On Strong Standard Completeness in Some MTL-Delta Expansions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00466763" target="_blank" >RIV/67985807:_____/17:00466763 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00500-016-2338-0" target="_blank" >http://dx.doi.org/10.1007/s00500-016-2338-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00500-016-2338-0" target="_blank" >10.1007/s00500-016-2338-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Strong Standard Completeness in Some MTL-Delta Expansions

Popis výsledku v původním jazyce

In this paper, inspired by the previous work of Franco Montagna on infinitary axiomatizations for standard BL-algebras, we focus on a uniform approach to the following problem: given a left-continuous t-norm *, find an axiomatic system (possibly with infinitary rules) which is strongly complete with respect to the standard algebra [0,1]*. This system will be an expansion of Monoidal t-norm-based logic. First, we introduce an infinitary axiomatic system L, expanding the language with Delta and countably many truth constants, and with only one infinitary inference rule, that is inspired in Takeuti–Titani density rule. Then we show that L is indeed strongly complete with respect to the standard algebra [0,1]*. Moreover, the approach is generalized to axiomatize expansions of these logics with additional operators whose intended semantics over [0,1] satisfy some regularity conditions.

Název v anglickém jazyce

On Strong Standard Completeness in Some MTL-Delta Expansions

Popis výsledku anglicky

In this paper, inspired by the previous work of Franco Montagna on infinitary axiomatizations for standard BL-algebras, we focus on a uniform approach to the following problem: given a left-continuous t-norm *, find an axiomatic system (possibly with infinitary rules) which is strongly complete with respect to the standard algebra [0,1]*. This system will be an expansion of Monoidal t-norm-based logic. First, we introduce an infinitary axiomatic system L, expanding the language with Delta and countably many truth constants, and with only one infinitary inference rule, that is inspired in Takeuti–Titani density rule. Then we show that L is indeed strongly complete with respect to the standard algebra [0,1]*. Moreover, the approach is generalized to axiomatize expansions of these logics with additional operators whose intended semantics over [0,1] satisfy some regularity conditions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GF15-34650L" target="_blank" >GF15-34650L: Modelování vágních kvantifikátorů v matematické fuzzy logice</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Soft Computing

ISSN

1432-7643

e-ISSN

—

Svazek periodika

21

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

23

Strana od-do

125-147

Kód UT WoS článku

000392065600012

EID výsledku v databázi Scopus

2-s2.0-84989837588