The Logic of Knowledge Bases

Levesque, Hector J.; Lakemeyer, Gerhard

doi:10.7551/mitpress/4290.001.0001

Cited by 82 publications

(71 citation statements)

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“…It was initiated by the first author's doctoral thesis [17], in which the Modal Reduction Theorem for the system AE was first established. The theorem for Levesque's system has later been discovered independently by Levesque and Lakemeyer and appears as Corollary 9.5.6 in [9]; their proof is similar in style to the proof in Section 5 but with a less general transformation strategy. The construction in the semantical proof of the Modal Reduction Theorem is inspired by a note of Segerberg [15] written in response to [17].…”

Section: History and Related Workmentioning

confidence: 81%

Only knowing with degrees of confidence

Waaler

Klüwer

Langholm

et al. 2007

Journal of Applied Logic

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A new logic of belief (in the "only knowing" family) with confidence levels is presented. The logic allows a natural distinction between explicit and implicit belief representations, where the explicit form directly expresses its models. The explicit form can be found by applying a set of equivalence preserving rewriting rules to the implicit form. The rewriting process is performed entirely within the logic, on the object level, provided we supply an explicit formalization of the logical space. We prove that the problem of deciding whether there exists a consistent explicit form is p 2 -complete, a complexity class to which many problems of nonmonotonic reasoning belong. The article also contains a conceptual analysis of basic notions like belief, co-belief and degrees of confidence.

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Section: History and Related Workmentioning

confidence: 81%

Only knowing with degrees of confidence

Waaler

Klüwer

Langholm

et al. 2007

Journal of Applied Logic

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“…Modalities O 1 , O 2 , O n and O ∞ are only belief modalities, generalizing only knowing (Levesque and Lakemeyer 2000). Intuitively, O iϕ means that all the agent believes to the degree at least i is ϕ.…”

Section: Graded Beliefs and Bbpsmentioning

confidence: 99%

From Knowledge-based Programs to Graded Belief-based Programs, Part I: On-line Reasoning*

Laverny

Lang

2005

Synthese

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Knowledge-based programs (KBPs) are a powerful notion for expressing action policies in which branching conditions refer to implicit knowledge and call for a deliberation task at execution time. However, branching conditions in KBPs cannot refer to possibly erroneous beliefs or to graded belief, such as "if my belief that ϕ holds is high then do some action α else perform some sensing action β". The purpose of this paper is to build a framework where such programs can be expressed. In this paper we focus on the execution of such a program (a companion paper investigates issues relevant to the off-line evaluation and construction of such programs). We define a simple graded version of doxastic logic KD45 as the basis for the definition of belief-based programs. Then we study the way the agent's belief state is maintained when executing such programs, which calls for revising belief states by observations (possibly unreliable or imprecise) and progressing belief states by physical actions (which may have normal as well as exceptional effects).

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“…We assume that the database domain is a fixed denumerable set of elements Δ and that every such element is denoted uniquely by a constant symbol, called its standard name [24]. We make use of the standard notion of relational model by using named attributes, each with an associated datatype, instead of tuples.…”

Section: Formal Frameworkmentioning

confidence: 99%

Reusing relational sources for semantic information access

Lubyte

2007

Proceedings of the ACM First Ph.D. Workshop in CIKM

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The rapid growth of available data arises the need for more sophisticated techniques for semantic access to information. It has been proved that using conceptual model or ontology over relational data sources is necessary to overcome many problems related with accessing the structured data. However, the task of wrapping the data residing in a database by means of an ontology is mainly done manually.The research we are carrying out studies the reuse of relational sources in the context of semantics-based access to information. This problem is tackled in two phases: (i) extracting semantics hidden in the relational sources by wrapping them by means of an ontology, (ii) understanding the methodology for semantic extension of such ontologies. In this paper we focus on the first sub-problem and present an automatic procedure for extracting from a relational database schema its conceptual view. The semantic mapping between the database and its conceptualization is captured by associating views over the data source to elements of the extracted ontology. To represent the extracted conceptual model we use an ontology language, rather that a graphical notation, in order to provide precise formal semantics. Our approach uses heuristics based on ideas of standard relational schema design and normalization. Under this we formally prove that our technique preserves the semantics of constraints in the database. Therefore, there is no data loss, and the extracted model constitutes a faithful wrapper of the relational database.

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The Logic of Knowledge Bases

Cited by 82 publications

References 0 publications

Only knowing with degrees of confidence

Only knowing with degrees of confidence

From Knowledge-based Programs to Graded Belief-based Programs, Part I: On-line Reasoning*

Reusing relational sources for semantic information access

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