Exact structure from motion is an ill-posed computation and therefore very sensitive to noise. In this work I describe how a qualitative shape representation, based on the sign of the Gaussian curvature, can be com(cid:173) puted directly from motion disparities, without the computation of an exact depth map or the directions of surface normals. I show that humans can judge the curvature sense of three points undergoing 3D motion from two, three and four views with success rate significantly above chance. A simple RBF net has been trained to perform the same task.

We introduce a framework for qualitative reasoning about directions in high-dimensional spaces, called EER, where our main motivation is to develop a form of commonsense reasoning about semantic spaces. The proposed framework is, however, more general; we show how qualitative spatial reasoning about points with several existing calculi can be reduced to the realisability problem for EER (or REER for short), including LR and calculi for reasoning about betweenness, collinearity and parallelism. Finally, we propose an efficient but incomplete inference method, and show its effectiveness for reasoning with EER as well as reasoning with some of the aforementioned calculi.

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.

To apply eyeshadow without a brush, should I use a cotton swab or a toothpick? Questions requiring this kind of physical commonsense pose a challenge to today's natural language understanding systems. While recent pretrained models (such as BERT) have made progress on question answering over more abstract domains - such as news articles and encyclopedia entries, where text is plentiful - in more physical domains, text is inherently limited due to reporting bias. Can AI systems learn to reliably answer physical common-sense questions without experiencing the physical world? In this paper, we introduce the task of physical commonsense reasoning and a corresponding benchmark dataset Physical Interaction: Question Answering or PIQA. Though humans find the dataset easy (95% accuracy), large pretrained models struggle (77%). We provide analysis about the dimensions of knowledge that existing models lack, which offers significant opportunities for future research.

The ability to persist in the spacial environment is, not only in the robotic context, an essential feature. Positional knowledge is one of the most important aspects of space and a number of methods to represent these information have been developed in the in the research area of spatial cognition. The basic qualitative spatial representation and reasoning techniques are presented in this thesis and several calculi are briefly reviewed. Features and applications of qualitative calculi are summarized. A new calculus for representing and reasoning about qualitative spatial orientation and distances is being designed. It supports an arbitrary level of granularity over ternary relations of points. Ways of improving the complexity of the composition are shown and an implementation of the calculus demonstrates its capabilities. Existing qualitative spatial calculi of positional information are compared to the new approach and possibilities for future research are outlined.

We introduce WIQA, the first large-scale dataset of "What if..." questions over procedural text. WIQA contains three parts: a collection of paragraphs each describing a process, e.g., beach erosion; a set of crowdsourced influence graphs for each paragraph, describing how one change a ffects another; and a large (40k) collection of "What if...?" multiple-choice questions derived from the graphs. For example, given a paragraph about beach erosion, would stormy weather result in more or less erosion (or have no e ff ect)? The task is to answer the questions, given their associated paragraph. WIQA contains three kinds of questions: perturbations to steps mentioned in the paragraph; external (out-of-paragraph) perturbations requiring commonsense knowledge; and irrelevant (no e ff ect) perturbations. We find that state-of-the-art models achieve 73.8% accuracy, well below the human performance of 96.3%. We analyze the challenges, in particular tracking chains of influences, and present the dataset as an open challenge to the community.

We introduce the first open-domain dataset, called QuaRTz, for reasoning about textual qualitative relationships. QuaRTz contains general qualitative statements, e.g., "A sunscreen with a higher SPF protects the skin longer.", twinned with 3864 crowdsourced situated questions, e.g., "Billy is wearing sunscreen with a lower SPF than Lucy. Who will be best protected from the sun?", plus annotations of the properties being compared. Unlike previous datasets, the general knowledge is textual and not tied to a fixed set of relationships, and tests a system's ability to comprehend and apply textual qualitative knowledge in a novel setting. We find state-of-the-art results are substantially (20%) below human performance, presenting an open challenge to the NLP community.

In this paper, we argue that simulation platforms enable a novel type of embodied spatial reasoning, one facilitated by a formal model of object and event semantics that renders the continuous quantitative search space of an open-world, real-time environment tractable. We provide examples for how a semantically-informed AI system can exploit the precise, numerical information provided by a game engine to perform qualitative reasoning about objects and events, facilitate learning novel concepts from data, and communicate with a human to improve its models and demonstrate its understanding. We argue that simulation environments, and game engines in particular, bring together many different notions of "simulation" and many different technologies to provide a highly-effective platform for developing both AI systems and tools to experiment in both machine and human intelligence.

Cognitive scientists of the embodied cognition tradition have been providing evidence that a large part of our creative reasoning and problemsolving processes are carried out by means of conceptual metaphor and blending, grounded on our bodily experience with the world. In this talk I shall aim at fleshing out a mathematical model that has been proposed in the last decades for expressing and exploring conceptual metaphor and blending with greater precision than has previously been done. In particular, I shall focus on the notion of aptness of a metaphor or blend and on the validity of metaphorical entailment. Towards this end, I shall use a generalisation of the category-theoretic notion of colimit for modelling conceptual metaphor and blending in combination with the idea of reasoning at a distance as modelled in the Barwise-Seligman theory of information flow. I shall illustrate the adequacy of the proposed model with an example of creative reasoning about space and time for solving a classical brainteaser. Furthermore, I shall argue for the potential applicability of such mathematical model for ontology engineering, computational creativity, and problem-solving in general.

The capability of making explainable inferences regarding physical processes has long been desired. One fundamental physical process is object motion. Inferring what causes the motion of a group of objects can even be a challenging task for experts, e.g., in forensics science. Most of the work in the literature relies on physics simulation to draw such infer- ences. The simulation requires a precise model of the under- lying domain to work well and is essentially a black-box from which one can hardly obtain any useful explanation. By contrast, qualitative reasoning methods have the advan- tage in making transparent inferences with ambiguous infor- mation, which makes it suitable for this task. However, there has been no suitable qualitative theory proposed for object motion in three-dimensional space. In this paper, we take this challenge and develop a qualitative theory for the motion of rigid objects. Based on this theory, we develop a reasoning method to solve a very interesting problem: Assuming there are several objects that were initially at rest and now have started to move. We want to infer what action causes the movement of these objects.