Answer Set Programming Modulo `Space-Time'

We present ASP Modulo `Space-Time', a declarative representational and computational framework to perform commonsense reasoning about regions with both spatial and temporal components. Supported are capabilities for mixed qualitative-quantitative reasoning, consistency checking, and inferring compositions of space-time relations; these capabilities combine and synergise for applications in a range of AI application areas where the processing and interpretation of spatio-temporal data is crucial. The framework and resulting system is the only general KR-based method for declaratively reasoning about the dynamics of `space-time' regions as first-class objects. We present an empirical evaluation (with scalability and robustness results), and include diverse application examples involving interpretation and control tasks

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

Qualitative Spatial Reasoning about Relative Orientation --- A Question of Consistency ---

Abstract. After the emergence of Allen s Interval Algebra Qualitative Spatial Reasoning has evolved into a fruitful field of research in artificial intelligence with possible applications in geographic information systems (GIS) and robot navigation Qualitative Spatial Reasoning abstracts from the detailed metric description of space using rich mathematical theories and restricts its language to a finite, often rather small, set of relations that fulfill certain properties. This approach is often deemed to be cognitively adequate . A major question in qualitative spatial reasoning is whether a description of a spatial situation given as a constraint network is consistent. The problem becomes a hard one since the domain of space (often R2 ) is infinite. In contrast many of the interesting problems for constraint satisfaction have a finite domain on which backtracking methods can be used. But because of the infinity of its domains these methods are generally not applicable to Qualitative Spatial Reasoning. Anyhow the method of path consistency or rather its generalization algebraic closure turned out to be helpful to a certain degree for many qualitative spatial calculi. The problem regarding this method is that it depends on the existence of a composition table, and calculating this table is not an easy task. For example the dipole calculus (operating on oriented dipoles) DRAf has 72 base relations and binary composition, hence its composition table has 5184 entries. Finding all these entries by hand is a hard, long and error-prone task. Finding them using a computer is also not easy, since the semantics of DRAf in the Euclidean Plane, its natural domain, rely on non-linear inequalities. This is not a special problem of the DRAf calculus. In fact, all calculi dealing with relative orientation share the property of having semantics based on non-linear inequalities in the Euclidean plane. This not only makes it hard to find a composition table, it also makes it particularly hard to decide consistency for these calculi. As shown in [79] algebraic closure is always just an approximation to consistency for these calculi, but it is the only method that works fast. Methods like Gröbner reasoning can decide consistency for these calculi but only for small constraint networks. Still finding a composition table for DRAf is a fruitful task, since we can use it analyze the properties of composition based reasoning for such a calculus and it is a starting point for the investigation of the quality of the approximation of consistency for this calculus. We utilize a new approach for calculating the composition table for DRAf using condensed semantics, i.e. the domain of the calculus is compressed in such a way that only finitely many possible configurations need to be investigated. In fact, only the configurations need to be investigated that turn out to represent special characteristics for the placement of three lines in the plane. This method turns out to be highly efficient for calculating the composition table of the calculus. Another method of obtaining a composition table is borrowing it via a suitable morphism. Hence, we investigate morphisms between qualitative spatial calculi. Having the composition table is not the end but rather the beginning of the problem. With that table we can compute algebraically closed refinements of constraint networks, but how meaningful is this process? We know that all constraint networks for which such a refinement does not exist are inconsistent, but what about the rest? In fact, they may be consistent or not. If they are all consistent, then we can be happy, since algebraic closure would decide consistency for the calculus at hand. We investigate LR, DRAf and DRAfp and show that for all these calculi algebraic closure does not decide consistency. In fact, for the LR calculus algebraic closure is an extremely bad approximation of consistency. For this calculus we introduce a new method for the approximation of consistency based on triangles, that performs far better than algebraic closure. A major weak spot of the field of Qualitative Spatial Reasoning is the area of applications. It is hard to refute the accusation of qualitative spatial calculi having only few applications so far. As a step into the direction of scrutinizing the applicability of these calculi, we examine the performance of DRA and OPRA in the issue of describing and navigating street networks based on local observations. Especially for OPRA we investigate a factorization of the base relations that is deemed cognitively adequate . Whenever possible we use real-world data in these investigations obtained from OpenStreetMap

Qualitative reasoning with directional relations

AbstractQualitative spatial reasoning (QSR) pursues a symbolic approach to reasoning about a spatial domain. Qualitative calculi are defined to capture domain properties in relation operations, granting a relation algebraic approach to reasoning. QSR has two primary goals: providing a symbolic model for human common-sense level of reasoning and providing efficient means for reasoning. In this paper, we dismantle the hope for efficient reasoning about directional information in infinite spatial domains by showing that it is inherently hard to decide consistency of a set of constraints that represents positions in the plane by specifying directions from reference objects. We assume that these reference objects are not fixed but only constrained through directional relations themselves. Known QSR reasoning methods fail to handle this information

Qualitative constraint satisfaction problems : algorithms, computational complexity, and extended framework

University of Technology, Sydney. Faculty of Engineering and Information Technology.Qualitative Spatial and Temporal Reasoning (QSTR) is a subfield of artificial intelligence that represents and reasons with spatial/temporal knowledge in a qualitative way. In the past three decades, researchers have proposed dozens of relational models (known as qualitative calculi), including, among others, Point Algebra (PA) and Interval Algebra (IA) for temporal knowledge, Cardinal Relation Algebra (CRA) and Cardinal Direction Calculus (CDC) for directional spatial knowledge, and the Region Connection Calculus RCC-5/RCC-8 for topological spatial knowledge. Relations are used in qualitative calculi for representing spatial/temporal information (e.g. Germany is to the east of France) and constraints (e.g. the to-be-established landfill should be disjoint from any lake). The reasoning tasks in QSTR are formalised via the qualitative constraint satisfaction problem (QCSP). As the central reasoning problem in QCSP, the consistency problem (which decides the consistency of a number of constraints in certain qualitative calculi) has been extensively investigated in the literature. For PA, IA, CRA, and RCC-5/RCC-8, the consistency problem can be solved by composition-based reasoning. For CDC, however, composition-based reasoning is incomplete, and the consistency problem in CDC remains challenging. Previous works in QCSP assume that qualitative constraints only concern completely unknown entities. Therefore, constraints about landmarks (i.e., fixed entities) cannot be properly expressed. This has significantly restricted the usefulness of QSTR in real-world applications. The main contributions of this thesis are as follows. (i) The composition-based method is one of the most important reasoning methods in QSTR. This thesis designs a semi-automatic algorithm for generating composition tables for general qualitative calculi. This provides a partial answer to the challenge proposed by Cohn in 1995. (ii) Schockaert et al. (2008) extend the RCC models interpreted in Euclidean topologies to the fuzzy context and show that composition-based reasoning is sufficient to solve fuzzy QCSP, where 31 composition rules are used. This thesis first shows that only six of the 31 composition rules are necessary, and then introduces a method which consistently fuzzifies any classical RCC models. This thesis also proposes a polynomial algorithm for realizing solutions of consistent fuzzy RCC constraints. (iii) Composition-based reasoning is incomplete for solving QCSP over the CDC. This thesis provides a cubic algorithm which for the first time solves the consistency problem of complete basic CDC networks, and further shows that the problem becomes NP-complete if the networks are allowed to be incomplete. This draws a sharp boundary between the tractable and intractable subclasses of the CDC. (iv) This thesis proposes a more general and more expressive QCSP framework, in which a variable is allowed to be a landmark (i.e., a fixed object), or to be chosen among several landmarks. The computational complexity of the consistency problems in the new framework is then investigated, covering all qualitative calculi mentioned above. For basic networks, the consistency problem remains tractable for Point Algebra, but becomes NP-complete for all the remaining qualitative calculi. A special case in which a variable is either a landmark or is totally unknown has also been studied. (v) A qualitative network is minimal if it cannot be refined without changing its solution set. Unlike the assumptions in the literature, this thesis shows that computing a solution of minimal networks is NP-complete for (partially ordered) PA, CRA, IA, and RCC-5/RCC-8. As a by-product, it has also been proved that determining the minimality of networks in these qualitative calculi is NP-complete

On Distributive Subalgebras of Qualitative Spatial and Temporal Calculi

Qualitative calculi play a central role in representing and reasoning about qualitative spatial and temporal knowledge. This paper studies distributive subalgebras of qualitative calculi, which are subalgebras in which (weak) composition distributives over nonempty intersections. It has been proven for RCC5 and RCC8 that path consistent constraint network over a distributive subalgebra is always minimal and globally consistent (in the sense of strong $n$-consistency) in a qualitative sense. The well-known subclass of convex interval relations provides one such an example of distributive subalgebras. This paper first gives a characterisation of distributive subalgebras, which states that the intersection of a set of $n\geq 3$ relations in the subalgebra is nonempty if and only if the intersection of every two of these relations is nonempty. We further compute and generate all maximal distributive subalgebras for Point Algebra, Interval Algebra, RCC5 and RCC8, Cardinal Relation Algebra, and Rectangle Algebra. Lastly, we establish two nice properties which will play an important role in efficient reasoning with constraint networks involving a large number of variables.Comment: Adding proof of Theorem 2 to appendi