Logic Journal of the IGPL 17 (4):325-350 (2009)

Non-deterministic matrices, a natural generalization of many-valued matrices, are semantic structures in which the value assigned to a complex formula may be chosen non-deterministically from a given set of options. We show that by combining non-deterministic matrices and distance-based considerations, one obtains a family of logics that are useful for reasoning with uncertainty. These logics are a conservative extension of those that are obtained by standard distance-based semantics, and so usual distance-based methods are easily simulated within our framework. We investigate the basic properties of the distance-preferential non-deterministic logics, consider their application for reasoning with incomplete and inconsistent information, and show the correspondence between some particular entailments in our framework and well-known problems like max-SAT
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DOI 10.1093/jigpal/jzp014
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Distance Semantics for Belief Revision.Daniel Lehmann, Menachem Magidor & Karl Schlechta - 2001 - Journal of Symbolic Logic 66 (1):295-317.

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