Optimistic vs. Pessimistic Interpretation of Linguistic Negation

Linguistic negation processing is a challenging problem studied by a large number of researchers from different communities, i.e. logic, linguistics, etc. We are interested in finding the positive interpretations of a negative sentence represented as "x is not A". In this paper, we do not focus on the single set of translations but on two approximation sets. The first one called pessimistic corresponds to the positive translations of the negative sentence that we can consider as sure. The second one called optimistic contains all the sentences that can be viewed as possible translations of the negative sentence. These approximation sets are computed according to the rough sets framework and based on a neighbourhood relation defined on the space of properties. Finally, we apply an original strategy of choice upon the two approximation sets which allows us to select the suitable translations of the initial negative sentence. It appears that we obtain results in good accordance with the ones linguistically expected.