Approximate Reasoning and non-Omniscient

Modal logics have been frequently used to represent the knowledge and belief owned by an agent. However, such systems make the unrealistic assumption that agents are logically omniscent, hence capable of performing extremely complex inferences. Our goal in this paper is twofold. First of all we show that an approximation pattern can be used for a stepwise procedure which determines the satisfiability of a formula in several modal systems like 85, ~, 2r and 84. This method is based on a generalization of the standard possible-world semantics for modal logic. Secondly, we use this semantics to define a modal language which allows the explicit representation of the knowledge owned by a resource-limited agent.