Rational closure for all description logics

2019 ◽  
Vol 274 ◽  
pp. 197-223 ◽  
Author(s):  
P.A. Bonatti
Keyword(s):  
Description Logics ◽  
Rational Closure

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

2015 ◽  
Vol 226 ◽  
pp. 1-33 ◽  
Author(s):  
L. Giordano ◽  
V. Gliozzi ◽  
N. Olivetti ◽  
G.L. Pozzato
Keyword(s):  
Propositional Logic ◽  
Description Logics ◽  
Rational Closure

scholarly journals Rational Closure For All Description Logics (Extended Abstract)

2020 ◽  
Author(s):  
Piero A. Bonatti
Keyword(s):  
Semantic Web ◽  
Description Logics ◽  
Natural Extension ◽  
Object Oriented ◽  
Object Oriented Programming ◽  
Biomedical Ontologies ◽  
Rational Closure ◽  
Nonmonotonic Logics

Many modern applications of description logics (DLs, for short), such as biomedical ontologies and semantic web policies, provide compelling motivations for extending DLs with an overriding mechanism analogous to the homonymous feature of object-oriented programming. Rational closure (RC) is one of the candidate semantics for such extensions, and one of the most intensively studied. So far, however, it has been limited to strict fragments of SROIQ(D) – the logic on which OWL2 is founded. In this paper we prove that RC cannot be extended to logics that do not satisfy the disjoint model union property, including SROIQ(D). Then we introduce a refinement of RC called stable rational closure that overcomes the dependency on the disjoint model union property. Our results show that stable RC is a natural extension of RC. However, its positive features come at a price: stable RC re-introduces one of the undesirable features of other nonmonotonic logics, namely, deductive closures may not exist and may not be unique.

scholarly journals Reasoning About Typicality and Probabilities in Preferential Description Logics

2020 ◽  
Author(s):  
Laura Giordano ◽  
Valentina Gliozzi ◽  
Antonio Lieto ◽  
Nicola Olivetti ◽  
Gian Luca Pozzato
Keyword(s):  
Knowledge Base ◽  
Minimal Model ◽  
Description Logics ◽  
The Other ◽  
Rational Closure ◽  
Preferential Semantics ◽  
Concept Combination ◽  
Basic Concepts ◽  
The One ◽  
Property Inheritance

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 inclusions of the form T(C) ⊑ D, whose intuitive meaning is that “normally/typically Cs are also Ds”. This extension is based on a minimal model semantics corresponding to a notion of rational closure, built upon preferential models. We recall the basic concepts underlying preferential Description Logics. We also present two extensions of the preferential semantics: on the one hand, we consider probabilistic extensions, based on a distributed semantics that is suitable for tackling the problem of commonsense concept combination, on the other hand, we consider other strengthening of the rational closure semantics and construction to avoid the so called “blocking of property inheritance problem”.

scholarly journals Reasoning about Exceptions in Ontologies: from the Lexicographic Closure to the Skeptical Closure

2020 ◽  
Vol 176 (3-4) ◽  
pp. 235-269
Author(s):  
Laura Giordano ◽  
Valentina Gliozzi
Keyword(s):  
Description Logics ◽  
Single Base ◽  
Efficient Approach ◽  
Rational Closure

Reasoning about exceptions in ontologies is nowadays one of the challenges the description logics community is facing. The paper describes a preferential approach for dealing with exceptions in Description Logics, based on the rational closure. 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 of concepts. In this work we outline a possible solution to this problem by introducing a weaker variant of the lexicographical closure, that we call skeptical closure, which requires to construct a single base. We develop a bi-preference semantics for defining a characterization of the skeptical closure.

scholarly journals Defeasible Inheritance-Based Description Logics

2013 ◽  
Vol 48 ◽  
pp. 415-473 ◽  
Author(s):  
G. Casini ◽  
U. Straccia
Keyword(s):  
Description Logics ◽  
Knowledge Bases ◽  
Propositional Knowledge ◽  
The Other ◽  
Closure Operation ◽  
Entailment Relation ◽  
Other Hand ◽  
Rational Closure ◽  
Structured Information

Defeasible inheritance networks are a non-monotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach to non-monotonic reasoning. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics (DLs), a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is built on top of the classical entailment relation and, thus, is amenable of an implementation based on existing reasoners. Eventually, we evaluate our approach on well-known landmark test examples.

scholarly journals Towards a Rational Closure for Expressive Description Logics: the Case of 𝒮𝒽𝒾𝓆

2018 ◽  
Vol 159 (1-2) ◽  
pp. 95-122 ◽  
Author(s):  
Laura Giordano ◽  
Valentina Gliozzi ◽  
Nicola Olivetti
Keyword(s):  
Description Logics ◽  
Rational Closure

scholarly journals On the relation between keys and link keys for data interlinking

Semantic Web ◽  
2020 ◽  
pp. 1-21
Author(s):  
Manuel Atencia ◽  
Jérôme David ◽  
Jérôme Euzenat
Keyword(s):  
Description Logics ◽  
The Other ◽  
Formal Framework ◽  
Precise Relationship

Both keys and their generalisation, link keys, may be used to perform data interlinking, i.e. finding identical resources in different RDF datasets. However, the precise relationship between keys and link keys has not been fully determined yet. A common formal framework encompassing both keys and link keys is necessary to ensure the correctness of data interlinking tools based on them, and to determine their scope and possible overlapping. In this paper, we provide a semantics for keys and link keys within description logics. We determine under which conditions they are legitimate to generate links. We provide conditions under which link keys are logically equivalent to keys. In particular, we show that data interlinking with keys and ontology alignments can be reduced to data interlinking with link keys, but not the other way around.

A Set-theoretic Approach to Reasoning Services for the Description Logic 𝒟 ℒ D 4,×

2020 ◽  
Vol 176 (3-4) ◽  
pp. 349-384
Author(s):  
Domenico Cantone ◽  
Marianna Nicolosi-Asmundo ◽  
Daniele Francesco Santamaria
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Theoretic Approach ◽  
The Novel ◽  
Data Types ◽  
Left Hand ◽  
Rule Languages ◽  
Tableau System ◽  
High Scalability ◽  
Better Than

In this paper we consider the most common TBox and ABox reasoning services for the description logic 𝒟ℒ〈4LQSR,x〉(D) ( 𝒟 ℒ D 4,× , for short) and prove their decidability via a reduction to the satisfiability problem for the set-theoretic fragment 4LQSR. 𝒟 ℒ D 4,× is a very expressive description logic. It combines the high scalability and efficiency of rule languages such as the SemanticWeb Rule Language (SWRL) with the expressivity of description logics. In fact, among other features, it supports Boolean operations on concepts and roles, role constructs such as the product of concepts and role chains on the left-hand side of inclusion axioms, role properties such as transitivity, symmetry, reflexivity, and irreflexivity, and data types. We further provide a KE-tableau-based procedure that allows one to reason on the main TBox and ABox reasoning tasks for the description logic 𝒟 ℒ D 4,× . Our algorithm is based on a variant of the KE-tableau system for sets of universally quantified clauses, where the KE-elimination rule is generalized in such a way as to incorporate the γ-rule. The novel system, called KEγ-tableau, turns out to be an improvement of the system introduced in [1] and of standard first-order KE-tableaux [2]. Suitable benchmark test sets executed on C++ implementations of the three mentioned systems show that in several cases the performances of the KEγ-tableau-based reasoner are up to about 400% better than the ones of the other two systems.

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