On the Complexity of Fragments of Modal Logics

We study and give a summary of the complexity of 15 basic normal monomodal logics under the restriction to the Horn fragment and/or bounded modal depth. As new results, we show that: a) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by k 2 in the modal logics K4 and KD4 is PSPACE-complete, in K is NP-complete; b) the satisfiability problem of modal formulas with modal depth bounded by 1 in K4, KD4, and S4 is NP-complete; c) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by 1 in K, K4, KD4, and S4 is PTIME-complete. In this work, we also study the complexity of the multimodal logics Ln under the mentioned restrictions, where L is one of the 15 basic monomodal logics. We show that, for n 2 : a) the satisfiability problem of sets of Horn modal clauses in K5n, KD5n, K45n, and KD45n is PSPACE-complete; b) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by k 2 in Kn, KBn, K5n, K45n, KB5...

• Type: Conference
• Year: 2004
• Where: AIML
• Authors: Linh Anh Nguyen
• Keywords: AIML 2004, AIML 2008, Horn Modal Clauses, Modal Depth, Satisfiability Problem