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

Allen's Interval Algebra Makes the Difference

Allen's Interval Algebra constitutes a framework for reasoning about temporal information in a qualitative manner. In particular, it uses intervals, i.e., pairs of endpoints, on the timeline to represent entities corresponding to actions, events, or tasks, and binary relations such as precedes and overlaps to encode the possible configurations between those entities. Allen's calculus has found its way in many academic and industrial applications that involve, most commonly, planning and scheduling, temporal databases, and healthcare. In this paper, we present a novel encoding of Interval Algebra using answer-set programming (ASP) extended by difference constraints, i.e., the fragment abbreviated as ASP(DL), and demonstrate its performance via a preliminary experimental evaluation. Although our ASP encoding is presented in the case of Allen's calculus for the sake of clarity, we suggest that analogous encodings can be devised for other point-based calculi, too.Comment: Part of DECLARE 19 proceeding

Qualitative Reasoning with Story-Based Motion Representations: Inverse and Composition

International audienceRepresentations of motion that are story-based constitute a promising tool to categorise the motion of entities, because they can be generated using any qualitative spatial representation, and they consider explicitly the speed of the entities. Up to the present, mainly categorisation properties of the story-based representations have been presented. In this paper we show how story-based representations allow for the reasoning operations that the qualitative calculi possess, namely, inverse and composition—We provide a method to compute the inverse, and a method that notably simplifies the computation of the composition

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

Tractable Fragments of Temporal Sequences of Topological Information

In this paper, we focus on qualitative temporal sequences of topological information. We firstly consider the context of topological temporal sequences of length greater than 3 describing the evolution of regions at consecutive time points. We show that there is no Cartesian subclass containing all the basic relations and the universal relation for which the algebraic closure decides satisfiability. However, we identify some tractable subclasses, by giving up the relations containing the non-tangential proper part relation and not containing the tangential proper part relation. We then formalize an alternative semantics for temporal sequences. We place ourselves in the context of the topological temporal sequences describing the evolution of regions on a partition of time (i.e. an alternation of instants and intervals). In this context, we identify large tractable fragments

Motion Categorisation: Representing Velocity Qualitatively

International audienceCategorising is arguably one of the first steps in cognition, because it enables high-level cognitive processing. For a similar reason, categorising is a first step—a preprocessing step—in artificial intelligence, specifically in decision-making, reasoning, and natural language processing. In this paper we categorise the motion of entities. Such categorisations, also known as qualitative representations, represent the preprocessing step for navigation problems with dynamical obstacles. As a central result, we present a general method to generate categorisations of motion based on categorisations of space. We assess its general validity by generating two categorisations of motion from two different spatial categorisations. We show examples of how the categorisations of motion describe and control trajectories. And we establish its soundness in cognitive and mathematical principles

Fine-Grained Complexity of Constraint Satisfaction Problems through Partial Polymorphisms: A Survey (Dedicated to the memory of Professor Ivo Rosenberg)

International audienceConstraint satisfaction problems (CSPs) are combi-natorial problems with strong ties to universal algebra and clone theory. The recently proved CSP dichotomy theorem states that finite-domain CSPs are always either tractable or NP-complete. However, among the intractable cases there is a seemingly large variance in complexity, which cannot be explained by the classical algebraic approach using polymorphisms. In this contribution we will survey an alternative approach based on partial polymorphisms, which is useful for studying the fine-grained complexity of NP-complete CSPs. Moreover, we will state some challenging open problems in the research field

A Survey on the Fine-grained Complexity of Constraint Satisfaction Problems Based on Partial Polymorphisms

International audienceConstraint satisfaction problems (CSPs) are combinatorial problems with strong ties to universal algebra and clone theory. The recently proved CSP dichotomy theorem states that each finite-domain CSP is either solvable in polynomial time, or that it is NP-complete. However, among the intractable CSPs there is a seemingly large variance in how fast they can be solved by exponential-time algorithms, which cannot be explained by the classical algebraic approach based on polymorphisms. In this contribution we will survey an alternative approach based on partial polymorphisms, which is useful for studying the fine-grained complexity of NP-complete CSPs. Moreover, we will state and discuss some challenging open problems in this research field

HyperQuaternionE:A hyperbolic embedding model for qualitative spatial and temporal reasoning

Qualitative spatial/temporal reasoning (QSR/QTR) plays a key role in research on human cognition, e.g., as it relates to navigation, as well as in work on robotics and artificial intelligence. Although previous work has mainly focused on various spatial and temporal calculi, more recently representation learning techniques such as embedding have been applied to reasoning and inference tasks such as query answering and knowledge base completion. These subsymbolic and learnable representations are well suited for handling noise and efficiency problems that plagued prior work. However, applying embedding techniques to spatial and temporal reasoning has received little attention to date. In this paper, we explore two research questions: (1) How do embedding-based methods perform empirically compared to traditional reasoning methods on QSR/QTR problems? (2) If the embedding-based methods are better, what causes this superiority? In order to answer these questions, we first propose a hyperbolic embedding model, called HyperQuaternionE, to capture varying properties of relations (such as symmetry and anti-symmetry), to learn inversion relations and relation compositions (i.e., composition tables), and to model hierarchical structures over entities induced by transitive relations. We conduct various experiments on two synthetic datasets to demonstrate the advantages of our proposed embedding-based method against existing embedding models as well as traditional reasoners with respect to entity inference and relation inference. Additionally, our qualitative analysis reveals that our method is able to learn conceptual neighborhoods implicitly. We conclude that the success of our method is attributed to its ability to model composition tables and learn conceptual neighbors, which are among the core building blocks of QSR/QTR

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