Abstract

When a person hopes something, this means that he or she hopes some proposition will be true. Thus, hope is a type of modality on propositions. Hope logic is the study of the logical structure among propositions with hope modalities. Rational hope is deductively enclosed, consistent, self-affirmed, etc. These properties can be regarded as axioms of hope logic. An important property of hope is that hope is not necessarily true, but it is hoped that that hope is true. This is a property particular to hope, and it can be regarded as ‘the hope axiom’. Using possible world semantics, different hope logic systems, which are sound and complete with respect to their frames, can be obtained by selecting different hope axioms