Bilattice Tableau Calculi with Rough Set Semantics

A bilattice is an algebraic lattice that can represent both degrees of truth and epistemic state with the amount of information for a proposition. Rough sets are an approximation space in terms of an equivalence relation and adopted to manage uncertain and inconsistent information. In the paper, we propose a construction of a bilattice with an approximation space of rough sets. The information system of rough sets can be represented with decision logic and this can be reconstructed with a deduction system based on a bilattice. We discuss a pair of rough sets as bilattice elements and construct a deductive system with tableau calculi with a consequence relation with four-valued semantics and showed a sketch of completeness theorem.