On the Complexity of Fragments of Modal Logics
نویسنده
چکیده
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
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