The paper introduces subjective logic, a framework for reasoning with uncertain probabilities, which is based on the Dempster-Shafer belief model. The framework uses elements from both probability calculus and binary logic, and is designed to capture the subjective nature of human beliefs. The paper defines a metric called "opinion" to represent subjective beliefs, which includes belief mass, disbelief, uncertainty, and relative atomicity functions. These functions are used to determine probability expectations and to order opinions based on probability expectation, uncertainty, and relative atomicity. The paper also introduces logical operators such as conjunction, disjunction, and negation for opinions, and demonstrates their compatibility with probability calculus. Additionally, it presents an alternative representation of uncertain probabilities using probability density functions (ppdfs) and defines a mapping between ppdfs and the Shaferian belief model. The paper includes examples to illustrate the concepts and operators, and discusses the application of subjective logic in reliability analysis and decision-making.The paper introduces subjective logic, a framework for reasoning with uncertain probabilities, which is based on the Dempster-Shafer belief model. The framework uses elements from both probability calculus and binary logic, and is designed to capture the subjective nature of human beliefs. The paper defines a metric called "opinion" to represent subjective beliefs, which includes belief mass, disbelief, uncertainty, and relative atomicity functions. These functions are used to determine probability expectations and to order opinions based on probability expectation, uncertainty, and relative atomicity. The paper also introduces logical operators such as conjunction, disjunction, and negation for opinions, and demonstrates their compatibility with probability calculus. Additionally, it presents an alternative representation of uncertain probabilities using probability density functions (ppdfs) and defines a mapping between ppdfs and the Shaferian belief model. The paper includes examples to illustrate the concepts and operators, and discusses the application of subjective logic in reliability analysis and decision-making.