Representation and Reduction of Decision System Based on Semantics of Extended Propositional Modal Logic

To direct at the characteristic of the decision system based on Rough set theory, the proposition modal logic is extended by adding the attribute constants as the basic symbols, and the formal system of the extended propositional modal logic as well as its semantics are described. Since every decision system based on Rough set theory can be expressed by a decision system based on the semantics of extended modal logic, the problem about the reduction of decision system based on Rough set theory can be transformed to be the problem of that based on modal logic semantics. In this article, the semantics of the extended propositional modal logic is studied by using the method of granular computing, the representation method of the semantic objects in the formal system is given, and also the coding mechanism of possible word is established. Take advantage of the possible word code, the notion of the discernibility code is defined and based on which the reduction algorithm based on modal logic semantics is given. Know from other reduction algorithms, the algorithm based on modal logic semantics can make the reduction both for attribute and value of attribute.