18 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
A polynomial Time Subsumption Algorithm for Nominal Safe ELO under Rational Closure
Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ELO⊥, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ELO⊥ under RC that relies entirely on a series of classical, monotonic EL⊥ subsumption tests. Therefore, any existing classical monotonic EL⊥ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability
A polynomial Time Subsumption Algorithm for Nominal Safe ELO_bot under Rational Closure
Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe ELO_bot, a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe ELO_bot under RC that relies entirely on a series of classical, monotonic EL_bot subsumption tests. Therefore, any existing classical monotonic EL_bot reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability
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
A Polynomial Time Subsumption Algorithm for Nominal Safe under Rational Closure
Description Logics (DLs) under Rational Closure (RC) is a well-known framework for non-monotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe , a notable and practically important DL representative of the OWL 2 profile OWL 2 EL. Our contribution here is to define a polynomial time subsumption procedure for nominal safe under RC that relies entirely on a series of classical, monotonic subsumption tests. Therefore, any existing classical monotonic reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability
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.Comment: 17 pages. arXiv admin note: text overlap with arXiv:1811.0236
UML class diagrams supporting formalism definition in the Draw-Net Modeling System
The Draw-Net Modeling System (DMS) is a customizable framework supporting the design and the solution of models expressed in any graph-based formalism, thanks to an open architecture. During the years, many formalisms (Petri Nets, Bayesian Networks, Fault Trees, etc.) have been included in DMS. A formalism defines all the primitives that can be used in a model (nodes, arcs, properties, etc.) and is stored into XML files. The paper describes a new way to manage formalisms: the user can create a new formalism by drawing a UML Class Diagrams (CD); then the corresponding XML files are automatically generated. If instead the user intends to edit an existing formalism, a "reverse engineering" function generates the CD from the XML files. The CD can be handled inside DMS, and acts an intuitive and graphical "meta-model" to represent the formalism. An application example is presented