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Register a new userRational Closure in SHIQ
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Added by
Gian Luca Pozzato
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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We define a notion of rational closure for the logic SHIQ, which does not enjoys the finite model property, building on the notion of rational closure introduced by Lehmann and Magidor in [23]. We provide a semantic characterization of rational closure in SHIQ in terms of a preferential semantics, based on a finite rank characterization of minimal models. We show that the rational closure of a TBox can be computed in EXPTIME using entailment in SHIQ.
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We define the notion of rational closure in the context of Description Logics extended with a tipicality operator. We start from ALC+T, an extension of ALC with a typicality operator T: intuitively allowing to express concepts of the form T(C), meant to select the most normal instances of a concept C. The semantics we consider is based on rational model. But we further restrict the semantics to minimal models, that is to say, to models that minimise the rank of domain elements. We show that this semantics captures exactly a notion of rational closure which is a natural extension to Description Logics of Lehmann and Magidors original one. We also extend the notion of rational closure to the Abox component. We provide an ExpTime algorithm for computing the rational closure of an Abox and we show that it is sound and complete with respect to the minimal model semantics.
Combining knowledge and beliefs of autonomous peers in distributed settings, is a ma- jor challenge. In this paper we consider peers that combine ontologies and reason jointly with their coupled knowledge. Ontologies are within the SHIQ fragment of Description Logics. Although there are several representation frameworks for modular Description Log- ics, each one makes crucial assumptions concerning the subjectivity of peers knowledge, the relation between the domains over which ontologies are interpreted, the expressivity of the constructors used for combining knowledge, and the way peers share their knowledge. However in settings where autonomous peers can evolve and extend their knowledge and beliefs independently from others, these assumptions may not hold. In this article, we moti- vate the need for a representation framework that allows peers to combine their knowledge in various ways, maintaining the subjectivity of their own knowledge and beliefs, and that reason collaboratively, constructing a tableau that is distributed among them, jointly. The paper presents the proposed E-SHIQ representation framework, the implementation of the E-SHIQ distributed tableau reasoner, and discusses the efficiency of this reasoner.
For a field k, let G be a reductive k-group and V an affine k-variety on which G acts. Using the notion of cocharacter-closed G(k)-orbits in V, we prove a rational version of the celebrated Hilbert-Mumford Theorem from geometric invariant theory. We initiate a study of applications stemming from this rationality tool. A number of examples are discussed to illustrate the concept of cocharacter-closure and to highlight how it differs from the usual Zariski-closure. When k is perfect, we give a criterion in terms of closed orbits for G to be k-anisotropic, answering a question of Borel.
Belief revision is an operation that aims at modifying old be-liefs so that they become consistent with new ones. The issue of belief revision has been studied in various formalisms, in particular, in qualitative algebras (QAs) in which the result is a disjunction of belief bases that is not necessarily repre-sentable in a QA. This motivates the study of belief revision in formalisms extending QAs, namely, their propositional clo-sures: in such a closure, the result of belief revision belongs to the formalism. Moreover, this makes it possible to define a contraction operator thanks to the Harper identity. Belief revision in the propositional closure of QAs is studied, an al-gorithm for a family of revision operators is designed, and an open-source implementation is made freely available on the web.
The notion of bounded rationality originated from the insight that perfectly rational behavior cannot be realized by agents with limited cognitive or computational resources. Research on bounded rationality, mainly initiated by Herbert Simon, has a longstanding tradition in economics and the social sciences, but also plays a major role in modern AI and intelligent agent design. Taking actions under bounded resources requires an agent to reflect on how to use these resources in an optimal way - hence, to reason and make decisions on a meta-level. In this paper, we will look at automated machine learning (AutoML) and related problems from the perspective of bounded rationality, essentially viewing an AutoML tool as an agent that has to train a model on a given set of data, and the search for a good way of doing so (a suitable ML pipeline) as deliberation on a meta-level.
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