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Nonmonotonic reasoning in Description Logics. Rational Closure for the ABox

Giovanni Casini, Thomas Meyer, Kody Moodley, Ivan Varzinczak
unpublished
In what follows we are going to present the adaptation for the ABox of a classical nonmonotonic form of reasoning, Lehmann and Magidor's Rational Closure.  ...  The introduction of defeasible reasoning in Description Logics has been a main research topic in the field in the last years.  ...  In what follows we are going to present the adaptation for the ABox of a classical nonmonotonic form of reasoning, Lehmann and Magidor's Rational Closure.  ... 
fatcat:k4w3quxibrajrox3xcj2j2kqhu

Semantic characterization of rational closure: From propositional logic to description logics

L. Giordano, V. Gliozzi, N. Olivetti, G.L. Pozzato
2015 Artificial Intelligence  
We are grateful to the anonymous referees for their careful reading and constructive criticisms, which greatly helped us to improve the final version of our work.  ...  Rational closure in description logics As recalled in the Introduction, nonmonotonic reasoning in Description Logic has attracted an increasing interest in the last years [40, 2, 1, 12, 30, 8, 23, 5,  ...  Our purpose is to investigate whether rational closure can be extended in order to support nonmonotonic reasoning to Description Logics.  ... 
doi:10.1016/j.artint.2015.05.001 fatcat:udeyt6pzebfifnhuxh5ckzuz3y

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 also extend the notion of rational closure to the Abox component.  ...  Introduction Recently, in the domain of Description Logics (DLs) a large amount of work has been done in order to extend the basic formalism with nonmonotonic reasoning features.  ... 
arXiv:1305.1060v1 fatcat:7t2qzzlyojcxzczfs65gex2d6a

Reasoning about Typicality and Probabilities in Preferential Description Logics [article]

Laura Giordano, Valentina Gliozzi, Antonio Lieto, Nicola Olivetti, Gian Luca Pozzato
2020 arXiv   pre-print
In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with  ...  We recall the basic concepts underlying preferential Description Logics.  ...  A simple but powerful nonmonotonic extension for defeasible reasoning in Description Logics is proposed in [9] [10] [11] .  ... 
arXiv:2004.09507v2 fatcat:a6lvdkq27rgpbkp3pkfot6dvvm

Reasoning About Surprising Scenarios in Description Logics of Typicality [chapter]

Gian Luca Pozzato
2016 Lecture Notes in Computer Science  
We continue our investigation on nonmonotonic procedures for preferential Description Logics in order to reason about plausible but surprising scenarios.  ...  We propose a decision procedure for reasoning in ALC + T exp R and we exploit it to show that entailment is in EXPTIME as for the underlying ALC.  ...  The author is partially supported by the project "ExceptionOWL: Nonmonotonic Extensions of Description Logics and OWL for defeasible inheritance with exceptions" by Università degli Studi di Torino and  ... 
doi:10.1007/978-3-319-49130-1_31 fatcat:igjhrekh3jchtj5wpq4zahjviq

Reasoning in Description Logics with Typicalities and Probabilities of Exceptions [chapter]

Gian Luca Pozzato
2017 Lecture Notes in Computer Science  
We introduce a nonmonotonic procedure for preferential Description Logics in order to reason about typicality by taking probabilities of exceptions into account.  ...  We propose a decision procedure for reasoning in ALC + T P R and we exploit it to show that entailment is EXPTIME-complete as for the underlying ALC.  ...  a notion of rational closure as defined in [11] for propositional logic.  ... 
doi:10.1007/978-3-319-61581-3_37 fatcat:ktmdinigpveofnkdcon6f55y5i

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

Piero A. Bonatti, Iliana M. Petrova, Luigi Sauro
2020 arXiv   pre-print
DL^N is a recent approach that extends description logics with defeasible reasoning capabilities.  ...  We also compare DL^N with some alternative nonmonotonic semantics, enlightening the relationships between the KLM postulates and DL^N.  ...  Nonmonotonic extensions should be applicable to all description logics, or at least to the standard OWL2-DL (i.e. the logic SROIQ(D)).  ... 
arXiv:2009.04978v2 fatcat:ppf7mbzloba6xlnnf4k6dh6bmy

A Description Logic of Typicality for Conceptual Combination [chapter]

Antonio Lieto, Gian Luca Pozzato
2018 Lecture Notes in Computer Science  
We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of combining prototypical concepts, an open problem in the fields of AI and cognitive modelling.  ...  Additionally, it embeds a set of cognitive heuristics for concept combination. We show that the complexity of reasoning in our logic is EXPTIME-complete as in ALC.  ...  This work is partially supported by the project "ExceptionOWL", Università di Torino and Compagnia di San Paolo, call 2014 "Excellent (young) PI".  ... 
doi:10.1007/978-3-030-01851-1_19 fatcat:z7eakpalubhqjjc43cnxpa6nam

A Description Logic Framework for Commonsense Conceptual Combination Integrating Typicality, Probabilities and Cognitive Heuristics [article]

Antonio Lieto, Gian Luca Pozzato
2019 arXiv   pre-print
We also show that reasoning in the proposed Description Logic is EXPTIME-complete as for the underlying ALC.  ...  The proposed logic relies on the logic of typicality ALC TR, whose semantics is based on the notion of rational closure, as well as on the distributed semantics of probabilistic Description Logics, and  ...  A Logic for Concept Combination In this section, we introduce a new nonmonotonic Description Logic T CL that combines the semantics based on the rational closure of ALC + T R Giordano et al. (2015) with  ... 
arXiv:1811.02366v4 fatcat:rdloqz76sfeihduqnxkwoo75ye

ASP for minimal entailment in a rational extension of SROEL

LAURA GIORDANO, DANIELE THESEIDER DUPRÉ
2016 Theory and Practice of Logic Programming  
AbstractIn this paper we exploit Answer Set Programming (ASP) for reasoning in a rational extensionSROEL(⊓,×)RTof the low complexity description logicSROEL(⊓, ×), which underlies the OWL EL ontology language  ...  In the extended language, a typicality operatorTis allowed to define conceptsT(C) (typicalC's) under a rational semantics.  ...  For the language in [27] , minimal ranked models have been shown to provide a semantic characterization to rational closure for the description logic ALC, generalizing to DLs the rational closure by Lehmann  ... 
doi:10.1017/s1471068416000399 fatcat:tf7as3upcrfohn44rbufhxuksy

A Multi-engine Theorem Prover for a Description Logic of Typicality [chapter]

Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Luca Pozzato, Luca Violanti
2015 Lecture Notes in Computer Science  
We describe DysToPic, a theorem prover for the preferential Description Logic ALC + Tmin.This is a nonmonotonic extension of standard ALC based on a typicality operator T, which enjoys a preferential semantics  ...  The performances of DysToPic are promising, and significantly better than the ones of its predecessor PreDeLo 1.0 recently introduced.  ...  Pozzato is supported by the project "ExceptionOWL" (U. di Torino and C. di San Paolo).  ... 
doi:10.1007/978-3-319-24309-2_13 fatcat:tytmvnnibjdgvh2bs2sxdc46ui

Modelling Object Typicality in Description Logics [chapter]

Katarina Britz, Johannes Heidema, Thomas Meyer
2009 Lecture Notes in Computer Science  
We define a general preferential semantic framework for reasoning with object typicality in description logics.  ...  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.  ...  [11, 12] define a nonmonotonic extension of the description logic ALC to reason about typicality, while Grossi et al.  ... 
doi:10.1007/978-3-642-10439-8_51 fatcat:abzaynlifjf5dgim7sot3ouepy

Decidability of Circumscribed Description Logics Revisited [chapter]

Piero Bonatti, Marco Faella, Carsten Lutz, Luigi Sauro, Frank Wolter
2015 Lecture Notes in Computer Science  
In particular, we consider circumscribed description logics without the finite model property (DL-LiteF and ALCFI) and with fixed roles (DL-LiteF and a fragment of DL-LiteR), improving upon previous decidability  ...  We revisit non-monotonic description logics based on circumscription (with preferences) and prove several decidability results for their satisfiability problem.  ...  of autoepistemic logics, preferential semantics and rational closure [8, 11, 14, 15, 10] .  ... 
doi:10.1007/978-3-319-14726-0_8 fatcat:flpryrz2ozallcdofnpn3vd4e4

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

Katarina Britz, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
2019 Lecture Notes in Computer Science  
In this paper we present an approach to defeasible reasoning for the description logic ALC.  ...  In addition to showing that the semantics is appropriate, these results pave the way for more eective decision procedures for defeasible reasoning in description logics.  ...  In most cases, as witnessed by the great deal of work in the nonmonotonic reasoning community, a move towards rationality is in order.  ... 
doi:10.1007/978-3-030-22102-7_7 fatcat:jqmd6rc2pbbk5lz2guo2lugete

Applying a description logic of typicality as a generative tool for concept combination in computational creativity

Antonio Lieto, Gian Luca Pozzato, Chiara Ghidini, Bernardo Magnini, Andrea Passerini
2019 Intelligenza Artificiale  
In this work we exploit a nonmonotonic Description Logic of typicality as a tool for the generation and the exploration of novel creative concepts.  ...  ) the distributed semantics of probabilistic Description Logics, that allows one to provide a probability distribution over worlds/scenarios, and (iii) established heuristics used by humans for concept  ...  Acknowledgements This work has been partially supported by the project "METALLIC #2: METodi di prova per il ragionamento Automatico per Logiche non-cLassIChe #2", Progetto di Ricerca INdAM GNCS 2019.  ... 
doi:10.3233/ia-180016 fatcat:3igyhqx6ivh3hll725vmrkozia
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