Encoding formulas with partially constrained weights in a possibilistic-like many-sorted propositional logic

Possibilistic logic offers a convenient tool for handling uncertain or prioritized formulas and coping with inconsistency. Propositional logic formulas are thus associated with weights belonging to a linearly ordered scale. However, especially in case of multiple source information, only partial knowledge may be available about the relative ordering between weights of formulas. In order to cope with this problem, a two-sorted counterpart of possibilistic logic is introduced. Pieces of information are encoded as clauses where special literals refer to the weights. Constraints between weights translate into logical formulas of the corresponding sort and are gathered in a distinct auxiliary knowledge base. An inference relation, which is sound and complete with respect to preferential model semantics, enables us to draw plausible conclusions from the two knowledge bases. The inference process is characterized by using ”forgetting variables” for handling the symbolic weights, and hence an inference process is obtained by means of a DNF compilation of the two knowledge bases.