An algebra of qualitative taxonomical relations for ontology alignments

inants2015aInternational audienceAlgebras of relations were shown useful in managing ontology alignments. They make it possible to aggregate alignments disjunctively or conjunctively and to propagate alignments within a network of ontologies. The previously considered algebra of relations contains taxonomical relations between classes. However, compositional inference using this algebra is sound only if we assume that classes which occur in alignments have nonempty extensions. Moreover, this algebra covers relations only between classes. Here we introduce a new algebra of relations, which, first, solves the limitation of the previous one, and second, incorporates all qualitative taxonomical relations that occur between individuals and concepts, including the relations "is a" and "is not". We prove that this algebra is coherent with respect to the simple semantics of alignments

Algebraic calculi for weighted ontology alignments

inants2016bInternational audienceAlignments between ontologies usually come with numerical attributes expressing the confidence of each correspondence. Semantics supporting such confidences must generalise the semantics of alignments without confidence. There exists a semantics which satisfies this but introduces a discontinuity between weighted and non-weighted interpretations. Moreover, it does not provide a calculus for reasoning with weighted ontology alignments. This paper introduces a calculus for such alignments. It is given by an infinite relation-type algebra, the elements of which are weighted taxonomic relations. In addition, it approximates the non-weighted case in a continuous manner

An algebra of qualitative taxonomical relations for ontology alignments

inants2015aInternational audienceAlgebras of relations were shown useful in managing ontology alignments. They make it possible to aggregate alignments disjunctively or conjunctively and to propagate alignments within a network of ontologies. The previously considered algebra of relations contains taxonomical relations between classes. However, compositional inference using this algebra is sound only if we assume that classes which occur in alignments have nonempty extensions. Moreover, this algebra covers relations only between classes. Here we introduce a new algebra of relations, which, first, solves the limitation of the previous one, and second, incorporates all qualitative taxonomical relations that occur between individuals and concepts, including the relations "is a" and "is not". We prove that this algebra is coherent with respect to the simple semantics of alignments

Context-based ontology matching and data interlinking

euzenat2015cContext-based matching finds correspondences between entities from two ontologies by relating them to other resources. A general view of context-based matching is designed by analysing existing such matchers. This view is instantiated in a path-driven approach that (a) anchors the ontologies to external ontologies, (b) finds sequences of entities (path) that relate entities to match within and across these resources, and (c) uses algebras of relations for combining the relations obtained along these paths. Parameters governing such a system are identified and made explicit. We discuss the extension of this approach to data interlinking and its benefit to cross-lingual data interlinking. First, this extension would require an hybrid algebra of relation that combines relations between individual and classes. However, such an algebra may not be particularly useful in practice as only in a few restricted case it could conclude that two individuals are the same. But it can be used for finding mistakes in link sets

Context-based ontology matching and data interlinking

euzenat2015cContext-based matching finds correspondences between entities from two ontologies by relating them to other resources. A general view of context-based matching is designed by analysing existing such matchers. This view is instantiated in a path-driven approach that (a) anchors the ontologies to external ontologies, (b) finds sequences of entities (path) that relate entities to match within and across these resources, and (c) uses algebras of relations for combining the relations obtained along these paths. Parameters governing such a system are identified and made explicit. We discuss the extension of this approach to data interlinking and its benefit to cross-lingual data interlinking. First, this extension would require an hybrid algebra of relation that combines relations between individual and classes. However, such an algebra may not be particularly useful in practice as only in a few restricted case it could conclude that two individuals are the same. But it can be used for finding mistakes in link sets

Calculs qualitatifs avec des univers hétérogènes

Représentation et raisonnement qualitatifs fonctionnent avec des relations non-numériques entre les objets d'un univers. Les formalismes généraux développés dans ce domaine sont basés sur différents types d'algèbres de relations, comme les algèbres de Tarski. Tous ces formalismes, qui sont appelés des calculs qualitatifs, partagent l'hypothèse implicite que l'univers est homogène, c'est-à-dire qu'il se compose d'objets de même nature. Toutefois, les objets de différents types peuvent aussi entretenir des relations. L'état de l'art du raisonnement qualitatif ne permet pas de combiner les calculs qualitatifs pour les différents types d'objets en un seul calcul.De nombreuses applications discriminent entre différents types d'objets. Par exemple, certains modèles spatiaux discriminent entre les régions, les lignes et les points, et différentes relations sont utilisées pour chaque type d'objets. Dans l'alignement d'ontologies, les calculs qualitatifs sont utiles pour exprimer des alignements entre un seul type d'entités, telles que des concepts ou des individus. Cependant, les relations entre les individus et les concepts, qui imposent des contraintes supplémentaires, ne sont pas exploitées.Cette thèse introduit la modularité dans les calculs qualitatifs et fournit une méthodologie pour la modélisation de calculs qualitatifs des univers hétérogènes. Notre contribution principale est un cadre basé sur une classe spéciale de schémas de partition que nous appelons modulaires. Pour un calcul qualitatif engendré par un schéma de partition modulaire, nous définissons une structure qui associe chaque symbole de relation avec un domaine et codomain abstrait à partir d'un treillis booléen de sortes. Un module d'un tel calcul qualitatif est un sous-calcul limité à une sorte donnée, qui est obtenu par une opération appelée relativisation à une sorte. D'un intérêt pratique plus grand est l'opération inverse, qui permet de combiner plusieurs calculs qualitatifs en un seul calcul. Nous définissons une opération appelée combinaison modulo liaison, qui combine deux ou plusieurs calculs qualitatifs sur différents univers, en fonction de quelques relations de liaison entre ces univers. Le cadre est suffisamment général pour soutenir la plupart des calculs spatio-temporels qualitatifs connus.Qualitative representation and reasoning operate with non-numerical relations holding between objects of some universe. The general formalisms developed in this field are based on various kinds of algebras of relations, such as Tarskian relation algebras. All these formalisms, which are called qualitative calculi, share an implicit assumption that the universe is homogeneous, i.e., consists of objects of the same kind. However, objects of different kinds may also entertain relations. The state of the art of qualitative reasoning does not offer a combination operation of qualitative calculi for different kinds of objects into a single calculus.Many applications discriminate between different kinds of objects. For example, some spatial models discriminate between regions, lines and points, and different relations are used for each kind of objects. In ontology matching, qualitative calculi were shown useful for expressing alignments between only one kind of entities, such as concepts or individuals. However, relations between individuals and concepts, which impose additional constraints, are not exploited.This dissertation introduces modularity in qualitative calculi and provides a methodology for modeling qualitative calculi with heterogeneous universes. Our central contribution is a framework based on a special class of partition schemes which we call modular. For a qualitative calculus generated by a modular partition scheme, we define a structure that associates each relation symbol with an abstract domain and codomain from a Boolean lattice of sorts. A module of such a qualitative calculus is a sub-calculus restricted to a given sort, which is obtained through an operation called relativization to a sort. Of a greater practical interest is the opposite operation, which allows for combining several qualitative calculi into a single calculus. We define an operation called combination modulo glue, which combines two or more qualitative calculi over different universes, provided some glue relations between these universes. The framework is general enough to support most known qualitative spatio-temporal calculi

Calculs qualitatifs avec des univers hétérogènes

Qualitative representation and reasoning operate with non-numerical relations holding between objects of some universe. The general formalisms developed in this field are based on various kinds of algebras of relations, such as Tarskian relation algebras. All these formalisms, which are called qualitative calculi, share an implicit assumption that the universe is homogeneous, i.e., consists of objects of the same kind. However, objects of different kinds may also entertain relations. The state of the art of qualitative reasoning does not offer a combination operation of qualitative calculi for different kinds of objects into a single calculus.Many applications discriminate between different kinds of objects. For example, some spatial models discriminate between regions, lines and points, and different relations are used for each kind of objects. In ontology matching, qualitative calculi were shown useful for expressing alignments between only one kind of entities, such as concepts or individuals. However, relations between individuals and concepts, which impose additional constraints, are not exploited.This dissertation introduces modularity in qualitative calculi and provides a methodology for modeling qualitative calculi with heterogeneous universes. Our central contribution is a framework based on a special class of partition schemes which we call modular. For a qualitative calculus generated by a modular partition scheme, we define a structure that associates each relation symbol with an abstract domain and codomain from a Boolean lattice of sorts. A module of such a qualitative calculus is a sub-calculus restricted to a given sort, which is obtained through an operation called relativization to a sort. Of a greater practical interest is the opposite operation, which allows for combining several qualitative calculi into a single calculus. We define an operation called combination modulo glue, which combines two or more qualitative calculi over different universes, provided some glue relations between these universes. The framework is general enough to support most known qualitative spatio-temporal calculi.Représentation et raisonnement qualitatifs fonctionnent avec des relations non-numériques entre les objets d'un univers. Les formalismes généraux développés dans ce domaine sont basés sur différents types d'algèbres de relations, comme les algèbres de Tarski. Tous ces formalismes, qui sont appelés des calculs qualitatifs, partagent l'hypothèse implicite que l'univers est homogène, c'est-à-dire qu'il se compose d'objets de même nature. Toutefois, les objets de différents types peuvent aussi entretenir des relations. L'état de l'art du raisonnement qualitatif ne permet pas de combiner les calculs qualitatifs pour les différents types d'objets en un seul calcul.De nombreuses applications discriminent entre différents types d'objets. Par exemple, certains modèles spatiaux discriminent entre les régions, les lignes et les points, et différentes relations sont utilisées pour chaque type d'objets. Dans l'alignement d'ontologies, les calculs qualitatifs sont utiles pour exprimer des alignements entre un seul type d'entités, telles que des concepts ou des individus. Cependant, les relations entre les individus et les concepts, qui imposent des contraintes supplémentaires, ne sont pas exploitées.Cette thèse introduit la modularité dans les calculs qualitatifs et fournit une méthodologie pour la modélisation de calculs qualitatifs des univers hétérogènes. Notre contribution principale est un cadre basé sur une classe spéciale de schémas de partition que nous appelons modulaires. Pour un calcul qualitatif engendré par un schéma de partition modulaire, nous définissons une structure qui associe chaque symbole de relation avec un domaine et codomain abstrait à partir d'un treillis booléen de sortes. Un module d'un tel calcul qualitatif est un sous-calcul limité à une sorte donnée, qui est obtenu par une opération appelée relativisation à une sorte. D'un intérêt pratique plus grand est l'opération inverse, qui permet de combiner plusieurs calculs qualitatifs en un seul calcul. Nous définissons une opération appelée combinaison modulo liaison, qui combine deux ou plusieurs calculs qualitatifs sur différents univers, en fonction de quelques relations de liaison entre ces univers. Le cadre est suffisamment général pour soutenir la plupart des calculs spatio-temporels qualitatifs connus

So, what exactly is a qualitative calculus?

International audienceThe paradigm of algebraic constraint-based reasoning, embodied in the notion of a qualitative calculus, is studied within two alternative frameworks. One framework defines a qualitative calculus as "a non-associative relation algebra (NA) with a qualitative representation", the other as "an algebra generated by jointly exhaustive and pairwise disjoint (JEPD) relations". These frameworks provide complementary perspectives: the first is intensional (axiom-based), whereas the second one is extensional (based on semantic structures). However, each definition admits calculi that lie beyond the scope of the other. Thus, a qualitatively representable NA may be incomplete or non-atomic, whereas an algebra generated by JEPD relations may have non-involutive converse and no identity element. The divergence of definitions creates a confusion around the notion of a qualitative calculus and makes the "what" question posed by Ligozat and Renz actual once again. Here we define the relation-type qualitative calculus unifying the intensional and extensional approaches. By introducing the notions of weak identity, inference completeness and Q-homomorphism, we give equivalent definitions of qualitative calculi both intensionally and extensionally. We show that "algebras generated by JEPD relations" and "qualitatively representable NAs" are embedded into the class of relation-type qualitative algebras