7 research outputs found
Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure
In this work we study a rational extension 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
-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.Comment: Accepted for publication on Fundamenta Informatica
Defeasible RDFS via Rational Closure
In the field of non-monotonic logics, the notion of Rational Closure (RC) is
acknowledged as a prominent approach. In recent years, RC has gained even more
popularity in the context of Description Logics (DLs), the logic underpinning
the semantic web standard ontology language OWL 2, whose main ingredients are
classes and roles. In this work, we show how to integrate RC within the triple
language RDFS, which together with OWL2 are the two major standard semantic web
ontology languages. To do so, we start from , which is the logic
behind RDFS, and then extend it to , allowing to state that two
entities are incompatible. Eventually, we propose defeasible via
a typical RC construction. The main features of our approach are: (i) unlike
most other approaches that add an extra non-monotone rule layer on top of
monotone RDFS, defeasible remains syntactically a triple
language and is a simple extension of by introducing some new
predicate symbols with specific semantics. In particular, any RDFS
reasoner/store may handle them as ordinary terms if it does not want to take
account for the extra semantics of the new predicate symbols; (ii) the
defeasible entailment decision procedure is build on top of the
entailment decision procedure, which in turn is an extension of
the one for via some additional inference rules favouring an
potential implementation; and (iii) defeasible entailment can be
decided in polynomial time.Comment: 47 pages. Preprint versio
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
\Pi^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.Comment: Paper presented at the 32nd International Conference on Logic
Programming (ICLP 2016), New York City, USA, 16-21 October 201
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
\Pi^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.Comment: Paper presented at the 32nd International Conference on Logic
Programming (ICLP 2016), New York City, USA, 16-21 October 201
A Lightweight Defeasible Description Logic in Depth: Quantification in Rational Reasoning and Beyond
Description Logics (DLs) are increasingly successful knowledge representation formalisms, useful for any application requiring implicit derivation of knowledge from explicitly known facts.
A prominent example domain benefiting from these formalisms since the 1990s is the biomedical field.
This area contributes an intangible amount of facts and relations between low- and high-level concepts such as the constitution of cells or interactions between studied illnesses, their symptoms and remedies.
DLs are well-suited for handling large formal knowledge repositories and computing inferable coherences throughout such data, relying on their well-founded first-order semantics.
In particular, DLs of reduced expressivity have proven a tremendous worth for handling large ontologies due to their computational tractability.
In spite of these assets and prevailing influence, classical DLs are not well-suited to adequately model some of the most intuitive forms of reasoning.
The capability for abductive reasoning is imperative for any field subjected to incomplete knowledge and the motivation to complete it with typical expectations.
When such default expectations receive contradicting evidence, an abductive formalism is able to retract previously drawn, conflicting conclusions.
Common examples often include human reasoning or a default characterisation of properties in biology, such as the normal arrangement of organs in the human body.
Treatment of such defeasible knowledge must be aware of exceptional cases - such as a human suffering from the congenital condition situs inversus - and therefore accommodate for the ability to retract defeasible conclusions in a non-monotonic fashion.
Specifically tailored non-monotonic semantics have been continuously investigated for DLs in the past 30 years.
A particularly promising approach, is rooted in the research by Kraus, Lehmann and Magidor for preferential (propositional) logics and Rational Closure (RC).
The biggest advantages of RC are its well-behaviour in terms of formal inference postulates and the efficient computation of defeasible entailments, by relying on a tractable reduction to classical reasoning in the underlying formalism.
A major contribution of this work is a reorganisation of the core of this reasoning method, into an abstract framework formalisation.
This framework is then easily instantiated to provide the reduction method for RC in DLs as well as more advanced closure operators, such as Relevant or Lexicographic Closure.
In spite of their practical aptitude, we discovered that all reduction approaches fail to provide any defeasible conclusions for elements that only occur in the relational neighbourhood of the inspected elements.
More explicitly, a distinguishing advantage of DLs over propositional logic is the capability to model binary relations and describe aspects of a related concept in terms of existential and universal quantification.
Previous approaches to RC (and more advanced closures) are not able to derive typical behaviour for the concepts that occur within such quantification.
The main contribution of this work is to introduce stronger semantics for the lightweight DL EL_bot with the capability to infer the expected entailments, while maintaining a close relation to the reduction method.
We achieve this by introducing a new kind of first-order interpretation that allocates defeasible information on its elements directly.
This allows to compare the level of typicality of such interpretations in terms of defeasible information satisfied at elements in the relational neighbourhood.
A typicality preference relation then provides the means to single out those sets of models with maximal typicality.
Based on this notion, we introduce two types of nested rational semantics, a sceptical and a selective variant, each capable of deriving the missing entailments under RC for arbitrarily nested quantified concepts.
As a proof of versatility for our new semantics, we also show that the stronger Relevant Closure, can be imbued with typical information in the successors of binary relations.
An extensive investigation into the computational complexity of our new semantics shows that the sceptical nested variant comes at considerable additional effort, while the selective semantics reside in the complexity of classical reasoning in the underlying DL, which remains tractable in our case