Foundations of Modal Deductive Databases ∗ Linh

Foundations of Modal Deductive Databases

We give formulations for modal deductive databases and present a modal query language called MDatalog. We define modal relational algebras and give the seminaive evaluation algorithm, the top-down evaluation algorithm, and the magic-set transformation for MDatalog queries. The results of this paper like soundness and completeness of the top-down evaluation algorithm or correctness of the magic-...

Multimodal Logic Programming and Its Applications to Modal Deductive Databases

On Modal Deductive Databases

We present a query language called MDatalog, which is an extension of Datalog for multimodal deductive databases. We define modal relational algebras and give the seminaive evaluation algorithm and the magic-set transformation for MDatalog queries. Results of this paper are proved for the multimodal logics of belief KDI4s5, KDI45, KD4s5s, KD45(m), which are extensions of the monomodal logic KD4...

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 ou...

Foundations of Modal Logic Programming: The Direct Approach