arXiv subjects

Laura Giordano

Publications and source records attributed to Laura Giordano.

28 records · Page 2Linked to original sources

arXiv2020

Reasoning about Typicality and Probabilities in Preferential Description Logics

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.

cs.AI↗

arXiv2019

Adding the Power-Set to Description Logics

We explore the relationships between Description Logics and Set Theory. The study is carried on using, on the set-theoretic side, a very rudimentary axiomatic set theory Omega, consisting of only four axioms characterizing binary union, set difference, inclusion, and the power-set. An extension of ALC, ALC^Omega, is then defined in which concepts are naturally interpreted as sets living in Omega-models. In ALC^Omega not only membership between concepts is allowed---even admitting circularity---but also the power-set construct is exploited to add metamodeling capabilities. We investigate translations of ALC^Omega into standard description logics as well as a set-theoretic translation. A polynomial encoding of ALC^Omega in ALCIO proves the validity of the finite model property as well as an ExpTime upper bound on the complexity of concept satisfiability. We develop a set-theoretic translation of ALC^Omega in the theory Omega, exploiting a technique originally proposed for translating normal modal and polymodal logics into Omega. Finally, we show that the fragment LC^Omega of ALC^Omega, which does not admit roles and individual names, is as expressive as ALC^Omega.

cs.LO↗

arXiv2018

Reasoning about exceptions in ontologies: from the lexicographic closure to the skeptical 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 variant of the lexicographical closure, that we call skeptical closure, which requires to construct a single base. We develop a bi-preference semantics semantics for defining a characterization of the skeptical closure.

cs.AI↗

arXiv2018

Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure

In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and Magidor's ranked models and allows for the definition of defeasible inclusions. We consider both rational entailment and minimal entailment. We show that deciding instance checking under minimal entailment is in general $Π^P_2$-hard, while, under rational entailment, instance checking can be computed in polynomial time. We develop a Datalog calculus for instance checking under rational entailment and exploit it, with stratified negation, for computing the rational closure of simple KBs in polynomial time.

cs.AI↗

arXiv2018

Reasoning about multiple aspects in DLs: Semantics and Closure Construction

Starting from the observation that rational closure has the undesirable property of being an "all or nothing" mechanism, we here propose a multipreferential semantics, which enriches the preferential semantics underlying rational closure in order to separately deal with the inheritance of different properties in an ontology with exceptions. We provide a multipreference closure mechanism which is sound with respect to the multipreference semantics.

cs.AI↗

arXiv2016

ASP for Minimal Entailment in a Rational Extension of SROEL

In this paper we exploit Answer Set Programming (ASP) for reasoning in a rational extension SROEL-R-T of the low complexity description logic SROEL, which underlies the OWL EL ontology language. In the extended language, a typicality operator T is allowed to define concepts T(C) (typical C's) under a rational semantics. 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. We show that, for arbitrary SROEL-R-T knowledge bases, instance checking under minimal entailment is Π^P_2-complete. 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, the asprin framework) for reasoning under minimal entailment. The paper is under consideration for acceptance in Theory and Practice of Logic Programming.

cs.AI↗

arXiv2014

Rational Closure in SHIQ

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.

cs.AI↗

arXiv2013

On Rational Closure in Description Logics of Typicality

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 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.

cs.AI↗

arXiv2011

Reasoning about Actions with Temporal Answer Sets

In this paper we combine Answer Set Programming (ASP) with Dynamic Linear Time Temporal Logic (DLTL) to define a temporal logic programming language for reasoning about complex actions and infinite computations. DLTL extends propositional temporal logic of linear time with regular programs of propositional dynamic logic, which are used for indexing temporal modalities. The action language allows general DLTL formulas to be included in domain descriptions to constrain the space of possible extensions. We introduce a notion of Temporal Answer Set for domain descriptions, based on the usual notion of Answer Set. Also, we provide a translation of domain descriptions into standard ASP and we use Bounded Model Checking techniques for the verification of DLTL constraints.

cs.AI↗

arXiv2006

Analytic Tableaux Calculi for KLM Logics of Nonmonotonic Reasoning

We present tableau calculi for some logics of nonmonotonic reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered, and we study their complexity.

cs.LO↗