A Summary of the Habilitation Thesis

In [H1], we develop a fixpoint semantics, the least model semantics, and an SLDresolution calculus in a direct way for positive modal logic programs in basic serial monomodal logics. In [H2], we extend the results and generalize the methods of [H1] for multimodal logics, giving a framework for developing semantics for positive logic programs in serial multimodal logics. In [H3], we report on our design and implementation of the modal logic programming system [18] based on the framework given in [H2]. The subject of modal deductive databases closely relates to modal logic programming. In [H5], using our theory of modal logic programming [H1, H2], we formulate modal deductive databases and give computational methods for the modal query language MDatalog. In [H5], we also estimate data complexity of MDatalog in some multimodal logics. The work [H4] contains our results on data complexity of MDatalog in basic monomodal logics.