bibtype J - Journal Article
ARLID 0531341
utime 20240103224301.0
mtime 20200731235959.9
SCOPUS 85089596847
WOS 000565532900046
DOI 10.2991/ijcis.d.200703.001
title (primary) (eng) Classical and Fuzzy Two-Layered Modal Logics for Uncertainty: Translations and Proof-Theory
specification
page_count 14 s.
serial
ARLID cav_un_epca*0344498
ISSN 1875-6891
title International Journal of Computational Intelligence Systems
volume_id 13
volume 1 (2020)
page_num 988-1001
publisher
name Springer
keyword Mathematical fuzzy logic
keyword Logics of uncertainty
keyword Łukasiewicz logic
keyword Probability logics
keyword Two-layered modal logics
keyword Hypersequent calculi
author (primary)
ARLID cav_un_auth*0378830
name1 Baldi
name2 P.
country IT
garant K
author
ARLID cav_un_auth*0100737
name1 Cintula
name2 Petr
institution UIVT-O
full_dept (cz) Oddělení teoretické informatiky
full_dept Department of Theoretical Computer Science
full_dept Department of Theoretical Computer Science
fullinstit Ústav informatiky AV ČR, v. v. i.
author
ARLID cav_un_auth*0293476
name1 Noguera
name2 Carles
institution UTIA-B
full_dept (cz) Matematická teorie rozhodování
full_dept Department of Decision Making Theory
department (cz) MTR
department MTR
full_dept Department of Decision Making Theory
fullinstit Ústav teorie informace a automatizace AV ČR, v. v. i.
source
url http://hdl.handle.net/11104/0310016
cas_special
project
project_id GA17-04630S
agency GA ČR
ARLID cav_un_auth*0349495
abstract (eng) 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.
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permalink http://hdl.handle.net/11104/0310016
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mrcbC86 2 Article Computer Science Artificial Intelligence|Computer Science Interdisciplinary Applications
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arlyear 2020
mrcbTft \nSoubory v repozitáři: 0531341-aoa.pdf
mrcbU14 85089596847 SCOPUS
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mrcbU34 000565532900046 WOS
mrcbU63 cav_un_epca*0344498 International Journal of Computational Intelligence Systems 1875-6891 1875-6883 Roč. 13 č. 1 2020 988 1001 Springer