An algebraic synthesis of the foundations of logic and probability
Information Sciences: an International Journal
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
The logical view of conditioning and its application to possibility and evidence theories
International Journal of Approximate Reasoning
Theoretical foundations for non-monotonic reasoning in expert systems
Logics and models of concurrent systems
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Recent results in the foundations of probability theory indicate that a conditional probability can be viewed as a probability attached to a mathematical entity called a measure-free conditional. Such a measure-free conditional can receive a semantics in terms of a trivalent logic and logical operations are defined on conditionals in terms of truth-tables. It is shown that these results can be useful to justify Cox's axiomatic framework for probability as well as its application to other theories of uncertainty (Shafer's plausibility functions and Zadeh's possibility measures). Moreover it is shown that measure-free conditionals have the properties of well-behaved non-monotonic inference rules.