Deductive reasoning about expressive statements using external graphical representations

Research in psychology on reasoning has often been restricted to relatively inexpressive statements involving quantifiers. This is limited to situations that typically do not arise in practical settings, such as ontology engineering. In order to provide an analysis of inference, we focus on reasoning tasks presented in external graphic representations where statements correspond to those involving multiple quantifiers and unary and binary relations. Our experiment measured participants’ performance when reasoning with two notations. The first used topology to convey information via node-link diagrams (i.e. graphs). The second used topological and spatial constraints to convey information (Euler diagrams with additional graph-like syntax). We found that topological- spatial representations were more effective than topological representations. Unlike topological-spatial representations, reasoning with topological representations was harder when involving multiple quantifiers and binary relations than single quantifiers and unary relations. These findings are compared to those for sentential reasoning tasks

Human inference beyond syllogisms: an approach using external graphical representations.

Research in psychology about reasoning has often been restricted to relatively inexpressive statements involving quantifiers (e.g. syllogisms). This is limited to situations that typically do not arise in practical settings, like ontology engineering. In order to provide an analysis of inference, we focus on reasoning tasks presented in external graphic representations where statements correspond to those involving multiple quantifiers and unary and binary relations. Our experiment measured participants' performance when reasoning with two notations. The first notation used topological constraints to convey information via node-link diagrams (i.e. graphs). The second used topological and spatial constraints to convey information (Euler diagrams with additional graph-like syntax). We found that topo-spatial representations were more effective for inferences than topological representations alone. Reasoning with statements involving multiple quantifiers was harder than reasoning with single quantifiers in topological representations, but not in topo-spatial representations. These findings are compared to those in sentential reasoning tasks

III: Small: A Theory of Topological Relations for Compound Spatial Objects

Spatial data collections with an incomplete coverage yield regions with holes and separations that often cannot be filled by interpolation. Geosensor networks typically generate such configurations, and with the proliferation of sensor colonies, there is now an urgent need to provide users with better information technologies of cognitively plausible methods to search for or compare available spatial data sets that may be incomplete. The objective of the investigations is to advance knowledge about qualitative spatial relations for spatial regions with holes and/or separations. The core activity is the study of the interplay between topological spatial relations with holed regions and topological spatial relations with separated regions to address the potentially complex configurations that feature both holes and separations. Three characteristics of such a set of topological relations are addressed: the formalization of a sound set of relations at a granularity that allows for the distinction of the salient features of holed and separated regions, while offering the opportunity to generalize to coarser relations in a meaningful and consistent way; the relaxation of such relations so that the determination of the most similar relations follows immediately from the applied methodology; and the qualitative inference of new information from the composition of such relations to identify inconsistencies and to drawn information that is not immediately available from individual relations. The hypothesis is that combining the relation formalization with sound similarity and composition reasoning yields critical insights for a sufficiently expressive, common approach to modeling topological relations for holed regions and regions with separations. The resulting theory of topological spatial relations highlights a parallelism between relations with holed regions and regions with separations, which is most apparent when these regions are embedded on the surface of the sphere, while some parts of these regularities are often hidden in the usual planar embedding. Since topological relations are qualitative spatial descriptions, they come close to people\u27s own reasoning, so that a better understanding of the relations for compound spatial objects will have ramifications for qualitative spatial reasoning, without a need for drawing graphical depictions to make inferences. It also lays the foundation for linguistic constructs to communicate in natural language spatial configurations, ultimately leading to talking maps. An immediate impact of this theory of topological relations between holed and separated regions is on the querying and reasoning about dataset that are gathered by geosensor networks. Additional information available online: http://www.spatial.maine.edu/~max/holesAndParts.htm

Reasoning about topological and cardinal direction relations between 2-dimensional spatial objects

Increasing the expressiveness of qualitative spatial calculi is an essential step towards meeting the requirements of applications. This can be achieved by combining existing calculi in a way that we can express spatial information using relations from multiple calculi. The great challenge is to develop reasoning algorithms that are correct and complete when reasoning over the combined information. Previous work has mainly studied cases where the interaction between the combined calculi was small, or where one of the two calculi was very simple. In this paper we tackle the important combination of topological and directional information for extended spatial objects. We combine some of the best known calculi in qualitative spatial reasoning, the RCC8 algebra for representing topological information, and the Rectangle Algebra (RA) and the Cardinal Direction Calculus (CDC) for directional information. We consider two different interpretations of the RCC8 algebra, one uses a weak connectedness relation, the other uses a strong connectedness relation. In both interpretations, we show that reasoning with topological and directional information is decidable and remains in NP. Our computational complexity results unveil the significant differences between RA and CDC, and that between weak and strong RCC8 models. Take the combination of basic RCC8 and basic CDC constraints as an example: we show that the consistency problem is in P only when we use the strong RCC8 algebra and explicitly know the corresponding basic RA constraints

Reasoning about topological and cardinal direction relations between 2-dimensional spatial objects

Increasing the expressiveness of qualitative spatial calculi is an essential step towards meeting the requirements of applications. This can be achieved by combining existing calculi in a way that we can express spatial information using relations from multiple calculi. The great challenge is to develop reasoning algorithms that are correct and complete when reasoning over the combined information. Previous work has mainly studied cases where the interaction between the combined calculi was small, or where one of the two calculi was very simple. In this paper we tackle the important combination of topological and directional information for extended spatial objects. We combine some of the best known calculi in qualitative spatial reasoning, the RCC8 algebra for representing topological information, and the Rectangle Algebra (RA) and the Cardinal Direction Calculus (CDC) for directional information. We consider two different interpretations of the RCC8 algebra, one uses a weak connectedness relation, the other uses a strong connectedness relation. In both interpretations, we show that reasoning with topological and directional information is decidable and remains in NP. Our computational complexity results unveil the significant differences between RA and CDC, and that between weak and strong RCC8 models. Take the combination of basic RCC8 and basic CDC constraints as an example: we show that the consistency problem is in P only when we use the strong RCC8 algebra and explicitly know the corresponding basic RA constraints

Modal Logics of Topological Relations

Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the Egenhofer-Franzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the two-variable fragment of first-order logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to highly undecidable, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity

Representing time and space for the semantic web

Representation of temporal and spatial information for the Semantic Web often involves qualitative defined information (i.e., information described using natural language terms such as "before" or "overlaps") since precise dates or coordinates are not always available. This work proposes several temporal representations for time points and intervals and spatial topological representations in ontologies by means of OWL properties and reasoning rules in SWRL. All representations are fully compliant with existing Semantic Web standards and W3C recommendations. Although qualitative representations for temporal interval and point relations and spatial topological relations exist, this is the first work proposing representations combining qualitative and quantitative information for the Semantic Web. In addition to this, several existing and proposed approaches are compared using different reasoners and experimental results are presented in detail. The proposed approach is applied to topological relations (RCC5 and RCC8) supporting both qualitative and quantitative (i.e., using coordinates) spatial relations. Experimental results illustrate that reasoning performance differs greatly between different representations and reasoners. To the best of our knowledge, this is the first such experimental evaluation of both qualitative and quantitative Semantic Web temporal and spatial representations. In addition to the above, querying performance using SPARQL is evaluated. Evaluation results demonstrate that extracting qualitative relations from quantitative representations using reasoning rules and querying qualitative relations instead of directly querying quantitative representations increases performance at query time

Topological Properties in Ontology-based Applications

Proceedings of: 11th International Conference on Intelligent Systems Design and Applications, Córdoba, Spain, 22 – 24 November, 2011.Representation and reasoning with spatial properties is essential in several application domains where ontologies are being successfully applied; e.g., Information Fusion systems. This requires a full characterization of the semantics of relations such as adjacent, included, overlapping, etc. Nevertheless, ontologies are not expressive enough to directly support widely-use spatial or topological theories, such as the Region Connection Calculus (RCC). In addition, these properties must be properly instantiated in the ontology, which may require expensive calculations. This paper presents a practical approach to represent and reason with topological properties in ontology-based systems, as well as some optimization techniques that have been applied in a video-based Information Fusion application.This work was supported in part by Projects CICYT TIN2008-06742-C02-02/TSI, CICYT TEC2008-06732-C02-02/TEC,CAM CONTEXTS (S2009/ TIC-1485) and DPS2008-07029-C02-02.Publicad