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A Fixpoint Semantics and an SLDResolution Calculus for Modal Logic Programs
, 2001
"... 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 SLDresolution calculus for MProlog in all of the basic serial modal logics KD, T, KDB, B, KD4, S4, KD5, KD45, and S5. For an MProlog program P ..."
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Cited by 15 (13 self)
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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 SLDresolution calculus for MProlog in all of the basic serial modal logics 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 TL,P, which has the least fixpoint IL,P. This fixpoint is a set of formulae, which may contain labeled forms of the modal operator ✸, and is called the least Lmodel generator of P. The standard model of IL,P is shown to be a least Lmodel of P. The SLDresolution calculus for MProlog is designed with a similar style as for classical logic programming. It is sound and complete. We also extend the calculus for MProlog in the almost serial modal logics KB, K 5, K 45, and KB5. 1
Multimodal Logic Programming and Its Applications to Modal Deductive Databases
, 2003
"... We give a general framework for developing the least model semantics, xpoint semantics, and SLDresolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. 8x 9y R i (x; y)) and some classical rstorder Horn formulas. Our appr ..."
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Cited by 13 (9 self)
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We give a general framework for developing the least model semantics, xpoint semantics, and SLDresolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. 8x 9y R i (x; y)) and some classical rstorder Horn formulas. Our approach is direct and no restriction on occurrences of 2 i and 3 i is required. We apply the framework for a large class of basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T , B, 4, 5 (in the form, e.g., 4 : 2 i ! 2 j 2k) and I : 2 i ! 2 j . Another part of the work is devoted to programming in multimodal logics intended for reasoning about multidegree belief, for use in distributed systems of belief, or for reasoning about epistemic states of agents in multiagent systems.
On modal deductive databases
 Proceedings of ADBIS 2005, LNCS 3631
, 2005
"... 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 topdown evaluation algorithm, and the magicset transformation for MDatalog queries. The results of this paper ..."
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Cited by 12 (8 self)
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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 topdown evaluation algorithm, and the magicset transformation for MDatalog queries. The results of this paper like soundness and completeness of the topdown evaluation algorithm or correctness of the magicset transformation are proved for the multimodal logics of belief KDI4s5, KDI45, KD4s5s, KD45(m), KD4Ig5a, and the class of serial contextfree grammar logics. We also show that MDatalog has PTIME data complexity in the logics KDI4s5, KDI45, KD4s5s, and KD45(m). 1
Foundations of Modal Logic Programming: The Direct Approach (release 2.0)”, manuscript (provided as a technical report), available at http://www.mimuw.edu. pl/~nguyen/papers.html
"... 1.1 Classical Logic Programming............................ 5 1.2 Previous Works on Modal Logic Programming.................. 7 ..."
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Cited by 5 (5 self)
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1.1 Classical Logic Programming............................ 5 1.2 Previous Works on Modal Logic Programming.................. 7
The data complexity of MDatalog in basic modal logics
 Proceedings of MFCS 2006, LNCS 4162
, 2006
"... Abstract. We study the data complexity of the modal query language MDatalog and its extension eMDatalog in basic modal logics. MDatalog is a modal extension of Datalog, while eMDatalog is the general modal Horn fragment with the allowedness condition. As the main results, we prove that the data comp ..."
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Abstract. We study the data complexity of the modal query language MDatalog and its extension eMDatalog in basic modal logics. MDatalog is a modal extension of Datalog, while eMDatalog is the general modal Horn fragment with the allowedness condition. As the main results, we prove that the data complexity of MDatalog and eMDatalog in K4, KD4, and S4 is PSPACEcomplete, in K is coNPcomplete, and in KD, T, KB, KDB,andB is PTIMEcomplete. 1
A Computational Method for Modal Deductive Databases
, 2003
"... We present a query language called MDatalog, which is an extension of Datalog for multimodal deductive database. We de ne modal relational algebras and give the seminaive evaluation algorithm and the magicset transformation for multimodal deductive databases. Our formulation is general, however ..."
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We present a query language called MDatalog, which is an extension of Datalog for multimodal deductive database. We de ne modal relational algebras and give the seminaive evaluation algorithm and the magicset transformation for multimodal deductive databases. Our formulation is general, however, the results are proved only for the multimodal logics KDI4s 5, KDI45, KD4s5s , KD45 (m) , which are multimodal extensions of the monomodal logic KD45. The logics KDI4s5 and KDI45 are intended for reasoning about multidegree belief, while KD4s5s is for use in distributed systems of belief, and KD45 (m) is for reasoning about epistemic states of agents. We show that MDatalog has PTIME data complexity in these logics.
IOS Press A Fixpoint Semantics and an SLDResolution Calculus for Modal Logic Programs
"... Abstract. 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 SLDresolution calculus for MProlog in all of the basic serial modal logics KD, T, KDB, B, KD4, S4, KD5, KD45, and S5. For an MProlog ..."
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Abstract. 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 SLDresolution calculus for MProlog in all of the basic serial modal logics 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 TL,P, which has the least fixpoint IL,P. This fixpoint is a set of formulae, which may contain labeled forms of the modal operator ✸, and is called the least Lmodel generator of P. The standard model of IL,P is shown to be a least Lmodel of P. The SLDresolution calculus for MProlog is designed with a similar style as for classical logic programming. It is sound and complete. We also extend the calculus for MProlog in the almost serial modal logics KB, K5, K45, and KB5. 1.
IOS Press Foundations of Modal Deductive Databases
"... Abstract. 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 topdown evaluation algorithm, and the magicset transformation for MDatalog queries. The results of t ..."
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Abstract. 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 topdown evaluation algorithm, and the magicset transformation for MDatalog queries. The results of this paper like soundness and completeness of the topdown evaluation algorithm or correctness of the magicset transformation are proved for the multimodal logics of belief KDI4s5, KDI45, KD4s5s, KD45 (m), KD4Ig5a, and the class of serial contextfree grammar logics. We also show that MDatalog has PTIME data complexity in the logics KDI4s5, KDI45, KD4s5s, and KD45 (m).
A Summary of the Habilitation Thesis “Selected Semantic and Computational Aspects of Modal Logic Programming”
"... The presented habilitation thesis consists of the following papers: [H1] L.A. Nguyen. A fixpoint semantics and an SLDresolution calculus for modal logic programs. Fundamenta Informaticae, 55(1):63–100, 2003. ..."
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The presented habilitation thesis consists of the following papers: [H1] L.A. Nguyen. A fixpoint semantics and an SLDresolution calculus for modal logic programs. Fundamenta Informaticae, 55(1):63–100, 2003.