Formal reasoning with rough sets in multiple-source approximation systems. (English) Zbl 1191.68684
Summary: We focus on families of Pawlak approximation spaces, called multiple-source approximation systems (MSASs). These reflect the situation where information arrives from multiple sources. The behaviour of rough sets in MSASs is investigated – different notions of lower and upper approximations, and definability of a set in a MSAS are introduced. In this context, a generalized version of an information system, viz. multiple-source knowledge representation (KR)-system, is discussed. Apart from the indiscernibility relation which can be defined on a multiple-source KR-system, two other relations, viz. similarity and inclusion are considered. To facilitate formal reasoning with rough sets in MSASs, a quantified propositional modal logic is proposed. Interpretations for sets of well-formed formulae (wffs) of are defined on MSASs, and the various properties of rough sets in MSASs translate into logically valid wffs of the system. is shown to be sound and complete with respect to this semantics. Some decidable problems are addressed. In particular, it is shown that for any -wff , it is possible to check whether is satisfiable in a certain class of interpretations with MSASs of a given finite cardinality. Moreover, it is also decidable whether any wff is satisfiable in the class of all interpretations with MSASs having domain of a given finite cardinality.
|68T37||Reasoning under uncertainty|