Extension of Description Logics for Reasoning About Typicality

2009

We present a nonmonotonic extension of the Description Logic ALC for reasoning about prototypical properties and inheritance with exception. The logic ALC is extended by introducing a typicality operator T which is intended to select the “most normal” instances of a concept. A minimal model semantics is defined for ALC + T, in order to perform nonmonotonic inferences. The resulting logic ALC + Tmin is able to infer defeasible properties of explicit and implicit individuals. The paper presents a tableau calculus for deciding ALC + Tmin entailment. The work was partially supported by Regione Piemonte, Project ICT4Law. Main contribution of this paper have been also presented at the 11th European Conference on Logics in Artificial Intelligence “JELIA 2008” [10].

Artificial Intelligence, 2013

In this paper we propose a non-monotonic extension of the Description Logic ALC for reasoning about prototypical properties and inheritance with exceptions. The resulting logic, called ALC + T min , is built upon a previously introduced (monotonic) logic ALC + T that is obtained by adding a typicality operator T to ALC. The operator T is intended to select the "most normal" or "most typical" instances of a concept, so that knowledge bases may contain subsumption relations of the form T(C) D ("T(C) is subsumed by D"), expressing that typical C-members are instances of concept D. From a knowledge representation point of view, the monotonic logic ALC + T is too weak to perform inheritance reasoning. In ALC + T min , in order to perform non-monotonic inferences, we define a "minimal model" semantics over ALC + T. The intuition is that preferred or minimal models are those that maximize typical instances of concepts. By means of ALC + T min we are able to infer defeasible properties of (explicit or implicit) individuals. We also present a tableau calculus for deciding ALC + T min entailment that allows to give a complexity upper bound for the logic, namely that query entailment is in co-NExp NP .

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2009

We present an extension of the low complexity Description Logic EL + ⊥ for reasoning about prototypical properties and inheritance with exceptions. We add to EL + ⊥ a typicality operator T, which is intended to select the "most normal" instances of a concept. In the resulting logic, called EL + ⊥ T, the knowledge base may contain subsumption relations of the form "T(C) is subsumed by P ", expressing that typical C-members have the property P. We show that the problem of entailment in EL + ⊥ T is in co-NP by proving a small model result.

2020

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) v 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.

2010

Extensions of Description Logics (DLs) to reason about typicality and defeasible inheritance have been largely investigated. In this paper, we consider two such extensions, namely (i) the extension of DLs with a typicality operator T, having the properties of Preferential nonmonotonic entailment P, and (ii) its variant with a typicality operator having the properties of the stronger Rational entailment R. The first one has been proposed in [1, 2]. Here, we investigate the second one and we show, by a representation theorem, that it is equivalent to the approach to preferential subsumption proposed in [3]. We compare the two extensions, preferential and rational, and argue that the first one is more suitable than the second one to reason about typicality, as the latter leads to unintuitive inferences.

2009

We present an extension \(\mathcal{EL}^{+^\bot}{\bf {\rm T}}\) of the description logic \(\mathcal{EL}^{+^\bot}\) for reasoning about prototypical properties and inheritance with exceptions. \(\mathcal{EL}^{+^\bot}{\bf {\rm T}}\) is obtained by adding to \(\mathcal{EL}^{+^\bot}\) a typicality operator T, which is intended to select the “typical” instances of a concept. In \(\mathcal{EL}^{+^\bot}{\bf {\rm T}}\) knowledge bases may contain inclusions of the form “T(C) is subsumed by P”, expressing that typical C-members have the property P. We show that the problem of entailment in \(\mathcal{EL}^{+^\bot}{\bf {\rm T}}\) is in co-NP.

Italian Conference on Theoretical Computer Science, 2017

We present RAT-OWL, a software system for reasoning about typicality in preferential Description Logics. It is implemented in the form of a Protégé 4.3 Plugin and it allows the user to reason in a nonmonotonic extension of Description Logics based on the notion of "rational closure". This logic extends standard Description Logics in order to express "typical" properties, that can be directly specified by means of a typicality operator T: a TBox can contain inclusions of the form T(C) D to represent that "typical Cs are also Ds". We show experimental results, indicating that the performances of RAT-OWL are promising.

2009

In this work we summarize our recent results on extending Description Logics for reasoning about prototypical properties and inheritance with exceptions. First, we focus our attention on the logic ALC. We present a nonmonotonic logic ALC + Tmin, which is built upon a monotonic logic ALC + T obtained by adding a typicality operator T to ALC. The operator T is intended to select the "most normal" or "most typical" instances of a concept, so that knowledge bases may contain subsumption relations of the form"T(C) is subsumed by P ", expressing that typical C-members have the property P . In order to perform nonmonotonic inferences, we define a "minimal model" semantics: the intuition is that preferred, or minimal models are those that maximise typical instances of concepts. By means of ALC +Tmin we are able to infer defeasible properties of (explicit or implicit) individuals. We also show that the satisfiability of an ALC + T-knowledge base is in EXPTIME, whereas deciding query entailment in ALC + Tmin is in co-NExp NP . We apply our approach based on the operator T also to the low complexity Description Logic EL + ⊥ . We propose an extension EL + ⊥ T and we show that the problem of entailment in EL + ⊥ T is in co-NP.

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 Magidor's original one. We also extend the notion of rational closure to the Abox component. We provide an EXP-TIME 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.

Lecture Notes in Computer Science, 2013

We describe PreDeLo 1.0, a theorem prover for preferential Description Logics (DLs). These are nonmonotonic extensions of standard DLs based on a typicality operator T, which enjoys a preferential semantics. PreDeLo 1.0 is a Prolog implementation of labelled tableaux calculi for such extensions, and it is able to deal with the preferential extension of the basic DL ALC as well as with the preferential extension of the lightweight DL DL-Litecore. The Prolog implementation is inspired by the "lean" methodology, whose basic idea is that each axiom or rule of the tableaux calculi is implemented by a Prolog clause of the program. Concerning ALC, PreDeLo 1.0 considers two extensions based, respectively, on Kraus, Lehmann and Magidor's preferential and rational entailment. In this paper, we also introduce a tableaux calculus for checking entailment in the rational extension of ALC.