Lattices of fuzzy sets and bipolar fuzzy sets, and mathematical morphology
Information Sciences: an International Journal
Expert Systems with Applications: An International Journal
LPNMR'11 Proceedings of the 11th international conference on Logic programming and nonmonotonic reasoning
Mathematical morphology on bipolar fuzzy sets: general algebraic framework
International Journal of Approximate Reasoning
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Looking at inference as a way of transforming information so as to make it more easily usable (or interpretable) allows to consider accepted and rejected propositions as equally relevant and naturally gives a bipolar view of reasoning. The four possibilities of transforming information from accepted or rejected propositions into accepted or rejected ones are analyzed and examples illustrating them are given. This analysis is not only interesting per se but can also be useful in increasing capabilities of existing theorem provers. A unified framework based on former work by the authors is extended by incorporating the idea of theory-anti-subsumption related to Plotkin's generalization. Working on some technical details of this framework should allow automated reasoning tools to deal with different ways of connecting accepted and rejected propositions. © 2008 Wiley Periodicals, Inc.