolean, intuitionistic, or fuzzy logic.
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
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-04630S" target="_blank" >GA17-04630S: Predicate graded logics and their applications to computer science</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
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
15
Issue of the periodical within the volume
2
Country of publishing house
GB - UNITED KINGDOM
Number of pages
18
Pages from-to
487-504
UT code for WoS article
000797598200010
EID of the result in the Scopus database
2-s2.0-85091839606