This paper introduces a framework called subjective logic for reasoning with uncertain propositions. It presents a metric for uncertain probabilities called opinion and a set of logical operators that can be used for logical reasoning with uncertain propositions. Subjective logic is based on elements from the Dempster-Shafer belief theory and is compatible with binary logic and probability calculus. The framework uses a belief model similar to the Dempster-Shafer theory of evidence, where uncertain probabilities are represented by belief masses and belief functions. The belief function is defined as the sum of belief masses on all substates of a given state. The disbelief function is defined as the sum of belief masses on all states that have an empty intersection with the given state. The uncertainty function is defined as the sum of belief masses on all states that have a non-empty intersection with the given state but are not subsets of it. The probability expectation function is defined as the sum of belief masses multiplied by the relative atomicity of the state. The relative atomicity is defined as the ratio of the number of atomic states in the intersection of two states to the number of atomic states in the second state. The framework also defines logical operators for propositional conjunction and disjunction, as well as negation. The operators are defined in terms of belief, disbelief, uncertainty, and relative atomicity functions. The framework is shown to be compatible with probability calculus, as it satisfies the Kolmogorov axioms of traditional probability theory. The paper also presents examples of the framework in action, including the Ellsberg paradox and a reliability analysis. The framework is shown to be able to handle uncertainty in a way that is consistent with both probability theory and logical reasoning.This paper introduces a framework called subjective logic for reasoning with uncertain propositions. It presents a metric for uncertain probabilities called opinion and a set of logical operators that can be used for logical reasoning with uncertain propositions. Subjective logic is based on elements from the Dempster-Shafer belief theory and is compatible with binary logic and probability calculus. The framework uses a belief model similar to the Dempster-Shafer theory of evidence, where uncertain probabilities are represented by belief masses and belief functions. The belief function is defined as the sum of belief masses on all substates of a given state. The disbelief function is defined as the sum of belief masses on all states that have an empty intersection with the given state. The uncertainty function is defined as the sum of belief masses on all states that have a non-empty intersection with the given state but are not subsets of it. The probability expectation function is defined as the sum of belief masses multiplied by the relative atomicity of the state. The relative atomicity is defined as the ratio of the number of atomic states in the intersection of two states to the number of atomic states in the second state. The framework also defines logical operators for propositional conjunction and disjunction, as well as negation. The operators are defined in terms of belief, disbelief, uncertainty, and relative atomicity functions. The framework is shown to be compatible with probability calculus, as it satisfies the Kolmogorov axioms of traditional probability theory. The paper also presents examples of the framework in action, including the Ellsberg paradox and a reliability analysis. The framework is shown to be able to handle uncertainty in a way that is consistent with both probability theory and logical reasoning.