Just-In-Time Constraint-Based Inference for Qualitative Spatial and Temporal Reasoning

We discuss a research roadmap for going beyond the state of the art in qualitative spatial and temporal reasoning (QSTR). Simply put, QSTR is a major field of study in Artificial Intelligence that abstracts from numerical quantities of space and time by using qualitative descriptions instead (e.g., precedes, contains, is left of); thus, it provides a concise framework that allows for rather inexpensive reasoning about entities located in space or time. Applications of QSTR can be found in a plethora of areas and domains such as smart environments, intelligent vehicles, and unmanned aircraft systems. Our discussion involves researching novel local consistencies in the aforementioned discipline, defining dynamic algorithms pertaining to these consistencies that can allow for efficient reasoning over changing spatio-temporal information, and leveraging the structures of the locally consistent related problems with regard to novel decomposability and theoretical tractability properties. Ultimately, we argue for pushing the envelope in QSTR via defining tools for tackling dynamic variants of the fundamental reasoning problems in this discipline, i.e., problems stated in terms of changing input data. Indeed, time is a continuous flow and spatial objects can change (e.g., in shape, size, or structure) as time passes; therefore, it is pertinent to be able to efficiently reason about dynamic spatio-temporal data. Finally, these tools are to be integrated into the larger context of highly active areas such as neuro-symbolic learning and reasoning, planning, data mining, and robotic applications. Our final goal is to inspire further discussion in the community about constraint-based QSTR in general, and the possible lines of future research that we outline here in particular

Collective Singleton-Based Consistency for Qualitative Constraint Networks

Partial singleton closure under weak composition, or partial singleton (weak) path-consistency for short, is essential for approximating satisfiability of qualitative constraints networks. Briefly put, partial singleton path-consistency ensures that each base relation of each of the constraints of a qualitative constraint network can define a singleton relation in the corresponding partial closure of that network under weak composition, or in its corresponding partially (weak) path-consistent subnetwork for short. In particular, partial singleton path-consistency has been shown to play a crucial role in tackling the minimal labeling problem of a qualitative constraint network, which is the problem of finding the strongest implied constraints of that network. In this paper, we propose a stronger local consistency that couples partial singleton path-consistency with the idea of collectively deleting certain unfeasible base relations by exploiting singleton checks. We then propose an efficient algorithm for enforcing this consistency that, given a qualitative constraint network, performs fewer constraint checks than the respective algorithm for enforcing partial singleton path-consistency in that network. We formally prove certain properties of our new local consistency, and motivate its usefulness through demonstrative examples and a preliminary experimental evaluation with qualitative constraint networks of Interval Algebra

Dynamic Branching in Qualitative Constraint Networks via Counting Local Models

We introduce and evaluate dynamic branching strategies for solving Qualitative Constraint Networks (QCNs), which are networks that are mostly used to represent and reason about spatial and temporal information via the use of simple qualitative relations, e.g., a constraint can be "Task A is scheduled after or during Task C". In qualitative constraint-based reasoning, the state-of-the-art approach to tackle a given QCN consists in employing a backtracking algorithm, where the branching decisions during search are governed by the restrictiveness of the possible relations for a given constraint (e.g., after can be more restrictive than during). In the literature, that restrictiveness is defined a priori by means of static weights that are precomputed and associated with the relations of a given calculus, without any regard to the particulars of a given network instance of that calculus, such as its structure. In this paper, we address this limitation by proposing heuristics that dynamically associate a weight with a relation, based on the count of local models (or local scenarios) that the relation is involved with in a given QCN; these models are local in that they focus on triples of variables instead of the entire QCN. Therefore, our approach is adaptive and seeks to make branching decisions that preserve most of the solutions by determining what proportion of local solutions agree with that decision. Experimental results with a random and a structured dataset of QCNs of Interval Algebra show that it is possible to achieve up to 5 times better performance for structured instances, whilst maintaining non-negligible gains of around 20% for random ones

Semi-Supervised Dimensionality Reduction by Linear Compression and Stretching

Dimensionality reduction is a fundamental and important research topic in the field of machine learning. This paper focuses on a dimensionality reduction technique that exploits semi-supervising information in the form of pairwise constraints; specifically, these constraints specify whether two instances belong to the same class or not. We propose two dual linear methods to accomplish dimensionality reduction under that setting. These two methods overcome the difficulty of maximizing between-class difference and minimizing within-class difference at the same time, by transforming the original data into a new space in such a way that the bi-objective problem is (almost) equivalently reduced to a single objective problem. Empirical evaluations on a broad range of public datasets show that the two proposed methods are superior to several existing methods for semi-supervised dimensionality reduction

Efficiently reasoning about qualitative constraints through variable elimination

© 2016 ACM. We introduce, study, and evaluate a novel algorithm in the context of qualitative constraint-based spatial and temporal reasoning, that is based on the idea of variable elimination, a simple and general exact inference approach in probabilistic graphical models. Given a qualitative constraint network M, our algorithm enforces a particular directional local consistency on M, which we denote by ←-consistency. Our discussion is restricted to distributive subclasses of relations, i.e., sets of relations closed under converse, intersection, and weak composition and for which weak composition distributes over non-empty intersections for all of their relations. We demonstrate that enforcing ←-consistency on a given qualitative constraint network defined over a distributive subclass of relations allows us to decide its satisfiability. The experimentation that we have conducted with random and real-world qualitative constraint networks defined over a distributive subclass of relations of the Region Connection Calculus, shows that our approach exhibits unparalleled performance against competing state-of-the-art approaches for checking the satisfiability of such constraint networks

Efficiently characterizing non-redundant constraints in large real world qualitative spatial networks

RCC8 is a constraint language that serves for qualitative spatial representation and reasoning by encoding the topological relations between spatial entities. We focus on efficiently characterizing non-redundant constraints in large real world RCC8 networks and obtaining their prime networks. For a RCC8 network N a constraint is redundant, if removing that constraint from N does not change the solution set of N. A prime network of N is a network which contains no redundant constraints, but has the same solution set as N. We make use of a particular partial consistency, namely, G⋄-consistency, and obtain new complexity results for various cases of RCC8 networks, while we also show that given a maximal distributive subclass for RCC8 and a network N defined on that subclass, the prunning capacity of G⋄-consistency and ⋄-consistency is identical on the common edges of G and the complete graph of N, when G is a triangulation of the constraint graph of N. Finally, we devise an algorithm based on G⋄-consistency to compute the unique prime network of a RCC8 network, and show that it significantly progresses the state-of-the-art for practical reasoning with real RCC8 networks scaling up to millions of nodes

On redundancy in linked geospatial data

RCC8 is a constraint language that serves for qualitative spatial representation and reasoning by encoding the topological relations between spatial entities. As such, RCC8 has been recently adopted by GeoSPARQL in an effort to enrich the Semantic Web with qualitative spatial relations. We focus on the redundancy that these data might harbor, which can throttle graph related applications, such as storing, representing, querying, and reasoning. For a RCC8 network N a constraint is redundant, if removing that constraint from N does not change the solution set of N. A prime network of N is a network which contains no redundant constraints, but has the same solution set as N. In this paper, we present a practical approach for obtaining the prime networks of RCC8 networks that originate from the Semantic Web, by exploiting the sparse and loosely connected structure of their constraint graphs, and, consequently, contribute towards offering Linked Geospatial Data of high quality. Experimental evaluation exhibits a vast decrease in the total number of non-redundant constraints that we can obtain from an initial network, while it also suggests that our approach significantly boosts the state-of-the-art approach