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Propositional logics from rough set theory. (English) Zbl 1186.68446
Peters, James F. (ed.) et al., Transactions on Rough Sets VI. Commemorating life and work of Zdisław Pawlak, Part I. Berlin: Springer (ISBN 978-3-540-71198-8/pbk). Lecture Notes in Computer Science 4374. Journal Subline, 1-25 (2007).

Summary: The article focusses on propositional logics with semantics based on rough sets. Many approaches to rough sets (including generalizations) have come to the fore since the inception of the theory, and resulted in different “rough logics” as well. The essential idea behind these logics is, quite naturally, to interpret well-formed formulae as rough sets in (generalized) approximation spaces. The syntax, in most cases, consists of modal operators along with the standard Boolean connectives, in order to reflect the concepts of lower and upper approximations. Non-Boolean operators make appearances in some cases too.

Information systems (“complete” and “incomplete”) have always been the “practical” source for approximation spaces. Characterization theorems have established that a rough set semantics based on these “induced” spaces, is no different from the one mentioned above. We also outline some other logics related to rough sets, e.g. logics of information systems – which, in particular, feature expressions corresponding to attributes in their language. These systems address various issues, such as the temporal aspect of information, multiagent systems, rough relations.

An attempt is made here to place this gamut of work, spread over the last 20 years, in one platform. We present the various relationships that emerge and indicate questions that surface.

MSC:
68T27Logic in artificial intelligence
68T37Reasoning under uncertainty
03B60Other nonclassical logic