20,813 research outputs found
Belief Revision in Expressive Knowledge Representation Formalisms
We live in an era of data and information, where an immeasurable amount of discoveries, findings, events, news, and transactions are generated every second. Governments, companies, or individuals have to employ and process all that data for knowledge-based decision-making (i.e. a decision-making process that uses predetermined criteria to measure and ensure the optimal outcome for a specific topic), which then prompt them to view the knowledge as valuable resource. In this knowledge-based view, the capability to create and utilize knowledge is the key source of an organization or individualâs competitive advantage. This dynamic nature of knowledge leads us to the study of belief revision (or belief change), an area which emerged from work in philosophy and then impacted further developments in computer science and artificial intelligence.
In belief revision area, the AGM postulates by AlchourrĂłn, GĂ€rdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. In this thesis, two research directions are considered. In the first, by considering the semantic point of view, we generalize K&Mâs approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of âbaseâ, such as belief sets, arbitrary or finite sets of sentences, or single sentences.
The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain âassignmentsâ: functions mapping belief bases to total â yet not transitive â âpreferenceâ relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&Mâs original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence. The second research direction in this thesis explores two approaches for revising description logic knowledge bases under fixed-domain semantics, namely model-based approach and individual-based approach. In this logical setting, models of the knowledge bases can be enumerated and can be computed to produce the revision result, semantically. We show a characterization of the AGM revision operator for this logic and present a concrete model-based revision approach via distance between interpretations. In addition, by weakening the KB based on certain domain elements, a novel individual-based revision operator is provided as an alternative approach
Algorithm for Adapting Cases Represented in a Tractable Description Logic
Case-based reasoning (CBR) based on description logics (DLs) has gained a lot
of attention lately. Adaptation is a basic task in the CBR inference that can
be modeled as the knowledge base revision problem and solved in propositional
logic. However, in DLs, it is still a challenge problem since existing revision
operators only work well for strictly restricted DLs of the \emph{DL-Lite}
family, and it is difficult to design a revision algorithm which is
syntax-independent and fine-grained. In this paper, we present a new method for
adaptation based on the DL . Following the idea of
adaptation as revision, we firstly extend the logical basis for describing
cases from propositional logic to the DL , and present a
formalism for adaptation based on . Then we present an
adaptation algorithm for this formalism and demonstrate that our algorithm is
syntax-independent and fine-grained. Our work provides a logical basis for
adaptation in CBR systems where cases and domain knowledge are described by the
tractable DL .Comment: 21 pages. ICCBR 201
Typicality-based revision for handling exceptions in Description Logics
Abstract. We continue our investigation on how to revise a Description Logic knowledge base when detecting exceptions. Our approach relies on the methodology for debugging a Description Logic terminology, addressing the problem of diagnosing inconsistent ontologies by identifying a minimal subset of axioms responsible for an inconsistency. In the approach we propose, once the source of the inconsistency has been localized, the identified TBox inclusions are revised in order to obtain a consistent knowledge base including the detected exception. We define a revision operator whose aim is to replace inclusions of the form "Cs are Ds" with "typical Cs are Ds", admitting the existence of exceptions, obtaining a knowledge base in the nonmonotonic logic ALC R min T which corresponds to a notion of rational closure for Description Logics of typicality. We also describe an algorithm implementing such a revision operator
Belief Revision, Minimal Change and Relaxation: A General Framework based on Satisfaction Systems, and Applications to Description Logics
Belief revision of knowledge bases represented by a set of sentences in a
given logic has been extensively studied but for specific logics, mainly
propositional, and also recently Horn and description logics. Here, we propose
to generalize this operation from a model-theoretic point of view, by defining
revision in an abstract model theory known under the name of satisfaction
systems. In this framework, we generalize to any satisfaction systems the
characterization of the well known AGM postulates given by Katsuno and
Mendelzon for propositional logic in terms of minimal change among
interpretations. Moreover, we study how to define revision, satisfying the AGM
postulates, from relaxation notions that have been first introduced in
description logics to define dissimilarity measures between concepts, and the
consequence of which is to relax the set of models of the old belief until it
becomes consistent with the new pieces of knowledge. We show how the proposed
general framework can be instantiated in different logics such as
propositional, first-order, description and Horn logics. In particular for
description logics, we introduce several concrete relaxation operators tailored
for the description logic \ALC{} and its fragments \EL{} and \ELext{},
discuss their properties and provide some illustrative examples
Prioritized base Debugging in Description Logics
International audienceThe problem investigated is the identification within an input knowledge base of axioms which should be preferably discarded (or amended) in order to restore consistency, coherence, or get rid of undesired consequences. Most existing strategies for this task in Description Logics rely on conflicts, either computing all minimal conflicts beforehand, or generating conflicts on demand, using diagnosis. The article studies how prioritized base revision can be effectively applied in the former case. The first main contribution is the observation that for each axiom appearing in a minimal conflict, two bases can be obtained for a negligible cost, representing what part of the input knowledge must be preserved if this axiom is discarded or retained respectively, and which may serve as a basis to obtain a semantically motivated preference relation over these axioms. The second main contributions is an algorithm which, assuming this preference relation is known, selects some of the maximal consistent/coherent subsets of the input knowledge base accordingly, without the need to compute all of of them
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