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Semantic Foundation for Preferential Description Logics [chapter]

Katarina Britz, Thomas Meyer, Ivan Varzinczak
2011 Lecture Notes in Computer Science  
In this paper we fill this gap by providing a natural and intuitive semantics for defeasible subsumption in the description logic ALC.  ...  We argue that our semantics paves the way for extending preferential and rational consequence, and therefore also rational closure, to a whole class of logics that have a semantics defined in terms of  ...  A defeasible subsumption relation is a rational subsumption relation if and only if it is defined by some ranked model.  ... 
doi:10.1007/978-3-642-25832-9_50 fatcat:yqsn7tbff5aizh7zedinz5jlvu

A KLM Perspective on Defeasible Reasoning for Description Logics [chapter]

Katarina Britz, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2019 Lecture Notes in Computer Science  
This investigation includes an algorithm for the computation of a form of defeasible entailment known as rational closure in the propositional case.  ...  The results discussed here are based on work done by Kraus, Lehmann and Magidor (KLM) on defeasible conditionals in the propositional case.  ...  In Section 4, we dicuss two obvious candidates for the notion of entailment in the context of defeasible DLs, namely preferential and modular entailment.  ... 
doi:10.1007/978-3-030-22102-7_7 fatcat:jqmd6rc2pbbk5lz2guo2lugete

Theoretical Foundations of Defeasible Description Logics [article]

Katarina Britz, Giovanni Casini, Thomas Meyer, Kody Moodley, Uli Sattler, Ivan Varzinczak
2019 arXiv   pre-print
In particular, we consider a natural and intuitive semantics for defeasible subsumption, and investigate KLM-style syntactic properties for both preferential and rational subsumption.  ...  We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional case.  ...  Rationality and context in defeasible subsumption. In F. Ferrarotti and S.  ... 
arXiv:1904.07559v1 fatcat:icpvjvw6izctjd7uhirgyifxji

Modelling Object Typicality in Description Logics [chapter]

Katarina Britz, Johannes Heidema, Thomas Meyer
2009 Lecture Notes in Computer Science  
We present a semantic model of typicality of concept members in description logics that accords well with a binary, globalist cognitive model of class membership and typicality.  ...  We propose the use of feature vectors to rank concept members according to their defining and characteristic features, which provides a modelling mechanism to specify typicality in composite concepts.  ...  After giving some background on rational preference orders, we introduce the notion of an ordered interpretation, and present a formal semantics of parameterised defeasible subsumption.  ... 
doi:10.1007/978-3-642-10439-8_51 fatcat:abzaynlifjf5dgim7sot3ouepy


Flavio Ferrarotti, Stefan Woltran
2019 Annals of Mathematics and Artificial Intelligence  
This yields a notion of contextualised rational defeasible subsumption, with contexts described by roles.  ...  -In the paper Contextual Rational Closure for Defeasible ALC, Katarina Britz and Ivan Varzinczak tackle the problem of extending description logics to support defeasible reasoning.  ...  List of Reviewers Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.  ... 
doi:10.1007/s10472-019-09667-1 fatcat:olcrp5b5tjdypocn2emuuy7pgu

Preferential Reasoning for Modal Logics

Katarina Britz, Thomas Meyer, Ivan Varzinczak
2011 Electronical Notes in Theoretical Computer Science  
In this paper we fill this gap by providing a natural and intuitive semantics for preferential and rational modal consequence.  ...  We then illustrate applications of our constructions to modal logics widely used in AI, notably in the contexts of reasoning about actions, knowledge and beliefs.  ...  [22] , and of defeasible subsumption for description logics [3, 12, 5] .  ... 
doi:10.1016/j.entcs.2011.10.006 fatcat:4bhmdz76ufa7rh7dho3zlpm3uq

Preferential Semantics for Plausible Subsumption in Possibility Theory

Guilin Qi, Zhizheng Zhang
2013 Minds and Machines  
In this paper, we propose several preferential semantics for plausible subsumption to deal with exceptions in description logic-based knowledge bases.  ...  We consider the properties of these semantics and their relationships. Entailment of these plausible subsumption relative to a knowledge base is also considered.  ...  And √ √ √ √ Or √ √ √ √ Left logical equivalence √ √ √ √ Right logical equivalence √ √ √ √ Left defeasible equivalence √ √ Right defeasible equivalence √ √ Right weakening √ √ Rational right weakening √  ... 
doi:10.1007/s11023-012-9300-4 fatcat:ghvnkbcn7bcfxngjpt4rpovnsm

An ASP approach for reasoning in a concept-aware multipreferential lightweight DL

Laura Giordano, Daniele Theseider Dupré
2020 Theory and Practice of Logic Programming  
Preferences are combined to define a preferential interpretation in which defeasible inclusions can be evaluated.  ...  We exploit Answer Set Programming (in particular, asprin) to achieve defeasible reasoning under the multipreference approach for the lightweight description logic ξ$\mathcal L_ \bot ^ + $.  ...  Bozzato et al. (2014; present extensions of the CKR (Contextualized Knowledge Repositories) framework in which defeasible axioms are allowed in the global context and exceptions can be handled by overriding  ... 
doi:10.1017/s1471068420000381 fatcat:o53oiwm5sfenle74de7frnat4m

A reconstruction of the multipreference closure [article]

Laura Giordano, Valentina Gliozzi
2020 arXiv   pre-print
It is well known that the rational closure does not allow an independent handling of the inheritance of different defeasible properties of concepts.  ...  Here, we reconstruct the notion of MP-closure in the propositional case and we show that it is a natural variant of Lehmann's lexicographic closure.  ...  ) framework [10] in which defeasible axioms are allowed in the global context and can be overridden by knowledge in a local context.  ... 
arXiv:1905.03855v2 fatcat:pcyihz765jebrdlit2b5a2lyxq

A framework for a modular multi-concept lexicographic closure semantics [article]

Laura Giordano, Daniele Theseider Dupré
2020 arXiv   pre-print
The idea is that of distributing the defeasible properties of concepts into different modules, according to their subject, and of defining a notion of preference for each module based on the lexicographic  ...  We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality.  ...  Acknowledgement: We thank the anonymous referees for their helpful comments and suggestions. This research is partially supported by INDAM-GNCS Project 2019.  ... 
arXiv:2009.00964v2 fatcat:zlhzj3epynavpear2yghztr7ne

Reasoning about exceptions in ontologies: from the lexicographic closure to the skeptical closure [article]

Laura Giordano, Valentina Gliozzi
2018 arXiv   pre-print
The rational closure has the merit of providing a simple and efficient approach for reasoning with exceptions, but it does not allow independent handling of the inheritance of different defeasible properties  ...  The paper describes a preferential approach for dealing with exceptions in Description Logics, based on the rational closure.  ...  Bozzato et al. in [10] present an extension of the CKR framework in which defeasible axioms are allowed in the global context and can be overridden by knowledge in a local context.  ... 
arXiv:1807.02879v1 fatcat:coong6ghe5bmdexwnn3xbe4qle

PTL: A Propositional Typicality Logic [chapter]

Richard Booth, Thomas Meyer, Ivan Varzinczak
2012 Lecture Notes in Computer Science  
Building on the existing link between propositional rational consequence and belief revision, we show that the same correspondence holds for rational consequence and belief revision on PTL.  ...  The semantics is in terms of ranked models as studied in KLM-style preferential reasoning. This allows us to show that rational consequence relations can be embedded in our logic.  ...  Thus, in a sense, option (ii) is too weak since it ignores, for the most part, the context in which defeasible incompatibility is supposed to hold.  ... 
doi:10.1007/978-3-642-33353-8_9 fatcat:mwucomtwcfe3vcp7nwaqa34bui

Defeasible reasoning in Description Logics: an overview on DL^N [article]

Piero A. Bonatti, Iliana M. Petrova, Luigi Sauro
2020 arXiv   pre-print
In this paper we provide an overview on DL^N, illustrating the underlying knowledge engineering requirements as well as the characteristic features that preserve DL^N from some recurrent semantic and computational  ...  DL^N is a recent approach that extends description logics with defeasible reasoning capabilities.  ...  of the underlying classical module extractors in such contexts).  ... 
arXiv:2009.04978v2 fatcat:ppf7mbzloba6xlnnf4k6dh6bmy

On Rational Closure in Description Logics of Typicality [article]

Laura Giordano and Valentina Gliozzi and Nicola Olivetti and Gian Luca Pozzato
2013 arXiv   pre-print
We define the notion of rational closure in the context of Description Logics extended with a tipicality operator.  ...  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.  ...  We then proceed to extend in a natural way the propositional construction of rational closure to ALC + T for inferring defeasible subsumptions from the TBox (TBox reasoning).  ... 
arXiv:1305.1060v1 fatcat:7t2qzzlyojcxzczfs65gex2d6a

ASP for minimal entailment in a rational extension of SROEL

2016 Theory and Practice of Logic Programming  
Relying on a Small Model result, where models correspond to answer sets of a suitable ASP encoding, we exploit Answer Set Preferences (and, in particular, theasprinframework) for reasoning under minimal  ...  It has been proven that instance checking under rational entailment has a polynomial complexity. To strengthen rational entailment, in this paper we consider a minimal model semantics.  ...  This subsumption is not in the language of normalized KBs, but it can be replaced by the subsumption A ⊑ ⊥, adding T(⊤) ⊑ X and X ⊓ C ⊑ A to K.  ... 
doi:10.1017/s1471068416000399 fatcat:tf7as3upcrfohn44rbufhxuksy
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