The logical view of conditioning and its application to possibility and evidence theories.

*(English)*Zbl 0696.03006Summary: The concept of conditioning is well known in probability theory, where it is used in artificial intelligence to quantify the uncertainty of rules, but is totally absent from logic, where material implication is widely used to express conditional statements. This problem has intrigued several researchers in the past. This paper is both a survey of works pertaining to the introduction of conditioning relations in logic and a discussion about how these conditioning relations leave some room for non-monotonicity and might be useful in formalizing the concept of production rules in expert systems. Moreover, it is shown how this formal setting leads to generalizing Cox’s axiomatic approach to conditional probability. Conditional probability, possibility, and belief functions are then obtained by solving functional equations. They obey the natural requirement that a conditional uncertainty measure be the measure of a conditional, such conditional being expressed as a conditioning relation between propositions that may fail to coincide with material implication.

##### Keywords:

conditioning; artificial intelligence; uncertainty; material implication; non-monotonicity; production rules; expert systems; possibility; belief functions
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\textit{D. Dubois} and \textit{H. Prade}, Int. J. Approx. Reasoning 4, No. 1, 23--46 (1990; Zbl 0696.03006)

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