How Much Propositional Logic Suffices for Rosser's Undecidability Theorem?

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

How Much Propositional Logic Suffices for Rosser's Undecidability Theorem?

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

How Much Propositional Logic Suffices for Rosser's Undecidability Theorem?

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA17-04630S" target="_blank" >GA17-04630S: Predikátové škálované logiky a jejich aplikace v informatice</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Review of Symbolic Logic

ISSN

1755-0203

e-ISSN

1755-0211

Svazek periodika

15

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

18

Strana od-do

487-504

Kód UT WoS článku

000797598200010

EID výsledku v databázi Scopus

2-s2.0-85091839606