In the framework of quantitative possibility theory, two representation modes were developed: logical-based representation in terms of quantitative possibilistic bases and graphical-based representation in terms of product-based possibilistic networks. This paper deals with logical and graphical representations of uncertain information using a quantitative possibility theory framework. We first provide a deep analysis of the relationships between these two forms of representational frameworks. Then, in the logical setting, we develop syntactic relations between penalty logic and quantitative possibilistic logic. These translations are (...) useful for different applications and are interesting for taking advantage of each format at the inferential level. We also provide an algorithm for reasoning with quantitative possibilistic logic. The algorithm takes inspiration from the syntactic relations between quantitative possibilistic logic bases and penalty logic. Finally, we provide experimental results that compar.. (shrink)