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183
Modal Languages And Bounded Fragments Of Predicate Logic
, 1996
"... Model Theory. These are nonempty families I of partial isomorphisms between models M and N , closed under taking restrictions to smaller domains, and satisfying the usual BackandForth properties for extension with objects on either side  restricted to apply only to partial isomorphisms of size ..."
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Cited by 213 (12 self)
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Model Theory. These are nonempty families I of partial isomorphisms between models M and N , closed under taking restrictions to smaller domains, and satisfying the usual BackandForth properties for extension with objects on either side  restricted to apply only to partial isomorphisms of size at most k . 'Invariance for kpartial isomorphism' means having the same truth value at tuples of objects in any two models that are connected by a partial isomorphism in such a set. The precise sense of this is spelt out in the following proof. 21 Proof (Outline.) kvariable formulas are preserved under partial isomorphism, by a simple induction. More precisely, one proves, for any assignment A and any partial isomorphism IÎI which is defined on the Avalues for all variables x 1 , ..., x k , that M, A = f iff N , IoA = f . The crucial step in the induction is the quantifier case. Quantified variables are irrelevant to the assignment, so that the relevant partial isomorphism can be res...
On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus
 Artificial Intelligence
, 1997
"... The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC8. ..."
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Cited by 108 (22 self)
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The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC8. We extend Bennett's encoding of RCC8 in modal logic. Based on this encoding, we prove that reasoning is NPcomplete in general and identify a maximal tractable subset of the relations in RCC8 that contains all base relations. Further, we show that for this subset pathconsistency is sufficient for deciding consistency. 1 Introduction When describing a spatial configuration or when reasoning about such a configuration, often it is not possible or desirable to obtain precise, quantitative data. In these cases, qualitative reasoning about spatial configurations may be used. One particular approach in this context has been developed by Randell, Cui, and Cohn [20], the socalled Region Connecti...
Econnections of abstract description systems
"... Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because nontrivial AI applications often comprise different aspects of the world, thus requiring suitable combinations of available formalisms modeling each of these aspects. It is chal ..."
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Cited by 95 (25 self)
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Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because nontrivial AI applications often comprise different aspects of the world, thus requiring suitable combinations of available formalisms modeling each of these aspects. It is challenging because the computational behavior of the resulting hybrids is often much worse than the behavior of their components. In this paper, we propose a new combination method which is computationally robust in the sense that the combination of decidable formalisms is again decidable, and which, nonetheless, allows nontrivial interactions between the combined components. The new method, called Econnection, is defined in terms of abstract description systems (ADSs), a common generalization of description logics, many logics of time and space, as well as modal and epistemic logics. The basic idea of Econnections is that the interpretation domains of n combined systems are disjoint, and that these domains are connected by means of nary ‘link relations. ’ We define several natural variants of Econnections and study indepth the transfer of decidability from the component systems to their Econnections. Key words: description logics, temporal logics, spatial logics, combining logics, decidability.
Logical foundations of peertopeer data integration
 In Proc. of the 23rd ACM SIGACT SIGMOD SIGART Sym. on Principles of Database Systems (PODS2004
, 2004
"... In peertopeer data integration, each peer exports data in terms of its own schema, and data interoperation is achieved by means of mappings among the peer schemas. Peers are autonomous systems and mappings are dynamically created and changed. One of the challenges in these systems is answering que ..."
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Cited by 85 (13 self)
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In peertopeer data integration, each peer exports data in terms of its own schema, and data interoperation is achieved by means of mappings among the peer schemas. Peers are autonomous systems and mappings are dynamically created and changed. One of the challenges in these systems is answering queries posed to one peer taking into account the mappings. Obviously, query answering strongly depends on the semantics of the overall system. In this paper, we compare the commonly adopted approach of interpreting peertopeer systems using a firstorder semantics, with an alternative approach based on epistemic logic. We consider several central properties of peertopeer systems: modularity, generality, and decidability. We argue that the approach based on epistemic logic is superior with respect to all the above properties. In particular, we show that, in systems in which peers have decidable schemas and conjunctive mappings, but are arbitrarily interconnected, the firstorder approach may lead to undecidability of query answering, while the epistemic approach always preserves decidability. This is a fundamental property, since the actual interconnections among peers are not under the control of any actor in the system. 1.
Generalized Model Checking: Reasoning about Partial State Spaces
, 2000
"... We discuss the problem of model checking temporal properties on partial Kripke structures, which were used in [BG99] to represent incomplete state spaces. We first extend the results of [BG99] by showing that the modelchecking problem for any 3valued temporal logic can be reduced to two modelchec ..."
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Cited by 74 (6 self)
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We discuss the problem of model checking temporal properties on partial Kripke structures, which were used in [BG99] to represent incomplete state spaces. We first extend the results of [BG99] by showing that the modelchecking problem for any 3valued temporal logic can be reduced to two modelchecking problems for the corresponding 2valued temporal logic. We then introduce a new semantics for 3valued temporal logics that can give more definite answers than the previous one. With this semantics, the evaluation of a formula OE on a partial Kripke structure M returns the third truth value? (read "unknown") only if there exist Kripke structures M1 and M2 that both complete M and such that M1 satisfies OE while M2 violates OE, hence making the value of OE on M truly unknown. The partial Kripke structure M can thus be viewed as a partial solution to the satisfiability problem which reduces the solution space to complete Kripke structures that are more complete than M wit...
An ontology of metalevel categories
 Principles of Knowledge Representation and Reasoning: Proceedings of the Fourth International Conference (KR94
, 1994
"... We focus in this paper on some metalevel ontological distinctions among unary predicates, like those between concepts and assertional properties. Three are the main contributions of this work, mostly based on a revisitation of philosophical (and linguistic) literature in the perspective of knowledg ..."
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Cited by 68 (17 self)
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We focus in this paper on some metalevel ontological distinctions among unary predicates, like those between concepts and assertional properties. Three are the main contributions of this work, mostly based on a revisitation of philosophical (and linguistic) literature in the perspective of knowledge representation. The first is a formal notion of ontological commitment, based on a modal logic endowed with mereological and topological primitives. The second is a formal account of Strawson's distinction between sortal and nonsortal predicates. Assertional
The Family of Stable Models
, 1993
"... The family of all stable models for a logic program has a surprisingly simple overall structure, once two naturally occurring orderings are made explicit. In a socalled knowledge ordering based on degree of definedness, every logic program P has a smallest stable model, s k P it is the well ..."
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Cited by 54 (4 self)
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The family of all stable models for a logic program has a surprisingly simple overall structure, once two naturally occurring orderings are made explicit. In a socalled knowledge ordering based on degree of definedness, every logic program P has a smallest stable model, s k P it is the wellfounded model. There is also a dual largest stable model, S k P , which has not been considered before. There is another ordering based on degree of truth. Taking the meet and the join, in the truth ordering, of the two extreme stable models s k P and S k P just mentioned, yields the alternating fixed points of [29], denoted s t P and S t P here. From s t P and S t P in turn, s k P and S k P can be produced again, using the meet and join of the knowledge ordering. All stable models are bounded by these four valuations. Further, the methods of proof apply not just to logic programs considered classically, but to logic programs over any bilattice meeting certain co...
EXPTIME tableaux for ALC
 ARTIFICIAL INTELLIGENCE
, 2000
"... The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semistructured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIMEcomplete. Second, experiments in automated reaso ..."
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Cited by 51 (3 self)
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The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semistructured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIMEcomplete. Second, experiments in automated reasoning have substantially broadened the meaning of “practical tractability”. Instances of realistic size for PSPACEcomplete problems are now within reach for implemented systems. Still, there is a gap between the reasoning services needed by the expressive logics mentioned above and those provided by the current systems. Indeed, the algorithms based on treeautomata, which are used to prove EXPTIMEcompleteness, require exponential time and space even in simple cases. On the other hand, current algorithms based on tableau methods can take advantage of such cases, but require double exponential time in the worst case. We propose a tableau calculus for the description logic ALC for checking the satisfiability of a concept with respect to a TBox with general axioms, and transform it into the first simple tableaubased decision procedure working in single exponential time. To guarantee the ease of implementation, we also discuss the effects that optimizations (propositional backjumping, simplification, semantic branching, etc.) might have on our complexity result, and introduce a few optimizations ourselves.
MultiValued Symbolic ModelChecking
 ACM TRANSACTIONS ON SOFTWARE ENGINEERING AND METHODOLOGY
, 2003
"... This paper introduces the concept and the general theory of multivalued model checking, and describes a multivalued symbolic modelchecker \Chi Chek. Multivalued ..."
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Cited by 50 (16 self)
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This paper introduces the concept and the general theory of multivalued model checking, and describes a multivalued symbolic modelchecker \Chi Chek. Multivalued