Granular Rough Mereological Logics with Applications to Dependencies in Information and Decision Systems

We are concerned with logical formulas induced from data sets, in particular, with decision rules. Contrary to the standard practice of many–valued logics in which formulas are semantically interpreted as their states /values of truth and logical calculi consist essentially in finding functional interpretations of logical functors, in the considered by us case, the semantic interpretation takes place in the universe of entities/objects and formulas are interpreted as their meanings, i.e., subsets of the object universe. Yet, the final evaluation of a formula should be its state of truth. In search of an adequate formal apparatus for this task, we turn to rough mereology and to the idea of intensionality vs. extensionality. Rough mereology allows for similarity measures (called rough inclusions) which in turn form a basis for the mechanism of granulation of knowledge. Granules of knowledge, defined as classes of satisfactorily similar objects, can be regarded as worlds in which properties of entities are evaluated as extensions of logical formulas. Obtained in this way granular rough mereological intensional logics reveal essential properties of rough set based reasoning.