As has been remarked on before, Space is Special [1,2]. Tobler's First Law of Geography [3] captures the notion that all things are related, but close things are more related. Tversky [2] eloquently argues for the special place for spatial representations, and in particular that (living) things must move and act in space to survive, that all thought begins as spatial thought and that spatial thinking comes from and is shaped by perceiving the world and acting in it, be it through learning or through evolution. Artificial Intelligence has thus naturally sought to endow artificial agents with spatial representations and ways of reasoning about space. Amongst these, I will focus on qualitative spatial representations and reasoning mechanisms (henceforth QSR, where the 'R' may stand for representation or reasoning or both, depending on the context). There have been many calculi developed for representing and reasoning about space in qualitative ways, covering aspects such as (mereo)topology, orientation/direction, size, distance and shape [4,5]. Whilst QSR has primarily been concerned with deductive reasoning, there have been and there are increasingly many connections between QSR and machine learning. In this talk I will discuss a number of such connections, ranging from the use of qualitative spatial representations in an inductive logic programming system to learn event classes occurring in video data, to the question of whether large language models (LLMs) are able to make inferences reliably about qualitative spatial relations, and whether they can be supported by symbolic reasoners. Learning rules for video interpretation: Dubba et al. [6] show how Inductive Logic Programming can be used to learn a set of rules which can be used to recognise event class instances where videos have been abstracted to a set of qualitative spatio-temporal relations. The method is demonstrated in two domains including one which involves recognising the events which are necessary to service an aircraft whilst it is turning around at an airport. Whilst the resulting rules are relatively simple and it might be wondered whether a hand-written set of rules could not be easily written and just as effective, it turns out that in a comparison with such a set of manually written rules, the learned model is more effective, because the latter does not take account of noise in the video data, where as the learned model was already trained on noisy data and was thus more robust in the face of noisy data at classification time. The paper also shows how the inductive process can be interleaved with abduction, using an embedded spatial theory to improve the learned model in the face of noisy training data.

A key question for QSR is how the relations in the calculus correspond to their use in language and their correspondence to the real world. Whilst relations are usually given plausible names in a relational calculus, there is no guarantee that these correspond to naturally occurring instances. Indeed, McDermott [7] notes the dangers of "wishful naming". Alomari et al. [8] present a system, named OLAV, which addresses the problem of bootstrapping knowledge in language and vision for autonomous robots. OLAV is able, for the first time, to (1) learn to form discrete concepts from sensory data; (2) ground language (n-grams) to these concepts (which include not only spatial relations, but also object attributes and actions); (3) induce a grammar for the language being used to describe the perceptual world; and moreover to do all this incrementally, without storing all previous data. The resulting grammar can then be used to parse novel commands for downstream action in a robotic system. Analysing polysemy in spatial prepositions: One challenge in assigning meanings to spatial prepositions is that they can frequently be polysemous, i.e. they can have multiple related senses (the polysemes). As the senses of polysemous terms are so closely intertwined, the theoretical and computational treatment of polysemy presents a difficult challenge for semantic models. To given an example: compare "book on a table", "balloon on the ceiling" and "picture on the wall". discuss this problem and shows how a model can be built in which these senses can be distinguished using data from human subjects. Can Large Language Models perform qualitative spatial reasoning reliably? Many claims (e.g. [10,11,12]) have been made since the emergence of Large Language Models (LLMs) as to their ability to reason. Spatial