Though there is a huge amount of the so-called epistemic logics that deal with propositional attitudes, i.e., sentences of the form “a knows that P”, their ‘wh-cousins’ of the form “a knows who is a P”, “a knows what the P is”, “a knows which Ps are Qs”, etc., have been, to the best of my knowledge, almost neglected. A similar disproportion can be observed between the analysis of Yes-No questions, which has been under scrutiny of many erotetic logics, and Wh-questions which have been dealt with just by a few authors. To fill this gap, we have analysed Wh-questions in Transparent Intensional Logic (TIL) and adjusted Gentzen’s system of natural deduction to TIL natural language processing; thus, our TIL question-answering system can answer not only Yes-No questions but also derive answers to Wh-questions. In this paper, I am going to apply these results to the analysis of sentences containing a ‘knowing-wh’ constituent. In addition, I will analyse the relation between ‘knowing-that’ and ‘knowing-wh’. For instance, if a knows that the Mayor of Ostrava is Mr Macura, can we logically derive that a knows who is the Mayor of Ostrava? Or, vice versa, if a knows who is the Mayor of Ostrava and the Mayor of Ostrava is Mr Macura, do these assumptions logically entail that a knows that the Mayor of Ostrava is Mr Macura? Though in case of rational human agents the answers seem to be a no-doubt YES, perhaps a rather surprising answer is in general negative. We have to specify rules for deriving the relation between knowing-that and knowing-wh, and if a software agent is rational but resource bounded, it does not have to have in its ontology the rules necessary to derive the answer. The goal of the paper is the specification of these rules. Hence, when applying these results into the design of a multi-agent system composed of software resource-bounded agents, we have to compute their inferable knowledge, which accounts not only for their explicit knowledge but also for their inferential abilities.