Belief Revision with Uncertain Inputs in the Possibilistic Setting

This paper discusses belief revision under uncertain inputs in the framework of possibility theory. Revision can be based on two possible definitions of the conditioning operation, one based on min operator which requires a purely ordinal scale only, and another based on product, for which a richer structure is needed, and which is a particular case of Dempster's rule of conditioning. Besides, revision under uncertain inputs can be understood in two different ways depending on whether the input is viewed, or not, as a constraint to enforce. Moreover, it is shown that M.A. Williams' transmutations, originally defined in the setting of Spohn's functions, can be captured in this framework, as well as Boutilier's natural revision.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

Computing Possible and Certain Answers over Order-Incomplete Data

This paper studies the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful fragment of SQL, namely positive relational algebra with aggregates, whose bag semantics we extend to the partially ordered setting. Our semantics leads to the study of two main computational problems: the possibility and certainty of query answers. We show that these problems are respectively NP-complete and coNP-complete, but identify tractable cases depending on the query operators or input partial orders. We further introduce a duplicate elimination operator and study its effect on the complexity results.Comment: 55 pages, 56 references. Extended journal version of arXiv:1707.07222. Up to the stylesheet, page/environment numbering, and possible minor publisher-induced changes, this is the exact content of the journal paper that will appear in Theoretical Computer Scienc