A fundamental use of knowledge bases (KBs) is query answering, i.e., retrieving the information entailed by the KB in response to a user query. When both the KB and the query are specified as logical formulae, the standard form of answer provided to users is the set of all certain answers (CAs): tuples of constants that satisfy the formula defining the query in every model of the logical theory defining the KB. Despite their wide adoption, CAs are known to be just a lossy representation of the information that a KB and a query provide. While several alternative answer languages have been proposed in the literature, no general consensus has emerged on the most suitable approach to query answering over ontological KBs, as each language comes with its own limitations. To address some of these issues, we introduce Regularly Recurrent Answers (RRAs), a novel answer language for queries over ontological KBs based on regular expressions. RRAs support the representation of infinite sets of tuples of constants via a simple (and arguably well understood) generation mechanism. We show that RRAs can capture a fundamental fragment of the certain information entailed by union of conjunctive queries and DL-Lite KBs, making them a strong candidate for informative query answering settings. Our contribution includes the formal definition of RRAs, a proof of their informativeness, and a study of the computational complexity of query answering problem using RRAs.

Neurosymbolic AI is growing in popularity thanks to its ability to combine neural perception and symbolic reasoning in end-to-end trainable models. However, recent findings reveal these are prone to shortcut reasoning, i.e., to learning unindented concepts--or neural predicates--which exploit spurious correlations to satisfy the symbolic constraints. In this paper, we address reasoning shortcuts at their root cause and we introduce Prototypical Neurosymbolic architectures. These models are able to satisfy the symbolic constraints (be right) because they have learnt the correct basic concepts (for the right reasons) and not because of spurious correlations, even in extremely low data regimes. Leveraging the theory of prototypical learning, we demonstrate that we can effectively avoid reasoning shortcuts by training the models to satisfy the background knowledge while taking into account the similarity of the input with respect to the handful of labelled datapoints. We extensively validate our approach on the recently proposed rsbench benchmark suite in a variety of settings and tasks with very scarce supervision: we show significant improvements in learning the right concepts both in synthetic tasks (MNIST-EvenOdd and Kand-Logic) and real-world, high-stake ones (BDD-OIA). Our findings pave the way to prototype grounding as an effective, annotation-efficient strategy for safe and reliable neurosymbolic learning.

Query answering for Knowledge Bases (KBs) amounts to extracting information from the various models of a KB, and presenting the user with an object that represents such information. In the vast majority of cases, this object consists of those tuples of constants that satisfy the query expression either in every model (certain answers) or in some model (possible answers). However, similarly to the case of incomplete databases, both these forms of answers are a lossy representation of all the knowledge inferable from the query and the queried KB. In this paper, we illustrate a formal framework to characterize the information that query answers for KBs are able to represent. As a first application of the framework, we study the informativeness of current query answering approaches, including the recently introduced partial answers. We then define a novel notion of answers, allowing repetition of variables across answer tuples. We show that these answers are capable of representing a meaningful form of information, and we also study their data complexity properties.