Classical and Fuzzy Two-Layered Modal Logics for Uncertainty: Translations and Proof-Theory

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F20%3A00531341" target="_blank" >RIV/67985556:_____/20:00531341 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985807:_____/20:00531341

Výsledek na webu

<a href="http://hdl.handle.net/11104/0310016" target="_blank" >http://hdl.handle.net/11104/0310016</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2991/ijcis.d.200703.001" target="_blank" >10.2991/ijcis.d.200703.001</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Classical and Fuzzy Two-Layered Modal Logics for Uncertainty: Translations and Proof-Theory

Popis výsledku v původním jazyce

This paper is a contribution to the study of two distinct kinds of logics for modelling uncertainty. Both approaches use logics with a two-layered modal syntax, but while one employs classical logic on both levels and infinitely-many multimodal operators, the other involves a suitable system of fuzzy logic in the upper layer and only one monadic modality. We take two prominent examples of the former approach, the probability logics Pr_lin and Pr_pol (whose modal operators correspond to all possible linear/polynomial inequalities with integer coefficients), and three prominent logics of the latter approach: Pr^L, Pr^L_triangle and Pr^PL_triangle (given by the Lukasiewicz logic and its expansions by the Baaz-Monteiro projection connective triangle and also by the product conjunction). We describe the relation between the two approaches by giving faithful translations of Pr_lin and Pr_pol into, respectively, Pr^L_triangle and Pr^PL_triangle, and vice versa. We also contribute to the proof theory of two-layered modal logics of uncertainty by introducing a hypersequent calculus for the logic Pr^L. Using this formalism, we obtain a translation of Pr_lin into the logic Pr^L, seen as a logic on hypersequents of relations, and give an alternative proof of the axiomatization of Pr_lin.

Název v anglickém jazyce

Classical and Fuzzy Two-Layered Modal Logics for Uncertainty: Translations and Proof-Theory

Popis výsledku anglicky

This paper is a contribution to the study of two distinct kinds of logics for modelling uncertainty. Both approaches use logics with a two-layered modal syntax, but while one employs classical logic on both levels and infinitely-many multimodal operators, the other involves a suitable system of fuzzy logic in the upper layer and only one monadic modality. We take two prominent examples of the former approach, the probability logics Pr_lin and Pr_pol (whose modal operators correspond to all possible linear/polynomial inequalities with integer coefficients), and three prominent logics of the latter approach: Pr^L, Pr^L_triangle and Pr^PL_triangle (given by the Lukasiewicz logic and its expansions by the Baaz-Monteiro projection connective triangle and also by the product conjunction). We describe the relation between the two approaches by giving faithful translations of Pr_lin and Pr_pol into, respectively, Pr^L_triangle and Pr^PL_triangle, and vice versa. We also contribute to the proof theory of two-layered modal logics of uncertainty by introducing a hypersequent calculus for the logic Pr^L. Using this formalism, we obtain a translation of Pr_lin into the logic Pr^L, seen as a logic on hypersequents of relations, and give an alternative proof of the axiomatization of Pr_lin.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied 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

2020

Kód důvěrnosti údajů

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

Název periodika

International Journal of Computational Intelligence Systems

ISSN

1875-6883

e-ISSN

—

Svazek periodika

13

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

14

Strana od-do

988-1001

Kód UT WoS článku

000565532900046

EID výsledku v databázi Scopus

2-s2.0-85089596847