Reasoning about Cardinal Directions between Extended Objects

Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between connected plane regions. CDC is perhaps the most expressive qualitative calculus for directional information, and has attracted increasing interest from areas such as artificial intelligence, geographical information science, and image retrieval. Given a network of CDC constraints, the consistency problem is deciding if the network is realizable by connected regions in the real plane. This paper provides a cubic algorithm for checking consistency of basic CDC constraint networks, and proves that reasoning with CDC is in general an NP-Complete problem. For a consistent network of basic CDC constraints, our algorithm also returns a 'canonical' solution in cubic time. This cubic algorithm is also adapted to cope with cardinal directions between possibly disconnected regions, in which case currently the best algorithm is of time complexity O(n^5)

Reasoning about Qualitative Direction and Distance between Extended Objects using Answer Set Programming

In this thesis, we introduce a novel formal framework to represent and reason about qualitative direction and distance relations between extended objects using Answer Set Programming (ASP). We take Cardinal Directional Calculus (CDC) as a starting point and extend CDC with new sorts of constraints which involve defaults, preferences and negation. We call this extended version as nCDC. Then we further extend nCDC by augmenting qualitative distance relation and name this extension as nCDC+. For CDC, nCDC, nCDC+, we introduce an ASP-based general framework to solve consistency checking problems, address composition and inversion of qualitative spatial relations, infer unknown or missing relations between objects, and find a suitable configuration of objects which fulfills a given inquiry.Comment: In Proceedings ICLP 2019, arXiv:1909.0764

Reasoning about Cardinal Directions between 3-Dimensional Extended Objects using Answer Set Programming

We propose a novel formal framework (called 3D-nCDC-ASP) to represent and reason about cardinal directions between extended objects in 3-dimensional (3D) space, using Answer Set Programming (ASP). 3D-nCDC-ASP extends Cardinal Directional Calculus (CDC) with a new type of default constraints, and nCDC-ASP to 3D. 3D-nCDC-ASP provides a flexible platform offering different types of reasoning: Nonmonotonic reasoning with defaults, checking consistency of a set of constraints on 3D cardinal directions between objects, explaining inconsistencies, and inferring missing CDC relations. We prove the soundness of 3D-nCDC-ASP, and illustrate its usefulness with applications. 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, 29 pages, 6 figure

Algebraic Properties of Qualitative Spatio-Temporal Calculi

Qualitative spatial and temporal reasoning is based on so-called qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms. But what exactly is a qualitative calculus? And to which extent do the qualitative calculi proposed meet these demands? The literature provides various answers to the first question but only few facts about the second. In this paper we identify the minimal requirements to binary spatio-temporal calculi and we discuss the relevance of the according axioms for representation and reasoning. We also analyze existing qualitative calculi and provide a classification involving different notions of a relation algebra.Comment: COSIT 2013 paper including supplementary materia

Constraint-Based Qualitative Simulation

We consider qualitative simulation involving a finite set of qualitative relations in presence of complete knowledge about their interrelationship. We show how it can be naturally captured by means of constraints expressed in temporal logic and constraint satisfaction problems. The constraints relate at each stage the 'past' of a simulation with its 'future'. The benefit of this approach is that it readily leads to an implementation based on constraint technology that can be used to generate simulations and to answer queries about them.Comment: 10 pages, to appear at the conference TIME 200

A Hybrid Reasoning Model for “Whole and Part” Cardinal Direction Relations

We have shown how the nine tiles in the projection-based model for cardinal directions can be partitioned into sets based on horizontal and vertical constraints (called Horizontal and Vertical Constraints Model) in our previous papers (Kor and Bennett, 2003 and 2010). In order to come up with an expressive hybrid model for direction relations between two-dimensional single-piece regions (without holes), we integrate the well-known RCC-8 model with the above-mentioned model. From this expressive hybrid model, we derive 8 basic binary relations and 13 feasible as well as jointly exhaustive relations for the x- and y-directions, respectively. Based on these basic binary relations, we derive two separate composition tables for both the expressive and weak direction relations. We introduce a formula that can be used for the computation of the composition of expressive and weak direction relations between “whole or part” regions. Lastly, we also show how the expressive hybrid model can be used to make several existential inferences that are not possible for existing models

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

Framework development for providing accessibility to qualitative spatial calculi

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.Qualitative spatial reasoning deals with knowledge about an infinite spatial domain using a finite set of qualitative relations without using numerical computation. Qualitative knowledge is relative knowledge where we obtain the knowledge on the basis of comparison of features with in the object domain rather then using some external scales. Reasoning is an intellectual facility by which, conclusions are drawn from premises and is present in our everyday interaction with the geographical world. The kind of reasoning that human being relies on is based on commonsense knowledge in everyday situations. During the last decades a multitude of formal calculi over spatial relations have been proposed by focusing on different aspects of space like topology, orientation and distance. Qualitative spatial reasoning engines like SparQ and GQR represents space and reasoning about the space based on qualitative spatial relations and bring qualitative reasoning closer to the geographic applications. Their relations and certain operations defined in qualitative calculi use to infer new knowledge on different aspects of space. Today GIS does not support common-sense reasoning due to limitation for how to formalize spatial inferences. It is important to focus on common sense geographic reasoning, reasoning as it is performed by human. Human perceive and represents geographic information qualitatively, the integration of reasoner with spatial application enables GIS users to represent and extract geographic information qualitatively using human understandable query language. In this thesis, I designed and developed common API framework using platform independent software like XML and JAVA that used to integrate qualitative spatial reasoning engines (SparQ) with GIS application. SparQ is set of modules that structured to provides different reasoning services. SparQ supports command line instructions and it has a specific syntax as set of commands. The developed API provides interface between GIS application and reasoning engine. It establishes connection with reasoner over TCP/IP, takes XML format queries as input from GIS application and converts into SparQ module specific syntax. Similarly it extracts given result, converts it into defined XML format and passes it to GIS application over the same TCP/IP connection. The most challenging part of thesis was SparQ syntax analysis for inputs and their outputs. Each module in Sparq takes module specific query syntax and generates results in multiple syntaxes like; error, simple result and result with comments. Reasoner supports both binary and ternary calculi. The input query syntax for binary-calculi is different for ternary-calculi in the terms of constraint-networks. Based on analysis I, identified commonalities between input query syntaxes for both binary and ternary calculi and designed XML structures for them. Similarly I generalized SparQ results into five major categories and designed XML structures. For ternary-calculi, I considered constraint-reasoning module and their specific operations and designed XML structure for both of their inputs and outputs