Constructing the Least Models for Positive Modal Logic Programs

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.

• Type: Journal
• Year: 2000
• Where: FUIN
• Authors: Linh Anh Nguyen
• Keywords: FUIN 2000, Modal Depth, Modal Logics, Positive Modal Logic