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30
Temporalizing description logics
, 1998
"... Traditional rst order predicate logic is known to be designed for representing and manipulating static knowledge (e.g. mathematical theories). So are manyof its applications. Knowledge representation systems based on concept description logics are not exceptions. ..."
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Cited by 59 (20 self)
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Traditional rst order predicate logic is known to be designed for representing and manipulating static knowledge (e.g. mathematical theories). So are manyof its applications. Knowledge representation systems based on concept description logics are not exceptions.
MultiDimensional Modal Logic as a Framework for SpatioTemporal Reasoning
 APPLIED INTELLIGENCE
, 2000
"... In this paper we advocate the use of multidimensional modal logics as a framework for knowledge representation and, in particular, for representing spatiotemporal information. We construct a twodimensional logic capable of describing topological relationships that change over time. This logic, ca ..."
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Cited by 35 (6 self)
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In this paper we advocate the use of multidimensional modal logics as a framework for knowledge representation and, in particular, for representing spatiotemporal information. We construct a twodimensional logic capable of describing topological relationships that change over time. This logic, called PSTL (Propositional SpatioTemporal Logic) is the Cartesian product of the wellknown temporal logic PTL and the modal logic S4u , which is the Lewis system S4 augmented with the universal modality. Although it is an open problem whether the full PSTL is decidable, we show that it contains decidable fragments into which various temporal extensions (both pointbased and interval based) of the spatial logic RCC8 can be embedded. We consider known decidability and complexity results that are relevant to computation with mulidimensional formalisms and discuss possible directions for further research.
Modal description logics: Modalizing roles
 Fundam. Inform
, 1999
"... In this paper, we construct a new concept description language intended for representing dynamic and intensional knowledge. The most important feature distinguishing this language from its predecessors in the literature is that it allows applications of modal operators to all kinds of syntactic term ..."
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Cited by 31 (14 self)
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In this paper, we construct a new concept description language intended for representing dynamic and intensional knowledge. The most important feature distinguishing this language from its predecessors in the literature is that it allows applications of modal operators to all kinds of syntactic terms: concepts, roles and formulas. Moreover, the language may contain both local (i.e., statedependent) and global (i.e., stateindependent) concepts, roles and objects. All this provides us with the most complete and natural means for re ecting the dynamic and intensional behaviour of application domains. We construct a satis ability checking (mosaictype) algorithm for this language (based on ALC) in(i) arbitrary multimodal frames, (ii) frames with universal accessibility relations (for knowledge) and (iii) frames with transitive, symmetrical and euclidean relations (for beliefs). On the other hand, it is shown that the satisfaction problem becomes undecidable if the underlying frames are arbitrary strict linear orders, hN; <i, or the language contains the common knowledge operator for n 2 agents. 1
The Product of Converse PDL and Polymodal K
 Journal of Logic and Computation
"... The product of two modal logics L1 and L2 is the modal logic determined by the class of frames of the form F G such that F and G validate L1 and L2, respectively. This paper proves the decidability of the product of converse PDL and polymodal K. Decidability results for products of modal logics of k ..."
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Cited by 15 (3 self)
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The product of two modal logics L1 and L2 is the modal logic determined by the class of frames of the form F G such that F and G validate L1 and L2, respectively. This paper proves the decidability of the product of converse PDL and polymodal K. Decidability results for products of modal logics of knowledge as well as temporal logics and polymodal K are discussed. All those products form rather expressive but still decidable fragments of modal predicate logics. Based on the equivalence of polymodal K and the description logic ALC we shall discuss the obtained fragments, extend the expressive power a bit, and compare them with other modal description logics. 1
A Tableau Decision Algorithm for Modalized ALC with Constant Domains
, 2002
"... The aim of this paper is to construct a tableau decision algorithm for the modal description logic KALC with constant domains. More precisely, we present a tableau procedure that is capable of deciding, given an ALCformula ' with extra modal operators (which are applied only to concepts and TBo ..."
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Cited by 13 (4 self)
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The aim of this paper is to construct a tableau decision algorithm for the modal description logic KALC with constant domains. More precisely, we present a tableau procedure that is capable of deciding, given an ALCformula ' with extra modal operators (which are applied only to concepts and TBox axioms, but not to roles), whether ' is satisfiable in a model with constant domains and arbitrary accessibility relations. Tableaubased
Knowledge in Multiagent Systems: Initial Configurations and Broadcast
 ACM TRANSACTIONS OF COMPUTATIONAL LOGIC
, 2000
"... ... this paper we study two special cases of this framework: full systems and hypercubes. Both model static situations in which no agent has any information about another agent's state. Full systems and hypercubes are an appropriate model for the initial congurations of many systems of interest. We ..."
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Cited by 12 (8 self)
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... this paper we study two special cases of this framework: full systems and hypercubes. Both model static situations in which no agent has any information about another agent's state. Full systems and hypercubes are an appropriate model for the initial congurations of many systems of interest. We establish a correspondence between full systems and hypercube systems and certain classes of Kripke frames. We show that these classes of systems correspond to the same logic. Moreover, this logic is also the same as that generated by the larger class of weakly directed frames. We provide a sound and complete axiomatization, S5WDn , of this logic, and study its computational complexity. Finally, we show that under certain natural assumptions, in a model where knowledge evolves over time, S5WDn characterises the properties of knowledge not just at the initial conguration, but also at all later congurations. In particular, this holds for homogeneous broadcast systems, which capture settings in which agents are initially ignorant of each others local states, operate synchronously, have perfect recall, and can communicate only by broadcasting.
On the complexity of fragments of modal logics
 Advances in Modal Logic  Volume 5
, 2005
"... abstract. We study and give a summary of the complexity of 15 basic normal monomodal logics under the restriction to the Horn fragment and/or bounded modal depth. As new results, we show that: a) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by k ≥ 2 in the modal ..."
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Cited by 9 (2 self)
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abstract. We study and give a summary of the complexity of 15 basic normal monomodal logics under the restriction to the Horn fragment and/or bounded modal depth. As new results, we show that: a) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by k ≥ 2 in the modal logics K 4 and KD4 is PSPACEcomplete, in K is NPcomplete; b) the satisfiability problem of modal formulas with modal depth bounded by 1 in K 4, KD4, and S4 is NPcomplete; c) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by 1 in K, K 4, KD4, and S4 is PTIMEcomplete. In this work, we also study the complexity of the multimodal logics Ln under the mentioned restrictions, where L is one of the 15 basic monomodal logics. We show that, for n ≥ 2: a) the satisfiability problem of sets of Horn modal clauses in K5n, KD5n, K45n, and KD45n is PSPACEcomplete; b) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by k ≥ 2 in Kn, KBn, K5n, K45n, KB5n is NPcomplete, and in KDn, Tn, KDBn, Bn,
Symbolic model checking for temporalepistemic logics
 ACM SIGACT News
, 2007
"... Abstract. We survey some of the recent work in verification via symbolic model checking of temporalepistemic logic. Specifically, we discuss OBDDbased and SATbased approaches for epistemic logic built on discrete and realtime branching time temporal logic. The underlying semantical model conside ..."
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Cited by 6 (1 self)
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Abstract. We survey some of the recent work in verification via symbolic model checking of temporalepistemic logic. Specifically, we discuss OBDDbased and SATbased approaches for epistemic logic built on discrete and realtime branching time temporal logic. The underlying semantical model considered throughout is the one of interpreted system, suitably extended whenever necessary. 1
All proper normal extensions of S5square have the polynomial size model property
 Studia Logica
, 2000
"... It is shown that all proper normal extensions of the bimodal system S5 have the polysize model property. In fact, every normal proper extension L of S5 complete with respect to a class of finite frames FL . To each such class corresponds a natural number b(L) { the bound of L. For every L, there e ..."
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Cited by 4 (1 self)
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It is shown that all proper normal extensions of the bimodal system S5 have the polysize model property. In fact, every normal proper extension L of S5 complete with respect to a class of finite frames FL . To each such class corresponds a natural number b(L) { the bound of L. For every L, there exists a polynomial P ( ) of degree b(L)+1 such that every Lsatisfiable formula ' is satisfiable on an Lframe whose universe is bounded by P (j'j), for j'j the number of subformulas of '. It is shown that this bound is optimal.