Algebraic foundations for qualitative calculi and networks

A qualitative representation $\phi$ is like an ordinary representation of a relation algebra, but instead of requiring $(a; b)^\phi = a^\phi | b^\phi$, as we do for ordinary representations, we only require that $c^\phi\supseteq a^\phi | b^\phi \iff c\geq a ; b$, for each $c$ in the algebra. A constraint network is qualitatively satisfiable if its nodes can be mapped to elements of a qualitative representation, preserving the constraints. If a constraint network is satisfiable then it is clearly qualitatively satisfiable, but the converse can fail. However, for a wide range of relation algebras including the point algebra, the Allen Interval Algebra, RCC8 and many others, a network is satisfiable if and only if it is qualitatively satisfiable. Unlike ordinary composition, the weak composition arising from qualitative representations need not be associative, so we can generalise by considering network satisfaction problems over non-associative algebras. We prove that computationally, qualitative representations have many advantages over ordinary representations: whereas many finite relation algebras have only infinite representations, every finite qualitatively representable algebra has a finite qualitative representation; the representability problem for (the atom structures of) finite non-associative algebras is NP-complete; the network satisfaction problem over a finite qualitatively representable algebra is always in NP; the validity of equations over qualitative representations is co-NP-complete. On the other hand we prove that there is no finite axiomatisation of the class of qualitatively representable algebras.Comment: 22 page

Geospatial Narratives and their Spatio-Temporal Dynamics: Commonsense Reasoning for High-level Analyses in Geographic Information Systems

The modelling, analysis, and visualisation of dynamic geospatial phenomena has been identified as a key developmental challenge for next-generation Geographic Information Systems (GIS). In this context, the envisaged paradigmatic extensions to contemporary foundational GIS technology raises fundamental questions concerning the ontological, formal representational, and (analytical) computational methods that would underlie their spatial information theoretic underpinnings. We present the conceptual overview and architecture for the development of high-level semantic and qualitative analytical capabilities for dynamic geospatial domains. Building on formal methods in the areas of commonsense reasoning, qualitative reasoning, spatial and temporal representation and reasoning, reasoning about actions and change, and computational models of narrative, we identify concrete theoretical and practical challenges that accrue in the context of formal reasoning about `space, events, actions, and change'. With this as a basis, and within the backdrop of an illustrated scenario involving the spatio-temporal dynamics of urban narratives, we address specific problems and solutions techniques chiefly involving `qualitative abstraction', `data integration and spatial consistency', and `practical geospatial abduction'. From a broad topical viewpoint, we propose that next-generation dynamic GIS technology demands a transdisciplinary scientific perspective that brings together Geography, Artificial Intelligence, and Cognitive Science. Keywords: artificial intelligence; cognitive systems; human-computer interaction; geographic information systems; spatio-temporal dynamics; computational models of narrative; geospatial analysis; geospatial modelling; ontology; qualitative spatial modelling and reasoning; spatial assistance systemsComment: ISPRS International Journal of Geo-Information (ISSN 2220-9964); Special Issue on: Geospatial Monitoring and Modelling of Environmental Change}. IJGI. Editor: Duccio Rocchini. (pre-print of article in press

A Generalised Approach for Encoding and Reasoning with Qualitative Theories in Answer Set Programming

Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly in the spatial and temporal domains, with several practical applications such as naval traffic monitoring, warehouse process optimisation and robot manipulation. Even if a number of specialised qualitative reasoning tools have been developed so far, an important barrier to the wider adoption of these tools is that only qualitative reasoning is supported natively, when real-world problems most often require a combination of qualitative and other forms of reasoning. In this work, we propose to overcome this barrier by using ASP as a unifying formalism to tackle problems that require qualitative reasoning in addition to non-qualitative reasoning. A family of ASP encodings is proposed which can handle any qualitative calculus with binary relations. These encodings are experimentally evaluated using a real-world dataset based on a case study of determining optimal coverage of telecommunication antennas, and compared with the performance of two well-known dedicated reasoners. Experimental results show that the proposed encodings outperform one of the two reasoners, but fall behind the other, an acceptable trade-off given the added benefits of handling any type of reasoning as well as the interpretability of logic programs. This paper is under consideration for acceptance in TPLP.Comment: Paper presented at the 36th International Conference on Logic Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September 2020, 18 pages, 3 figure

Geospatial images in the acquisition of spatial knowledge for wayfinding

Geospatial images such as maps and aerial photographs are important sources of spatial knowledge that people use for wayfinding. The rapid development of geodata acquisition and digital graphics has recently led to rather complete geographic coverage of both traditional and novel types of geospatial images. Divergent types of geospatial images vary in their support of human acquisition of spatial knowledge. However evaluative studies about the acquisition of spatial knowledge from the diversity of geospatial images have been rare. In this article we review a variety of literature about the acquisition of spatial knowledge while paying particular attention to the role of geospatial images. Based on the literature we present a framework of image parameters that characterize the acquisition of spatial knowledge from geospatial images: vantage point number of visible vertical features and visual realism. With the help of the framework we evaluate commonly used geospatial images. In concordance with the previous experiments our evaluation shows that the different types of geospatial images have large differences in the types of spatial knowledge they support and to what extent. However further experimentation is needed in order to better understand the human cognitive needs for geospatial images and to develop more useful geospatial images for wayfinding

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

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

Qualitative Spatial Configuration Queries Towards Next Generation Access Methods for GIS

For a long time survey, management, and provision of geographic information in Geographic Information Systems (GIS) have mainly had an authoritative nature. Today the trend is changing and such an authoritative geographic information source is now accompanied by a public and freely available one which is usually referred to as Volunteered Geographic Information (VGI). Actually, the term VGI does not refer only to the mere geographic information, but, more generally, to the whole process which assumes the engagement of volunteers to collect and maintain such information in freely accessible GIS. The quick spread of VGI gives new relevance to a well-known challenge: developing new methods and techniques to ease down the interaction between users and GIS. Indeed, in spite of continuous improvements, GIS mainly provide interfaces tailored for experts, denying the casual user usually a non-expert the possibility to access VGI information. One main obstacle resides in the different ways GIS and humans deal with spatial information: GIS mainly encode spatial information in a quantitative format, whereas human beings typically prefer a qualitative and relational approach. For example, we use expressions like the lake is to the right-hand side of the wood or is there a supermarket close to the university? which qualitatively locate a spatial entity with respect to another. Nowadays, such a gap in representation has to be plugged by the user, who has to learn about the system structure and to encode his requests in a form suitable to the system. Contrarily, enabling gis to explicitly deal with qualitative spatial information allows for shifting the translation effort to the system side. Thus, to facilitate the interaction with human beings, GIS have to be enhanced with tools for efficiently handling qualitative spatial information. The work presented in this thesis addresses the problem of enabling Qualitative Spatial Configuration Queries (QSCQs) in GIS. A QSCQ is a spatial database query which allows for an automatic mapping of spatial descriptions produced by humans: A user naturally expresses his request of spatial information by drawing a sketch map or producing a verbal description. The qualitative information conveyed by such descriptions is automatically extracted and encoded into a QSCQ. The focus of this work is on two main challenges: First, the development of a framework that allows for managing in a spatial database the variety of spatial aspects that might be enclosed in a spatial description produced by a human. Second, the conception of Qualitative Spatial Access Methods (QSAMs): algorithms and data structures tailored for efficiently solving QSCQs. The main objective of a QSAM is that of countering the exponential explosion in terms of storage space occurring when switching from a quantitative to a qualitative spatial representation while keeping query response time acceptable

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