Modern analytic philosophy can apply the possible-worlds semantics for the analysis of philosophical problems. The dissertation determines ontological basis for the possible-worlds semantics, so that it is fully applicable to the analysis of problems of the philosophy of consciousness, including the issue of the identity of consciousness and body. The analysis of relational and object methods for determining the ontology of possible-worlds semantics for objects and functions takes place, while the possibility consideres of determining the object method as a special case of relative method. The attitude of the reachability as a means of model of «relative» transitions between the possible worlds is the key to relational approach to the ontology of possible-worlds semantics. The dissertation formulates the logical system based on the assumption of incomplete comparison individual areas for the attitude of the reachability.