A proof-theoretical investigation of global intuitionistic (fuzzy) logic

被引：8

作者：

Ciabattoni, A ^{[1
]}

机构：

[1] TU Wien, Inst Diskrete Math & Geometrie, Res Grp Computat Log, Vienna, Austria

来源：

ARCHIVE FOR MATHEMATICAL LOGIC | 2005年 / 44卷 / 04期

关键词：

modal predicate logics; globalization; hypersequent calculi; cut-elimination;

D O I：

10.1007/s00153-004-0265-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We perform a proof-theoretical investigation of two modal predicate logics: global intuitionistic logic GI and global intuitionistic fuzzy logic GIF. These logics were introduced by Takeuti and Titani to formulate an intuitionistic set theory and an intuitionistic fuzzy set theory together with their metatheories. Here we define analytic Gentzen style calculi for GI and GIF. Among other things, these calculi allows one to prove Herbrand's theorem for suitable fragments of GI and GIF.

引用

页码：435 / 457

页数：23

共 50 条

[21] PROOF-THEORETICAL ANALYSIS - WEAK SYSTEMS OF FUNCTIONS AND CLASSES
GORDEEV, L
[J]. ANNALS OF PURE AND APPLIED LOGIC, 1988, 38 (01) : 1 - 121
[22] PROOF-THEORETICAL SEMANTICS AND FREGEAN IDENTITY CRITERIA FOR PROPOSITIONS
SUNDHOLM, G
[J]. MONIST, 1994, 77 (03): : 294 - 314
[23] A COMPLETENESS THEOREM FOR INTUITIONISTIC PREDICATE LOGIC - AN INTUITIONISTIC PROOF
DRAGALIN, AG
[J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 1987, 34 (1-2): : 1 - 19
[24] Intuitionistic Fuzzy Implications and the Axioms of Intuitionistic Logic
Angelova, Nora A.
Atanassov, Krassimir T.
[J]. PROCEEDINGS OF THE 2015 CONFERENCE OF THE INTERNATIONAL FUZZY SYSTEMS ASSOCIATION AND THE EUROPEAN SOCIETY FOR FUZZY LOGIC AND TECHNOLOGY, 2015, 89 : 1578 - 1584
[25] INTUITIONISTIC FUZZY-LOGIC
ATANASSOV, KT
GARGOV, GK
[J]. DOKLADI NA BOLGARSKATA AKADEMIYA NA NAUKITE, 1990, 43 (03): : 9 - 12
[26] CORRESPONDENCE OF PROOF-INTUITIONISTIC LOGIC EXTENSIONS TO PROOF-LOGIC EXTENTIONS
MURAVITSKII, AI
[J]. DOKLADY AKADEMII NAUK SSSR, 1985, 281 (04): : 789 - 793
[27] INTUITIONISTIC FUZZY-LOGIC AND INTUITIONISTIC FUZZY SET-THEORY
TAKEUTI, G
TITANI, S
[J]. JOURNAL OF SYMBOLIC LOGIC, 1984, 49 (03) : 851 - 866
[28] INTERPOLATION PROPERTY FOR EXTENSIONS OF INTUITIONISTIC PROOF LOGIC
SIMONOVA, IG
[J]. MATHEMATICAL NOTES, 1990, 47 (5-6) : 483 - 490
[29] A connection based proof method for intuitionistic logic
Otten, J
Kreitz, C
[J]. THEOREM PROVING WITH ANALYTIC TABLEAUX AND RELATED METHODS, 1995, 918 : 122 - 137
[30] Medical diagnosis with the aid of using fuzzy logic and intuitionistic fuzzy logic
Satyajit Das
Debashree Guha
Bapi Dutta
[J]. Applied Intelligence, 2016, 45 : 850 - 867

← 1 2 3 4 5 →