Coping with semilattices of relations in logics with relative accessibility relations

We present a class of polymodal logics for which the set of terms indexing the modal connectives can be hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. The semantical structures of the logics contains a family of binary relations that can be viewed as an homomorphism between semilattices. Various results related to decidability, axiomatization and computational complexity are established by faithfully translating the logics into more standard modal logics. The paper is a short survey of results obtained by translation for various logics of the above kind from the literature.

• Type: Conference
• Year: 1998
• Where: RELMICS
• Authors: Stéphane Demri
• Keywords: Boolean Terms, Logics, Polymodal Logics, RELMICS 1998, Theoretical Computer Science