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544
Reasoning about Knowledge and Probability
 Journal of the ACM
, 1994
"... : We provide a model for reasoning about knowledge and probability together. We allow explicit mention of probabilities in formulas, so that our language has formulas that essentially say "according to agent i, formula ' holds with probability at least b." The language is powerful enough to allow r ..."
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Cited by 156 (15 self)
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: We provide a model for reasoning about knowledge and probability together. We allow explicit mention of probabilities in formulas, so that our language has formulas that essentially say "according to agent i, formula ' holds with probability at least b." The language is powerful enough to allow reasoning about higherorder probabilities, as well as allowing explicit comparisons of the probabilities an agent places on distinct events. We present a general framework for interpreting such formulas, and consider various properties that might hold of the interrelationship between agents' probability assignments at different states. We provide a complete axiomatization for reasoning about knowledge and probability, prove a small model property, and obtain decision procedures. We then consider the effects of adding common knowledge and a probabilistic variant of common knowledge to the language. A preliminary version of this paper appeared in the Proceedings of the Second Conference on T...
Supporting Ontological Analysis of Taxonomic Relationships
, 2001
"... Taxonomies are an important part of conceptual modeling. They provide substantial structural information, and are typically the key elements in integration efforts, however there has been little guidance as to what makes a proper taxonomy. We have adopted several notions from the philosophical pract ..."
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Cited by 146 (2 self)
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Taxonomies are an important part of conceptual modeling. They provide substantial structural information, and are typically the key elements in integration efforts, however there has been little guidance as to what makes a proper taxonomy. We have adopted several notions from the philosophical practice of formal ontology, and adapted them for use in information systems. These tools, identity, essence, unity, and dependence, provide a solid logical framework within which the properties that form a taxonomy can be analyzed. This analysis helps make intended meaning more explicit, improving human understanding and reducing the cost of integration.
A Framework for KnowledgeBased Temporal Abstraction
, 1997
"... A new domainindependent knowledgebased inference structure is presented, specific to the task of abstracting higherlevel concepts from timestamped data. The framework includes a model of time, parameters, events, and contexts. A formal specification of a domains temporalabstraction knowledge su ..."
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Cited by 131 (37 self)
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A new domainindependent knowledgebased inference structure is presented, specific to the task of abstracting higherlevel concepts from timestamped data. The framework includes a model of time, parameters, events, and contexts. A formal specification of a domains temporalabstraction knowledge supports acquisition, maintenance, reuse, and sharing of that knowledge.
Belief, awareness, and limited reasoning
 ARTIFICIAL INTELLIGENCE
, 1988
"... Several new logics for belief and knowledge are introduced and studied, all of which have the property that agents are not logically omniscient. In particular, in these logics, the set of beliefs of an agent does not necessarily contain all valid formulas. Thus, these logics are more suitable than t ..."
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Cited by 120 (12 self)
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Several new logics for belief and knowledge are introduced and studied, all of which have the property that agents are not logically omniscient. In particular, in these logics, the set of beliefs of an agent does not necessarily contain all valid formulas. Thus, these logics are more suitable than traditional logics for modelling beliefs of humans (or machines) with limited reasoning capabilities. Our first logic is essentially an extension of Levesque's logic of implicit and explicit belief, where we extend to allow multiple agents and higherlevel belief (i.e., beliefs about beliefs). Our second logic deals explicitly with "awareness," where, roughly speaking, it is necessary to be aware of a concept before one can have beliefs about it. Our third logic gives a model of "local reasoning," where an agent is viewed as a "society of minds," each with its own cluster of beliefs, which may contradict each other.
Verification Tools for FiniteState Concurrent Systems
"... Temporal logic model checking is an automatic technique for verifying finitestate concurrent systems. Specifications are expressed in a propositional temporal logic, and the concurrent system is modeled as a statetransition graph. An efficient search procedure is used to determine whether or not t ..."
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Cited by 118 (3 self)
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Temporal logic model checking is an automatic technique for verifying finitestate concurrent systems. Specifications are expressed in a propositional temporal logic, and the concurrent system is modeled as a statetransition graph. An efficient search procedure is used to determine whether or not the statetransition graph satisfies the specification. When the technique was first developed ten years ago, it was only possible to handle concurrent systems with a few thousand states. In the last few years, however, the size of the concurrent systems that can be handled has increased dramatically. By representing transition relations and sets of states implicitly using binary decision diagrams, it is now possible to check concurrent systems with more than 10 120 states. In this paper we describe in detail how the new implementation works and
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...
L.: Toward a Geometry of Common Sense: A Semantics and a Complete Axiomatization of Mereotopology
 in: IJCAI95
"... Mereological and topological notions of connection, part, interior and complement are central to spatial reasoning and to the semantics of natural language expressions concerning locations and relative positions. While several authors have proposed axioms for these notions, no one with the exception ..."
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Cited by 103 (0 self)
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Mereological and topological notions of connection, part, interior and complement are central to spatial reasoning and to the semantics of natural language expressions concerning locations and relative positions. While several authors have proposed axioms for these notions, no one with the exception of Tarski [18], who based his axiomatization of mereological notions on a Euclidean metric, has attempted to give them a semantics. We offer an alternative to Tarski, starting with mereotopological notions that have proved useful in the semantic analysis of spatial expressions. We also give a complete axiomatization of this account of mereotopological reasoning. 1
The ProofTheory and Semantics of Intuitionistic Modal Logic
, 1994
"... Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpret ..."
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Cited by 102 (0 self)
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Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpreted in an intuitionistic metatheory then the induced modal logics no longer satisfy certain intuitionistically invalid principles. This thesis investigates the intuitionistic modal logics that arise in this way. Natural deduction systems for various intuitionistic modal logics are presented. From one point of view, these systems are selfjustifying in that a possible world interpretation of the modalities can be read off directly from the inference rules. A technical justification is given by the faithfulness of translations into intuitionistic firstorder logic. It is also established that, in many cases, the natural deduction systems induce wellknown intuitionistic modal logics, previously given by Hilbertstyle axiomatizations. The main benefit of the natural deduction systems over axiomatizations is their
Interpolation in Modal Logic
, 1999
"... The interpolation property and Robinson's consistency property are important tools for applying logic to software engineering. We provide a uniform technique for proving the Interpolation Property, using the notion of bisimulation. For modal logics, this leads to simple, easytocheck conditions ..."
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Cited by 82 (6 self)
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The interpolation property and Robinson's consistency property are important tools for applying logic to software engineering. We provide a uniform technique for proving the Interpolation Property, using the notion of bisimulation. For modal logics, this leads to simple, easytocheck conditions on the logic which imply interpolation. We apply this result to fibering of modal logics and to modal logics of knowledge and belief.