A computational model of the referential semantics of projective prepositions

In this paper we present a framework for interpreting locative expressions containing the prepositions in front of and behind. These prepositions have different semantics in the viewer-centred and intrinsic frames of reference (Vandeloise, 1991). We define a model of their semantics in each frame of reference. The basis of these models is a novel parameterized continuum function that creates a 3-D spatial template. In the intrinsic frame of reference the origin used by the continuum function is assumed to be known a priori and object occlusion does not impact on the applicability rating of a point in the spatial template. In the viewer-centred frame the location of the spatial template’s origin is dependent on the user’s perception of the landmark at the time of the utterance and object occlusion is integrated into the model. Where there is an ambiguity with respect to the intended frame of reference, we define an algorithm for merging the spatial templates from the competing frames of reference, based on psycholinguistic observations in (Carlson-Radvansky, 1997)

A survey of qualitative spatial representations

Representation and reasoning with qualitative spatial relations is an important problem in artificial intelligence and has wide applications in the fields of geographic information system, computer vision, autonomous robot navigation, natural language understanding, spatial databases and so on. The reasons for this interest in using qualitative spatial relations include cognitive comprehensibility, efficiency and computational facility. This paper summarizes progress in qualitative spatial representation by describing key calculi representing different types of spatial relationships. The paper concludes with a discussion of current research and glimpse of future work

Towards a typology of spatial relations and properties for urban applications

Relations that occur between features located in space–like the fact that a street is surrounded by very high buildings, that an airport is close to a city- as well as spatial properties of features–like the height and width of a door- play an important role for many urban applications. Digital models of cities can assist in the evaluation of these relations and properties either through visualisation or through computation, mainly based on geometrical information. Hence, considering the objective of explaining to potential users of these city models what useful information they can derive from these data and how, a possible way to address this objective lies in the usage of a pivot model composed of relevant spatial properties and relations, connected to information meaningful to the user and connected to the possible computation of them on available data. This paper firstly sets the ground for a typology of such relevant relations and properties that are shared by different applications and that can be derived/approximated from existing data. It then proposes a model to describe these properties and relations and connect them to their possible computation based on data (2D or 3D). An important aspect of this model is to distinguish between a conceptual layer where relations occur between “real world” features and an implementation layer where they are calculated based on database features and geometries

Grounding Dynamic Spatial Relations for Embodied (Robot) Interaction

This paper presents a computational model of the processing of dynamic spatial relations occurring in an embodied robotic interaction setup. A complete system is introduced that allows autonomous robots to produce and interpret dynamic spatial phrases (in English) given an environment of moving objects. The model unites two separate research strands: computational cognitive semantics and on commonsense spatial representation and reasoning. The model for the first time demonstrates an integration of these different strands.Comment: in: Pham, D.-N. and Park, S.-B., editors, PRICAI 2014: Trends in Artificial Intelligence, volume 8862 of Lecture Notes in Computer Science, pages 958-971. Springe

Reasoning with Mixed Qualitative-Quantitative Representations of Spatial Knowledge

Drastic transformations in human settlements are caused by extreme events. As a consequence, descriptions of an environment struck by an extreme event, based on spatial data collected before the event, become suddenly unreliable. On the other hand, time critical actions taken for responding to extreme events require up-to-date spatial information. Traditional methods for spatial data collection are not able to provide updated information rapidly enough, calling for the development of new data collection methods. Reports provided by actors involved in the response operations can be considered as an alternative source of spatial information. Indeed, reports often convey spatial descriptions of the environment. The extraction of spatial descriptions from such reports can serve a fundamental role to update existing information which is usually maintained within, and by means of, Geographic Information Systems. However, spatial information conveyed by human reports has qualitative characteristics, that strongly differ from the quantitative nature of spatial information stored in Geographic Information Systems. Methodologies for integrating qualitative and quantitative spatial information are required in order to exploit human reports for updating existing descriptions of spatial knowledge. Although a significant amount of research has been carried on how to represent and reason on qualitative data and qualitative information, relatively little work exists on developing techniques to combine the different methodologies. The work presented in this thesis extends previous works by introducing a hybrid reasoning system--able to deal with mixed qualitative-quantitative representations of spatial knowledge--combining techniques developed separately for qualitative spatial reasoning and quantitative data analysis. The system produces descriptions of the spatial extent of those entities that have been modified by the event (such as collapsed buildings), or that were not existing before the event (such as fire or ash clouds). Furthermore, qualitative descriptions are produced for all entities in the environment. The former descriptions allow for overlaying on a map the information interpreted from human reports, while the latter triggers warning messages to people involved in decision making operations. Three main system functionalities are investigated in this work: The first allows for translating qualitative information into quantitative descriptions. The second aims at translating quantitative information into qualitative relations. Finally, the third allows for performing inference operations with information given partly qualitatively and partly quantitatively for boosting the spatial knowledge the system is able to produce

Reasoning with Mixed Qualitative-Quantitative Representations of Spatial Knowledge

Drastic transformations in human settlements are caused by extreme events. As a consequence, descriptions of an environment struck by an extreme event, based on spatial data collected before the event, become suddenly unreliable. On the other hand, time critical actions taken for responding to extreme events require up-to-date spatial information. Traditional methods for spatial data collection are not able to provide updated information rapidly enough, calling for the development of new data collection methods. Reports provided by actors involved in the response operations can be considered as an alternative source of spatial information. Indeed, reports often convey spatial descriptions of the environment. The extraction of spatial descriptions from such reports can serve a fundamental role to update existing information which is usually maintained within, and by means of, Geographic Information Systems. However, spatial information conveyed by human reports has qualitative characteristics, that strongly differ from the quantitative nature of spatial information stored in Geographic Information Systems. Methodologies for integrating qualitative and quantitative spatial information are required in order to exploit human reports for updating existing descriptions of spatial knowledge. Although a significant amount of research has been carried on how to represent and reason on qualitative data and qualitative information, relatively little work exists on developing techniques to combine the different methodologies. The work presented in this thesis extends previous works by introducing a hybrid reasoning system--able to deal with mixed qualitative-quantitative representations of spatial knowledge--combining techniques developed separately for qualitative spatial reasoning and quantitative data analysis. The system produces descriptions of the spatial extent of those entities that have been modified by the event (such as collapsed buildings), or that were not existing before the event (such as fire or ash clouds). Furthermore, qualitative descriptions are produced for all entities in the environment. The former descriptions allow for overlaying on a map the information interpreted from human reports, while the latter triggers warning messages to people involved in decision making operations. Three main system functionalities are investigated in this work: The first allows for translating qualitative information into quantitative descriptions. The second aims at translating quantitative information into qualitative relations. Finally, the third allows for performing inference operations with information given partly qualitatively and partly quantitatively for boosting the spatial knowledge the system is able to produce

Undecidable First-Order Theories of Affine Geometries

Tarski initiated a logic-based approach to formal geometry that studies first-order structures with a ternary betweenness relation (\beta) and a quaternary equidistance relation (\equiv). Tarski established, inter alia, that the first-order (FO) theory of (R^2,\beta,\equiv) is decidable. Aiello and van Benthem (2002) conjectured that the FO-theory of expansions of (R^2,\beta) with unary predicates is decidable. We refute this conjecture by showing that for all n>1, the FO-theory of monadic expansions of (R^2,\beta) is \Pi^1_1-hard and therefore not even arithmetical. We also define a natural and comprehensive class C of geometric structures (T,\beta), where T is a subset of R^2, and show that for each structure (T,\beta) in C, the FO-theory of the class of monadic expansions of (T,\beta) is undecidable. We then consider classes of expansions of structures (T,\beta) with restricted unary predicates, for example finite predicates, and establish a variety of related undecidability results. In addition to decidability questions, we briefly study the expressivity of universal MSO and weak universal MSO over expansions of (R^n,\beta). While the logics are incomparable in general, over expansions of (R^n,\beta), formulae of weak universal MSO translate into equivalent formulae of universal MSO. This is an extended version of a publication in the proceedings of the 21st EACSL Annual Conferences on Computer Science Logic (CSL 2012).Comment: 21 pages, 3 figure