The process of rational inquiry can be defined as the evolution of the beliefs of a rational agent as a consequence of its internal inference procedures and its interaction with the environment. These beliefs can be modelled in a formal way using doxastic logics. The possible worlds model and its associated Kripke semantics provide an intuitive semantics for these logics, but they seem to commit us to model agents that are logically omniscient and perfect reasoners. These problems can be avoided with a syntactic view of possible worlds, defining them as arbitrary sets of sentences in a propositional belief logic. In this article this syntactic view of possible worlds is taken, and a dynamic analysis of the agent's beliefs is suggested in order to model the process of rational inquiry in which the agent is permanently engaged. One component of this analysis, the logical one, is summarily described. This dimension of analysis is performed using a modified version of the analytic tableaux method, and it models the evolution of the beliefs due to the agent's inference power. It is shown how non-perfect reasoning is achieved in two ways: on one hand, the agent's deductive abilities can be controlled by restricting the tautologies that it is allowed to use in the course of this logical analysis; on the other hand, the agent is not obliged to perform an exhaustive analysis of the initial tableau.