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Constructing the Least Models for Positive Modal Logic Programs (2000)
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BibTeX
@MISC{Nguyen00constructingthe,
author = {Linh Anh Nguyen},
title = {Constructing the Least Models for Positive Modal Logic Programs},
year = {2000}
}
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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 2 fKD5;KD45;S5g, or L 2 fKD;T ; KDB;Bg 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. 1.
