We give formulations for modal deductive databases and present a modal query language called MDatalog. We define modal relational algebras and give the seminaive evaluation algorithm, the top-down evaluation algorithm...
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We give formulations for modal deductive databases and present a modal query language called MDatalog. We define modal relational algebras and give the seminaive evaluation algorithm, the top-down evaluation algorithm, and the magic-set transformation for MDatalog queries. The results of this paper like soundness and completeness of the top-down evaluation algorithm or correctness of the magic-set transformation are proved for the multimodallogics of belief K DI4(s)5, KDI45, KD4(s)5(s), KD45((m)), KD4I(g)5(a), and the class of serial context-free grammar logics. We also show that MDatalog has PTIME data complexity in the logics KDI4(s)5, KDI45, KD4(s)5(s), and KD45((m)).
We propose a modal logic programming language called MProlog, which is as expressive as the general modal Horn fragment. We give a fixpoint semantics and an SLD-resolution calculus for MProlog in all of the basic seri...
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We propose a modal logic programming language called MProlog, which is as expressive as the general modal Horn fragment. We give a fixpoint semantics and an SLD-resolution calculus for MProlog in all of the basic serial modallogics KD, T, KDB, B, KD4, S4, KD5, KD45, and S5. For an MProlog program P and for L being one of the mentioned logics, we define an operator T-L,T-P, which has the least fixpoint I-L,I-p. This fixpoint is a set of formulae, which may contain labeled forms of the modal operator lozenge, and is called the least L-model generator of P. The standard model of I-L,I-p is shown to be a least L-model of P. The SLD-resolution calculus for MProlog is designed with a similar style as for classical logicprogramming. It is sound and complete. We also extend the calculus for MProlog in the almost serial modallogics KB, K5, K45, and KB5.
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