Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
A logic-based analysis of Dempster-Shafer theory
International Journal of Approximate Reasoning
Representing and reasoning with probabilistic knowledge
Representing and reasoning with probabilistic knowledge
Uncertainty, belief, and probability
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
On consistent approximations of belief functions in the mass space
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
An algebraic semantics for possibilistic logic
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
A Fuzzy Modal Logic for Belief Functions
Fundamenta Informaticae - The 1st International Workshop on Knowledge Representation and Approximate Reasoning (KR&AR)
Belief functions on distributive lattices
Artificial Intelligence
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We present BFL, a hybrid logic for representing uncertain knowledge. BFL attaches a quantified notion of belief -- based on Dempster-Shafer's theory of belief functions -- to classical first-order logic. The language of BFL is composed of objects of the form F:[a,b], where F is a first-order sentence, and a and b are numbers in the [0,1] interval (with a≤b). Intuitively, a measures the strength of our belief in the truth of F, and (1-b) that in its falseness. A number of properties of first-order logic nicely generalize to BFL; in return, BFL gives us a new perspective on some important points of Dempster-Shafer theory (e.g., the role of Dempster's combination rule.)