A note on normal forms for the closed fragment of system IL

Abstract

In [8], P. Hájek and Švejdar determined normal forms for the system ILF, and showed that we can eliminate the modal operator $rhd$ from $IL$--formulas. The normal form for the closed fragment of the interpretability logic $IL$ is an open problem (see [13]). We prove that in some cases we can eliminate the modal operator $rhd$. We give an example where it is impossible to eliminate $rhd.