Impossible Worlds in Belief Modeling

Abstract

This article discusses one approach to belief modeling that has been developed to overcome the problems of the standard possible world semantics, namely the semantics with impossible worlds. It is shown that the introduction of impossible worlds in itself does not allow coping with these problems, as long as the worlds remain closed with respect to some accepted logic. The essence of the problem of modeling bounded rationality is revealed and the method of its solution in the semantics developed by M. Jago and later developed by him together with F. Berto is characterized. It is concluded that the task was indeed solved in the semantics of M. Jago. However, the peculiarities of this semantics made it difficult to build epistemic and doxastic logics on its basis and the subsequent proof of theorems. Nevertheless, the prospects for this approach and, in general, the semantics of beliefs using impossible worlds are assessed as favorable against the backdrop of significant success and rapid development of this whole trend in recent times.