Deriving topological relations from topologically augmented direction relation matrices

Topological relations and direction relations represent two pieces of the qualitative spatial reasoning triumvirate. Researchers have previously attempted to use the direction relation matrix to derive a topological relation, finding that no single direction relation matrix can isolate a particular topological relation. In this paper, the technique of topological augmentation is applied to the same problem, identifying a unique topological relation in 28.6% of all topologically augmented direction relation matrices, and furthermore achieving a reduction in a further 40.4% of topologically augmented direction relation matrices when compared to their vanilla direction relation matrix counterpart.

A Cognitively-Inspired Model for Making Sense of Hasse Diagrams

In this paper, we present a model of the sense-making process for diagrams, and describe it for the case of Hasse diagrams. Sense-making is modeled as the construction of networks of conceptual blends among image schemas and the diagram’s geometric configuration. As a case study, we specify four image schemas and the geometric configuration of a Hasse diagram, with typed FOL theories. In addition, for the diagram geometry, we utilise Qualitative Spatial Reasoning formalisms. Using an algebraic specification language, we can compute conceptual blends as category-theoretic colimits. Our model approaches sense-making as a process where the image schemas and the diagram geometry both structure each other through a complex network of conceptual blends. This yields a final blend in which the sort of inferences we confer to diagrammatic representations emerge. We argue that this approach to sense-making in diagrams is more cognitively apt than the mainstream view of a diagram being a syntactic representation of some underlying logical semantics. Moreover, our model could be applied to various types of stimuli and is thus valuable for the general field of AI.

Image Schemas and Conceptual Blending in Diagrammatic Reasoning: The Case of Hasse Diagrams

In this work, we propose a formal, computational model of the sense-making of diagrams by using the theories of image schemas and conceptual blending, stemming from cognitive linguistics. We illustrate our model here for the case of a Hasse diagram, using typed first-order logic to formalise the image schemas and to represent the geometry of a diagram. The latter additionally requires the use of some qualitative spatial reasoning formalisms. We show that, by blending image schemas with the geometrical configuration of a diagram, we can formally describe the way our cognition structures the understanding of, and the reasoning with, diagrams. In addition to a theoretical interest for diagrammatic reasoning, we also briefly discuss the cognitive underpinnings of good practice in diagram design, which are important for fields such as human-computer interaction and data visualization.

A Bit on the Right, A Bit on the Left: Towards Logical Bundle Adjustment

This article proposes an innovative approach fully based on logic to determine the relative positions and orientations of objects in a scene photographed from different points of view as well as those of the cameras used to take the pictures. The proposal is absolutely not based on 2D feature extraction, projective geometry or least squares adjustment but on a logical approach based on an enumeration of simple relationships between the objects visible in the photos. It is an approach imitating a natural and unconscious reasoning that each of us makes by observing a scene: is this object more to the right than this one? And is this other one further away from me than the one who’s partially hiding it from me? It is therefore a question of approaching the problem by identifying and recognizing objects in photographs and not by measuring millions of points in space without having any idea of the object to which they belong. This article presents a ”proof of concept” based on virtual experimentation: in a discrete 3D space, a simple scene, composed of spheres of different colors and cameras, is modelled in a 3D format. In this work the positioning of the spheres and cameras is limited to a plane. Cameras are placed in the scene in order to see the spheres and then for each camera an image is generated. The application reads each image and deducts relationships between object and camera. These relationships based on the visible occlusions between the projections of the objects onto the photographs, are formalized according to Allen’s relationships. A knowledge base is implemented to allow an iterative process of SPARQL queries for qualitative spatial reasoning leading to a set of possible solutions. Finally, the system deduces the relative positions between objects and cameras and the result is imported and can be used within several photogrammetry software suites.

Standpoint semantics for polysemy in spatial prepositions

In this paper, we present a formalism for handling polysemy in spatial expressions based on supervaluation semantics called standpoint semantics for polysemy (SSP). The goal of this formalism is, given a prepositional phrase, to define its possible spatial interpretations. For this, we propose to characterize spatial prepositions by means of a triplet $\langle $image schema, semantic feature, spatial axis$\rangle $. The core of SSP is predicate grounding theories, which are formulas of a first-order language that define a spatial preposition through the semantic features of its trajector and landmark. Precisifications are also established, which are a set of formulae of a qualitative spatial reasoning formalism that aims to provide the spatial characterization of the trajector with respect to the landmark. In addition to the theoretical model, we also present results of a computational implementation of SSP for the preposition ‘in’.

Query Answering With Non-Monotonic Rules: A Case Study of Archaeology Qualitative Spatial Reasoning

This paper deals with querying ontology-based knowledge bases equipped with non-monotonic rules through a case study within the framework of Cultural Heritage. It focuses on 3D underwater surveys on the Xlendi wreck which is represented by an OWL2 knowledge base with a large dataset. The paper aims at improving the interactions between the archaeologists and the knowledge base providing new queries that involve non-monotonic rules in order to perform qualitative spatial reasoning. To this end, the knowledge base initially represented in OWL2-QL is translated into an equivalent Answer Set Programming (ASP) program and is enriched with a set of non-monotonic ASP rules suitable to express default and exceptions. An ASP query answering approach is proposed and implemented. Furthermore due to the increased expressiveness of non-monotonic rules it provides spatial reasoning and spatial relations between artifacts query answering which is not possible with query answering languages such as SPARQL and SQWRL.

Qualitative Spatial Representation for the Humanities

‘Qualitative spatial reasoning and representation’ is a range of techniques developed in Artificial Intelligence to meet the need for a computational treatment of qualitative spatial relations. Examples of such relations include ‘next to’, ‘overlapping’, ‘to the left of’, ‘separate from’, ‘including’, and so on. These relations occur within the data found in the spatial humanities, but the computational techniques described here do not appear to have been used in connection with this context. While Geographical Information Systems (GIS) are widely used as a means of visualizing and exploring material in the spatial humanities, GIS technology is acknowledged to be ill-suited to information that is vague, uncertain, ambiguous, imprecise or having other qualities that in a scientific setting could be regarded as imperfections. In the humanities such ‘imperfections’ are of course important, and qualitative spatial relations are one source of data that challenges scientifically based GIS. This article reviews the origin of qualitative spatial reasoning and representation in A. N. Whitehead's mereotopology and argues for exploring how these methods could complement GIS as a computational technique in the humanities. Qualitative representation is applicable to modelling spatial arrangements in many domains, not just geographical space. This is demonstrated through an example of spatial relations in lines of printed text.