ABSTRACT. Striking advances in machine learning are transforming how we build sequential decision-making systems---from conversational agents and logistics planners to robots, and more generally to computer programs that automate a myriad of everyday tasks. The synthesis of decision-making systems from data presents fundamental challenges to how we effectively integrate and leverage human know-how, reflect human norms and preferences, adhere to safety and regulatory constraints, and how we build systems that are taskable by and understandable to the humans they interact with. In this talk, I’ll discuss how language---both formal and natural language—provides a signal-symbol nexus for building human-compatible AI sequential decision-making systems. Not only does language provide an expressive and concise vehicle for communication, but I’ll show that exploiting the compositional syntax and semantics of language can greatly improve the efficiency of learning.

ABSTRACT. Generalized planning aims to find policies that solve large classes of symbolic planning problems. State abstraction plays a crucial role for generalization---mapping numerous states to a single abstract representation allows for omitting unnecessary details and finding policies that generalize to arbitrary instances within the same problem class. In this paper, we describe a state abstraction technique based on classical methods from first-order reasoning: Skolemization, unification, and regression. We use Skolemization to characterize groups of similar objects through common properties, including relational interdependencies. Unification specializes terms as much as necessary, where the most general unifier provides the most general action that achieves a subgoal, and regression determines under which condition this action leads to the goal. Together, these techniques enable a form of dynamic abstraction and refinement, allowing for the synthesis of general policies that are provably correct on all instances, while outperforming comparable methods both in terms of expressivity and efficiency.

ABSTRACT. Abstraction is widely used in reasoning about action, for instance to facilitate planning or to provide explanations of agent behavior. In this paper, we present an incremental method to synthesize an abstract basic action theory (BAT) in the situation calculus that suppresses uninteresting details from a concrete BAT based on specifications provided by a knowledge engineer. The engineer can introduce abstract actions that are implemented by/mapped into Golog programs over the low-level theory and drop some low-level actions from the abstract BAT. She can also perform state abstraction by introducing high-level fluents that are mapped to low-level state formulas and drop some low-level fluents from the abstract BAT. The method allows the engineer to synthesize the abstract BAT step-by-step, providing the mapping along the way. The abstraction steps are validated to ensure that the resulting high-level BAT is guaranteed to be a sound and/or complete abstraction of the original low-level BAT. Abstraction steps that would fail to yield a sound/complete abstraction are rejected with an explanation for the failure, which guides the engineer towards a solution. Regression and SMT reasoning are used to automatically generate the axiomatization of the new abstract actions and fluents.

ABSTRACT. We present planned work on using abstraction to support the presentation of argumentative reasoning in computational argumentation. Building on our previous symbolic methods for abstracting potentially complex argumentation frameworks, we aim to extend the approach with a machine learning component. In this setting, the latter component determines the parts of the framework that are relevant based on user-input, while symbolic AI ensures that the reasoning presented remains sound at every level of abstraction.

ABSTRACT. Abstraction is a key problem-solving technique in knowledge representation and a common representational operation allowing complex parts to be treated as simpler wholes. In combination with association (co-activation or linking via a typed relationship, as in a subject-verb-object triple), abstraction is one of the central operations cognitive agents use to build complex concepts and statements. We refer to the compositional operation which supports abstraction as "containment", arguing that it can be underprioritised in knowledge representation systems. We propose the association-containment approach: that the operations of containment and association, by which nodes may contain other knowledge graphs and may be employed as a triple's subject, object, or link, give significant representational power. We show that diverse information formats, including sentences, can be effectively represented as association-containment graphs. We apply this approach to converting dependency parse trees into association-containment form. We describe simple transformation rules which can be repeatedly applied to progressively convert dependency parse trees. These results demonstrate the flexibility of the association-containment approach and suggest its utility for knowledge representation.

ABSTRACT. Knowledge base embeddings are widely applied, used for instance to improve link prediction tasks on knowledge graphs by exploiting the geometric regularities occurring during learning.. Techniques where ontological concepts are interpreted as boxes have shown to be particularly useful in this context, as they are both suitably expressive and of low computational cost allowing practical implementations. However, in order to use those regularities for learning reliably, it is necessary to determine and understand the possible biases in the approach: how do we distinguish what is learned due to regularities in the data from what is simply based on the representational limitations of the embedding? In this paper, we establish that there are some severe limitations in expressivity when modeling description logic ontologies with box embeddings in intended target languages such as ELO. We illustrate that, under some weak assumptions, box semantics always satisfy Helly's Property, and is thus too weak to semantically capture ELO in an adequate way. We then characterize how so-called Helly-satisfiable ELO ontologies can be determined and discuss other restrictions of representability arising from Helly's Property, namely the restricted faithfulness of the embeddings.

ABSTRACT. Once upon a time, there was a user who heard of an ontology that perfectly suited their needs. They found a way to open it and... Depending on what happens next, what follows may become either a fairy tale or a nightmare. In this talk, we will not only revisit some approaches to building abstractions over conceptual models and ontologies, but also explore the philosophical side of the story. What does it mean, from a logical point of view, to construct an abstraction? What role does abstraction play in the explanation process? Does it have explanatory power? What role does the user play, and why should we care about their goals? There is no promise of a happily ever after, but there may be a few clues to help you navigate your own journey.

ABSTRACT. This talk aims to explore the role of arbitrary objects in foundational projects based on abstractionist theories. The driving hypothesis of the talk is that mathematical objects implicitly defined by abstraction principles can be understood as arbitrary objects, as defined by Horsten’s Arbitrary Object Theory (AOT, cf. [9], [10]). To support this claim, we will develop a theory of arbitrary abstract objects (AAOT) by extending Horsten’s AOT ([10]) with a schematic abstraction principle (@𝜑= @𝜓↔𝐸𝑞.(𝜑,𝜓)). We will then prove that abstract terms denote arbitrary objects.

ABSTRACT. This paper aims to provide a framework that allows a systematic analysis of some open issues related to the notion of 'concept'. It has two main goals. The first is to offer a unified framework that can account for different conceptual representations (prototype theory, exemplar theory, knowledge view) - in other words for the multifaceted nature of concepts. Here the focus is on the structure conceptual representation have. The second is to develop a framework capable of capturing the continuity and evolution of concepts over time. To this end, the paper proposes treating concepts as forms of embodiment à la Kit Fine.