TY - JOUR
T1 - A semantic study of the first-order predicate logic with uncertainty involved
AU - Zhang, Xingfang
AU - Li, Xiang
N1 - Publisher Copyright:
© 2014, Springer Science+Business Media New York.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - In this paper, we provide a semantic study of the first-order predicate logic for situations involving uncertainty. We introduce the concepts of uncertain predicate proposition, uncertain predicate formula, uncertain interpretation and degree of truth in the framework of uncertainty theory. Compared with classical predicate formula taking true value in $$\{0,1\}$${0,1}, the degree of truth of uncertain predicate formula may take any value in the unit interval $$[0,1]$$[0,1]. We also show that the uncertain first-order predicate logic is consistent with the classical first-order predicate logic on some laws of the degree of truth.
AB - In this paper, we provide a semantic study of the first-order predicate logic for situations involving uncertainty. We introduce the concepts of uncertain predicate proposition, uncertain predicate formula, uncertain interpretation and degree of truth in the framework of uncertainty theory. Compared with classical predicate formula taking true value in $$\{0,1\}$${0,1}, the degree of truth of uncertain predicate formula may take any value in the unit interval $$[0,1]$$[0,1]. We also show that the uncertain first-order predicate logic is consistent with the classical first-order predicate logic on some laws of the degree of truth.
KW - Degree of truth
KW - Uncertain first-order predicate logic
KW - Uncertain measure
KW - Uncertain predicate formula
KW - Uncertain variable
UR - https://www.scopus.com/pages/publications/84927123350
U2 - 10.1007/s10700-014-9184-2
DO - 10.1007/s10700-014-9184-2
M3 - Article
AN - SCOPUS:84927123350
SN - 1568-4539
VL - 13
SP - 357
EP - 367
JO - Fuzzy Optimization and Decision Making
JF - Fuzzy Optimization and Decision Making
IS - 4
ER -