A New Logic For Uncertainty

TL;DR

This paper introduces a new uncertain propositional logic that integrates fuzziness and randomness, aiming to establish a logical foundation for modeling uncertainty across various scientific disciplines.

Contribution

It presents a novel logic system combining fuzzy and probabilistic semantics to better reflect real-world uncertainties.

Findings

Defines a new uncertain propositional logic framework.

Integrates fuzziness with probabilistic and possibility semantics.

Lays groundwork for a formal uncertainty theory.

Abstract

Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking truth value semantics and randomicity by taking probabilistic semantics or possibility semantics. As the first step for purpose of establishing a logic system which completely reflect the uncertainty of the objective world, this logic will lead to a set of logical foundations for uncertainty theory as what classical logic done in certain or definite situations or circumstances.