Abstract This paper is intended to contribute to the formal study of uncertainty from u broad perspective. Its aim is to demonstrate that, in addition to prepositional calculus and probability theory, both fuzzy set theory and Dempster-Shafer evidence theory can be represented by the formal and semantic structures of modal logic. In particular, it is shown that the concept of multiple worlds in modal logic can be employed for constructing membership-grade functions of fuzzy sets, as well as belief and plausibility measures of evidence theory. It is also shown that additional theories of uncertainty, which have not been considered us yet. emerge naturally from the framework of modal logic. When looking at these various uncertainty theories emerging from modal logic from a metatheoretical perspective, a hierarchical ordering of the theories is recognized. We refer to the hierarchically ordered collection of uncertainly theories captured within the realm of modal logic as hierarchical uncertainty metatheory....
[1]
M. Black.
Vagueness. An Exercise in Logical Analysis
,
1937,
Philosophy of Science.
[2]
W. Weaver.
Science and complexity.
,
1948,
American scientist.
[3]
G. Choquet.
Theory of capacities
,
1954
.
[4]
Max J. Cresswell,et al.
A New Introduction to Modal Logic
,
1998
.
[5]
菅野 道夫,et al.
Theory of fuzzy integrals and its applications
,
1975
.
[6]
Glenn Shafer,et al.
A Mathematical Theory of Evidence
,
2020,
A Mathematical Theory of Evidence.
[7]
Graeme Forbes,et al.
The metaphysics of modality
,
1985
.
[8]
Kenneth J. Jr. Konyndyk,et al.
Introductory Modal Logic
,
1986
.
[9]
George J. Klir,et al.
Fuzzy sets, uncertainty and information
,
1988
.
[10]
I. Graham.
Non-standard logics for automated reasoning
,
1990
.
[11]
Enrique H. Ruspini,et al.
On the semantics of fuzzy logic
,
1991,
Int. J. Approx. Reason..
[12]
G. Klir,et al.
Fuzzy Measure Theory
,
1993
.