One of the purposes of perception is to bridge between sensors and conceptual understanding. Marr's Primal Sketch combined initial edge-finding with multiple downstream processes to capture aspects of visual perception such as grouping and stereopsis. Given the progress made in multiple areas of AI since then, we have developed a new framework inspired by Marr's work, the Hybrid Primal Sketch, which combines computer vision components into an ensemble to produce sketch-like entities which are then further processed by CogSketch, our model of high-level human vision, to produce both more detailed shape representations and scene representations which can be used for data-efficient learning via analogical generalization. This paper describes our theoretical framework, summarizes several previous experiments, and outlines a new experiment in progress on diagram understanding.

Allen's interval algebra is one of the most well-known calculi in qualitative temporal reasoning with numerous applications in artificial intelligence. Recently, there has been a surge of improvements in the fine-grained complexity of NP-hard reasoning tasks, improving the running time from the naive $2^{O(n^2)}$ to $O^*((1.0615n)^{n})$, with even faster algorithms for unit intervals a bounded number of overlapping intervals (the $O^*(\cdot)$ notation suppresses polynomial factors). Despite these improvements the best known lower bound is still only $2^{o(n)}$ (under the exponential-time hypothesis) and major improvements in either direction seemingly require fundamental advances in computational complexity. In this paper we propose a novel framework for solving NP-hard qualitative reasoning problems which we refer to as dynamic programming with sublinear partitioning. Using this technique we obtain a major improvement of $O^*((\frac{cn}{\log{n}})^{n})$ for Allen's interval algebra. To demonstrate that the technique is applicable to more domains we apply it to a problem in qualitative spatial reasoning, the cardinal direction point algebra, and solve it in $O^*((\frac{cn}{\log{n}})^{2n/3})$ time. Hence, not only do we significantly advance the state-of-the-art for NP-hard qualitative reasoning problems, but obtain a novel algorithmic technique that is likely applicable to many problems where $2^{O(n)}$ time algorithms are unlikely.

There is presently great interest in the abilities of neural networks to mimic "qualitative reasoning" by manipulating neural incodings of symbols. Less work has been performed on using neural networks to process floating point numbers and it is sometimes stated that neural networks are somehow inherently inaccu(cid:173) rate and therefore best suited for "fuzzy" qualitative reasoning. Nevertheless, the potential speed of massively parallel operations make neural net "number crunching" an interesting topic to explore. In this paper we discuss some of our work in which we demonstrate that for certain applications neural networks can achieve significantly higher numerical accuracy than more conventional tech(cid:173) niques. In particular, prediction of future values of a chaotic time series can be performed with exceptionally high accuracy.

Simultaneous localization and mapping (SLAM) are essential in numerous robotics applications, such as autonomous navigation. Traditional SLAM approaches infer the metric state of the robot along with a metric map of the environment. While existing algorithms exhibit good results, they are still sensitive to measurement noise, sensor quality, and data association and are still computationally expensive. Alternatively, some navigation and mapping missions can be achieved using only qualitative geometric information, an approach known as qualitative spatial reasoning (QSR). We contribute a novel probabilistic qualitative localization and mapping approach in this work. We infer both the qualitative map and the qualitative state of the camera poses (localization). For the first time, we also incorporate qualitative probabilistic constraints between camera poses (motion model), improving computation time and performance. Furthermore, we take advantage of qualitative inference properties to achieve very fast approximated algorithms with good performance. In addition, we show how to propagate probabilistic information between nodes in the qualitative map, which improves estimation performance and enables inference of unseen map nodes - an important building block for qualitative active planning. We also conduct a study that shows how well we can estimate unseen nodes. Our method particularly appeals to scenarios with few salient landmarks and low-quality sensors. We evaluate our approach in simulation and on a real-world dataset and show its superior performance and low complexity compared to the state-of-the-art. Our analysis also indicates good prospects for using qualitative navigation and planning in real-world scenarios.

Qualitative reasoning is an important subfield of artificial intelligence where one describes relationships with qualitative, rather than numerical, relations. Many such reasoning tasks, e.g., Allen's interval algebra, can be solved in $2^{O(n \cdot \log n)}$ time, but single-exponential running times $2^{O(n)}$ are currently far out of reach. In this paper we consider single-exponential algorithms via a multivariate analysis consisting of a fine-grained parameter $n$ (e.g., the number of variables) and a coarse-grained parameter $k$ expected to be relatively small. We introduce the classes FPE and XE of problems solvable in $f(k) \cdot 2^{O(n)}$, respectively $f(k)^n$, time, and prove several fundamental properties of these classes. We proceed by studying temporal reasoning problems and (1) show that the Partially Ordered Time problem of effective width $k$ is solvable in $16^{kn}$ time and is thus included in XE, and (2) that the network consistency problem for Allen's interval algebra with no interval overlapping with more than $k$ others is solvable in $(2nk)^{2k} \cdot 2^{n}$ time and is included in FPE. Our multivariate approach is in no way limited to these to specific problems and may be a generally useful approach for obtaining single-exponential algorithms.

This paper tackles the problem of evaluating the degree of inconsistency in spatial and temporal qualitative reasoning. We first introduce postulates to propose a formal framework for measuring inconsistency in this context. Then, we provide two inconsistency measures that can be useful in various AI applications. The first one is based on the number of constraints that we need to relax to get a consistent qualitative constraint network. The second inconsistency measure is based on variable restrictions to restore consistency. It is defined from the minimum number of variables that we need to ignore to recover consistency. We show that our proposed measures satisfy required postulates and other appropriate properties. Finally, we discuss the impact of our inconsistency measures on belief merging in qualitative reasoning.

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.

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.