Reasoning with inconsistent possibilistic description logics ontologies with disjunctive assertions

We present a preliminary framework for reasoning with possibilistic description logics ontologies with disjunctive assertions (PoDLoDA ontologies for short). Given a PoDLoDA ontology, its terminological box is expressed in the description logic programming fragment but its assertional box allows four kinds of statements: an individual is a member of a concept, two individuals are related through a role, an individual is a member of the union of two or more concepts or two individuals are related through the union of two or more roles. Axioms and statements in PoDLoDA ontologies have a numerical certainty degree attached. A disjunctive assertion expresses a doubt respect to the membership of either individuals to union of concepts or pairs of individuals to the union of roles. Because PoDLoDA ontologies allow to represent incomplete and potentially inconsistent information, instance checking is addressed through an adaptation of Bodanza’s Suppositional Argumentation System that allows to reason with modus ponens and constructive dilemmas. We think that our approach will be of use for implementers of reasoning systems in the Semantic Web where uncertainty of membership of individuals to concepts or roles is present.Facultad de Informátic

Reasoning with inconsistent possibilistic description logics ontologies with disjunctive assertions

We present a preliminary framework for reasoning with possibilistic description logics ontologies with disjunctive assertions (PoDLoDA ontologies for short). Given a PoDLoDA ontology, its terminological box is expressed in the description logic programming fragment but its assertional box allows four kinds of statements: an individual is a member of a concept, two individuals are related through a role, an individual is a member of the union of two or more concepts or two individuals are related through the union of two or more roles. Axioms and statements in PoDLoDA ontologies have a numerical certainty degree attached. A disjunctive assertion expresses a doubt respect to the membership of either individuals to union of concepts or pairs of individuals to the union of roles. Because PoDLoDA ontologies allow to represent incomplete and potentially inconsistent information, instance checking is addressed through an adaptation of Bodanza’s Suppositional Argumentation System that allows to reason with modus ponens and constructive dilemmas. We think that our approach will be of use for implementers of reasoning systems in the Semantic Web where uncertainty of membership of individuals to concepts or roles is present.Facultad de Informátic

On the Application of Argument Accrual to Reasoning with Inconsistent Possibilistic Ontologies

We present an approach for performing instance checking in a suitable subset of possibilistic description logic programming ontologies by using argument accrual. Ontologies are interpreted in possibilistic logic programming under Dung's grounded semantics. We present a reasoning framework with a case study and a Java-based implementation for enacting the proposed approach.XVII Workshop Agentes y Sistemas Inteligentes (WASI).Red de Universidades con Carreras en Informática (RedUNCI

On the Application of Argument Accrual to Reasoning with Inconsistent Possibilistic Ontologies

We present an approach for performing instance checking in a suitable subset of possibilistic description logic programming ontologies by using argument accrual. Ontologies are interpreted in possibilistic logic programming under Dung's grounded semantics. We present a reasoning framework with a case study and a Java-based implementation for enacting the proposed approach.XVII Workshop Agentes y Sistemas Inteligentes (WASI).Red de Universidades con Carreras en Informática (RedUNCI

A preliminary framework for reasoning with inconsistent possibilistic description logics ontologies with disjunctive assertions

We present a preliminary framework for reasoning with possibilistic description logics ontologies with disjunctive assertions (PDLDA ontologies for short). PDLDA ontologies are composed of a terminology as well as an assertional box that allows to declare three kinds of assertional statements: an individual is a member of one concept, two individuals are related through a role, an individual is a member of the union of two or more concepts or two individuals are related through the union of two or more roles. Each axiom in the ontologies has a certainty degree as is usual in possibilistic logics. For reasoning with PDLDA ontologies, we interpret them in terms of a adaptation of Bodanza's Suppositional Argumentation System. Our framework allows to reason with modus ponens and constructive dilemmas. We use it for determining the membership of individuals to concepts when there is doubt to exactly which one of the concepts in the union the individual belongs. We think that our approach will be of use for implementers of reasoning systems in the Semantic Web where uncertainty of membership of individuals to concepts or roles is present.XVI Workshop Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

A preliminary framework for reasoning with inconsistent possibilistic description logics ontologies with disjunctive assertions

We present a preliminary framework for reasoning with possibilistic description logics ontologies with disjunctive assertions (PDLDA ontologies for short). PDLDA ontologies are composed of a terminology as well as an assertional box that allows to declare three kinds of assertional statements: an individual is a member of one concept, two individuals are related through a role, an individual is a member of the union of two or more concepts or two individuals are related through the union of two or more roles. Each axiom in the ontologies has a certainty degree as is usual in possibilistic logics. For reasoning with PDLDA ontologies, we interpret them in terms of a adaptation of Bodanza's Suppositional Argumentation System. Our framework allows to reason with modus ponens and constructive dilemmas. We use it for determining the membership of individuals to concepts when there is doubt to exactly which one of the concepts in the union the individual belongs. We think that our approach will be of use for implementers of reasoning systems in the Semantic Web where uncertainty of membership of individuals to concepts or roles is present.XVI Workshop Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

Expressive probabilistic description logics

AbstractThe work in this paper is directed towards sophisticated formalisms for reasoning under probabilistic uncertainty in ontologies in the Semantic Web. Ontologies play a central role in the development of the Semantic Web, since they provide a precise definition of shared terms in web resources. They are expressed in the standardized web ontology language OWL, which consists of the three increasingly expressive sublanguages OWL Lite, OWL DL, and OWL Full. The sublanguages OWL Lite and OWL DL have a formal semantics and a reasoning support through a mapping to the expressive description logics SHIF(D) and SHOIN(D), respectively. In this paper, we present the expressive probabilistic description logics P-SHIF(D) and P-SHOIN(D), which are probabilistic extensions of these description logics. They allow for expressing rich terminological probabilistic knowledge about concepts and roles as well as assertional probabilistic knowledge about instances of concepts and roles. They are semantically based on the notion of probabilistic lexicographic entailment from probabilistic default reasoning, which naturally interprets this terminological and assertional probabilistic knowledge as knowledge about random and concrete instances, respectively. As an important additional feature, they also allow for expressing terminological default knowledge, which is semantically interpreted as in Lehmann's lexicographic entailment in default reasoning from conditional knowledge bases. Another important feature of this extension of SHIF(D) and SHOIN(D) by probabilistic uncertainty is that it can be applied to other classical description logics as well. We then present sound and complete algorithms for the main reasoning problems in the new probabilistic description logics, which are based on reductions to reasoning in their classical counterparts, and to solving linear optimization problems. In particular, this shows the important result that reasoning in the new probabilistic description logics is decidable/computable. Furthermore, we also analyze the computational complexity of the main reasoning problems in the new probabilistic description logics in the general as well as restricted cases

Towards a Practical Implementation of a Reasoner for Inconsistent Possibilistic Description Logic Programming Ontologies

This work reports on our e orts to implement a practical reasoner based on Dung-style argumentation semantics for potentially inconsistent possibilistic ontologies. Our Java-based implementation targets a subset of the description logic programming fragment that we codify in a Racer-like syntax suitably adapted for representing certainty degrees of both axioms and assertions. We introduce our approach with a running example, discuss implementation issues and present time complexity results.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Towards a Practical Implementation of a Reasoner for Inconsistent Possibilistic Description Logic Programming Ontologies

This work reports on our e orts to implement a practical reasoner based on Dung-style argumentation semantics for potentially inconsistent possibilistic ontologies. Our Java-based implementation targets a subset of the description logic programming fragment that we codify in a Racer-like syntax suitably adapted for representing certainty degrees of both axioms and assertions. We introduce our approach with a running example, discuss implementation issues and present time complexity results.Sociedad Argentina de Informática e Investigación Operativa (SADIO