Authors: Nguyen, Linh Anh
Article Type:
Research Article
Abstract:
We give algorithms to construct the least L-model for a given positive modal logic program P, where L can be one of the modal logics KD, T, KDB, B, KD4, S4, KD5, KD45, and S5. If L ∈ {KD5,KD45,S5}, or L ∈ {KD,T,KDB,B} and the modal depth of P is finitely bounded, then the least L-model of P can be constructed in PTIME and coded in polynomial space. We also show that if P has no flat models then it has the least models in KB, K5, K45, and KB5. As a consequence, the problem of checking the satisfiability of
…a set of modal Horn formulae with finitely bounded modal depth in KD, T, KB, KDB, or B is decidable in PTIME. The known result that the problem of checking the satisfiability of a set of Horn formulae in K5, KD5, K45, KD45, KB5, or S5 is decidable in PTIME is also studied in this work via a different method.
Show more
DOI: 10.3233/FI-2000-42102
Citation: Fundamenta Informaticae,
vol. 42, no. 1, pp. 29-60, 2000
Price: EUR 27.50