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.

Spatial information is often expressed using qualitative terms such as natural language expressions instead of coordinates; reasoning over such terms has several practical applications, such as bus routes planning. Representing and reasoning on trajectories is a specific case of qualitative spatial reasoning that focuses on moving objects and their paths. In this work, we propose two versions of a trajectory calculus based on the allowed properties over trajectories, where trajectories are defined as a sequence of non-overlapping regions of a partitioned map. More specifically, if a given trajectory is allowed to start and finish at the same region, 6 base relations are defined (TC-6). If a given trajectory should have different start and finish regions but cycles are allowed within, 10 base relations are defined (TC-10). Both versions of the calculus are implemented as ASP programs; we propose several different encodings, including a generalised program capable of encoding any qualitative calculus in ASP. All proposed encodings are experimentally evaluated using a real-world dataset. Experiment results show that the best performing implementation can scale up to an input of 250 trajectories for TC-6 and 150 trajectories for TC-10 for the problem of discovering a consistent configuration, a significant improvement compared to previous ASP implementations for similar qualitative spatial and temporal calculi.

Qualitative reasoning can generate ambiguous behaviors due to the lack of quantitative information. Despite many different research results focusing on ambiguities reduction, fundamentally it is impossible to totally remove ambiguities with only qualitative methods and to guarantee the consistency of results. This prevents the wide use of qualitative reasoning techniques in practical situations, particularly in conceptual design, where qualitative reasoning is considered intrinsically useful. To improve this situation, this paper initially investigates the origin of ambiguities in qualitative reasoning. Then it proposes a method based on intelligent interventions of the user who is able to detect ambiguities, to prioritize interventions on these ambiguities, and to reduce ambiguities based on the least commitment strategy. This interaction method breaks through the limit of qualitative reasoning in practical applications to conceptual design. The method was implemented as a new feature in a software tool called the Knowledge Intensive Engineering Framework in order to be tested and used for a printer design.

Numerical simulation of partial differential equations (PDEs) plays a crucial role in predicting the behavior-of physical systems and in modern engineering design. However, to produce reliable results with a PDE simulator, a human expert must typically expend considerable time and effort in setting up the simulation. Most of this effort is spent in generating the grid, the discretization of the spatial domain that the PDE simulator requires as input. To properly design a grid, the gridder must not only consider the characteristics of the spatial domain, but also the physics of the situation and the peculiarities of the numerical simulator. This article describes an intelligent gridder that is capable of analyzing the topology of the spatial domain and of predicting approximate physical behaviors based on the geometry of the spatial domain to automatically generate grids for computational fluid dynamics simulators. Typically, gridding programs are given a partitioning of the spatial domain to assist the gridder. Our gridder is capable of performing this partitioning. This enables the gridder to automatically grid spatial domains with a wide range of configurations.

The “sketch” drawn by a human designer represents a shape class of wider variability than can be captured by traditional CAD models; these typically work with parametrizations based on a nearly finished shape. Traditional Qualitative Reasoning is also unable to model this degree of ambiguity in shape. Cognitively, shapes are often represented in terms of an axial model. In defining 2D contours, such an axial representation is called the Medial Axis Transform or MAT. By perturbing the parameters of the MAT—length, link angle, and the node radius—one can define a shape class. Unlike the contour-to-MAT transform, which is well-known to be unstable, the MAT-to-contour process is an integrative process and is very stable. The variation in these parameters can be controlled by defining a suitable discretization over the parameter space. This leads to a broad class of similar shapes from which an optimized shape can be obtained for a given set of criteria. The optimizing criteria may involve the boundary description for each shape; the axial model is only used for generating the shape class. This Qualitative MAT model has been tested in several design optimization contexts, using Genetic Algorithms, and we show results for Automobile contours, IC engine parts, building profiles, etc.

Qualitative physics, a subfield of artificial intelligence, adapts intuitive and non-numerical reasoning for descriptive analysis of physical systems. The application of a set-based qualitative algebra to matrix analysis (QMA) allows for the development of a qualitative matrix stiffness methodology for linear elastic structural analysis. The unavoidable introduction of arithmetic ambiguity requires the reinforcement of physical constraints complementary to standard matrix operations. The overall analysis technique incorporates such constraints within the set-based framework with logic programming. Truss, beam, and frame structures demonstrate constraint relationships, which prune spurious solutions resulting from qualitative arithmetic relations. Though QMA is not a panacea for all structural applications, it provides greater insight into new notions of physical analysis.

In this article, an approach is presented for the representation and reasoning over qualitative spatial relations. A set-theoretic approach is used for representing the topology of objects and underlying space by retaining connectivity relationships between objects and space components in a structure, denoted, adjacency matrix. Spatial relations are represented by the intersection of components, and spatial reasoning is achieved by the application of general rules for the propagation of the intersection constraints between those components. The representation approach is general and can be adapted for different space resolutions and granularities of relations. The reasoning mechanism is simple and the spatial compositions are achieved in a finite definite number of steps, controlled by the complexity needed in the representation of objects and the granularity of the spatial relations required. The application of the method is presented over geometric structures that takes into account qualitative surface height information. It is also shown how directional relationships can be used in a hybrid approach for richer composition scenarios. The main advantage of this work is that it offers a unified platform for handling different relations in the qualitative space, which is a step toward developing general spatial reasoning engines for large spatial databases.