A New Space Bound for the Modal Logics K 4 , KD 4 and S 4 Linh

Clausal Tableau Systems and Space Bounds for the Modal Logics

We propose so called clausal tableau systems for the common modal logics K , KD , T , KB , KDB and B . There is a measure such that for each tableau rule of these systems the measure of all its denominators is smaller than the measure of its numerator. Basing on these systems, we give a decision procedure for the logics, which uses O(n)-space for the logics T , KB , KDB and B , and O(n. logn)-s...

A New Space Bound for the Modal Logics

We propose so called clausal tableau systems for the common modal logics K4, KD4 and S4. Basing on these systems, we give more efficient decision procedures than those hitherto known for the considered logics. In particular space requirements for our logics are reduced from the previously established bound O(n. logn) to O(n. logn).

A New Space Bound for the Modal Logics K4, KD4 and S4

The Data Complexity of MDatalog in Basic Modal Logics

We study the data complexity of the modal query language MDatalog and its extension eMDatalog in basic modal logics. MDatalog is a modal extension of Datalog, while eMDatalog is the general modal Horn fragment with the allowedness condition. As the main results, we prove that the data complexity of MDatalog and eMDatalog in K4, KD4, and S4 is PSPACE-complete, in K is coNP-complete, and in KD , ...

An SLD-Resolution Calculus for Basic Serial Multimodal Logics

We develop semantics for modal logic programs in basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T , B, 4, 5 (in the form, e.g., 4 : iφ → j kφ) and I : iφ → jφ. We do not assume any special restriction for the form of programs and goals. Our fixpoint semantics and SLD-resolution calculus are defined using the direct approach ...