Automata-theoretic decision procedures for solving model-checking and satisfiability problems for temporal, dynamic, and description logics have flourished during the past decades. In the paper we define an EXPTIME decision procedure based on the emptiness problem of Büchi automata on infinite trees for the very expressive information logic SIM designed for reasoning about information systems. This logic involves modal parameters satisfying certain properties to capture the relevant nominals at the formula level, Boolean expressions and nominals at the modal level, an implicit intersection operation for relations, and a universal modality. The original combination of known techniques allows us to solve the open question related to the EXPTIME-completeness of SIM. Furthermore, we discuss how variants of SIM can be treated similarly although the decidability status of some of them is still unknown.