Product-based Causal Networks and Quantitative Possibilistic Bases

Salem Benferhat, Faïza Khellaf, and Aïcha Mokhtari

In possibility theory, there are two kinds of possibilistic causal networks depending if possibilistic conditioning is based on the minimum or on the product operator. Similarly there are also two kinds of possibilistic logic: standard (min-based) possibilistic logic and quantitative (product-based) possibilistic logic. Recently, several equivalent transformations between standard possibilistic logic and min-based causal networks have been proposed. This paper goes one step further and shows that product-based causal networks can be encoded in product-based knowledge bases. The converse transformation is also provided.

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