A new generation of increasingly autonomous and self-learning systems, which we call embodied systems, is about to be developed. When deploying these systems into a real-life context we face various engineering challenges, as it is crucial to coordinate the behavior of embodied systems in a beneficial manner, ensure their compatibility with our human-centered social values, and design verifiably safe and reliable human-machine interaction. We are arguing that raditional systems engineering is coming to a climacteric from embedded to embodied systems, and with assuring the trustworthiness of dynamic federations of situationally aware, intent-driven, explorative, ever-evolving, largely non-predictable, and increasingly autonomous embodied systems in uncertain, complex, and unpredictable real-world contexts. We are also identifying a number of urgent systems challenges for trustworthy embodied systems, including robust and human-centric AI, cognitive architectures, uncertainty quantification, trustworthy self-integration, and continual analysis and assurance.

Probabilistic model checking has been developed for verifying systems that have stochastic and nondeterministic behavior. Given a probabilistic system, a probabilistic model checker takes a property and checks whether or not the property holds in that system. For this reason, probabilistic model checking provide rigorous guarantees. So far, however, probabilistic model checking has focused on propositional models where a state is represented by a symbol. On the other hand, it is commonly required to make relational abstractions in planning and reinforcement learning. Various frameworks handle relational domains, for instance, STRIPS planning and relational Markov Decision Processes. Using propositional model checking in relational settings requires one to ground the model, which leads to the well known state explosion problem and intractability. We present pCTL-REBEL, a lifted model checking approach for verifying pCTL properties of relational MDPs. It extends REBEL, a relational model-based reinforcement learning technique, toward relational pCTL model checking. PCTL-REBEL is lifted, which means that rather than grounding, the model exploits symmetries to reason about a group of objects as a whole at the relational level. Theoretically, we show that pCTL model checking is decidable for relational MDPs that have a possibly infinite domain, provided that the states have a bounded size. Practically, we contribute algorithms and an implementation of lifted relational model checking, and we show that the lifted approach improves the scalability of the model checking approach.

The human capability to reason about one domain by using knowledge of other domains has been researched for more than 50 years, but models that are formally sound and predict cognitive process are sparse. We propose a formally sound method that models associative reasoning by adapting logical reasoning mechanisms. In particular it is shown that the combination with large commensense knowledge within a single reasoning system demands for an efficient and powerful association technique. This approach is also used for modelling mind-wandering and the Remote Associates Test (RAT) for testing creativity. In a general discussion we show implications of the model for a broad variety of cognitive phenomena including consciousness.

Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely. To avoid disparate efforts,the Open Geometry Prover Community Project aims at the integration of the different efforts for the development of geometry automated theorem provers, under a common "umbrella". In this article the necessary steps to such integration are specified and the current implementation of some of those steps is described.

The burgeoning of AI has prompted recommendations that AI techniques should be "human-centered". However, there is no clear definition of what is meant by Human Centered Artificial Intelligence, or for short, HCAI. This paper aims to improve this situation by addressing some foundational aspects of HCAI. To do so, we introduce the term HCAI agent to refer to any physical or software computational agent equipped with AI components and that interacts and/or collaborates with humans. This article identifies five main conceptual components that participate in an HCAI agent: Observations, Requirements, Actions, Explanations and Models. We see the notion of HCAI agent, together with its components and functions, as a way to bridge the technical and non-technical discussions on human-centered AI. In this paper, we focus our analysis on scenarios consisting of a single agent operating in dynamic environments in presence of humans.

Automated Deduction in Geometry (ADG) is a forum to exchange ideas and views, to present research results and progress, and to demonstrate software tools at the intersection between geometry and automated deduction. Relevant topics include (but are not limited to): polynomial algebra, invariant and coordinate-free methods; probabilistic, synthetic, and logic approaches, techniques for automated geometric reasoning from discrete mathematics, combinatorics, and numerics; interactive theorem proving in geometry; symbolic and numeric methods for geometric computation, geometric constraint solving, automated generation/reasoning and manipulation with diagrams; design and implementation of geometry software, automated theorem provers, special-purpose tools, experimental studies; applications of ADG in mechanics, geometric modelling, CAGD/CAD, computer vision, robotics and education. Traditionally, the ADG conference is held every two years. The previous editions of ADG were held in Nanning in 2018, Strasbourg in 2016, Coimbra in 2014, Edinburgh in 2012, Munich in 2010, Shanghai in 2008, Pontevedra in 2006, Gainesville in 2004, Hagenberg in 2002, Zurich in 2000, Beijing in 1998, and Toulouse in 1996. The 13th edition of ADG was supposed to be held in 2020 in Hagenberg, Austria, but due to the COVID-19 pandemic, it was postponed for 2021, and held online (still hosted by RISC Institute, Hagenberg, Austria), September 15-17, 2021 (https://www.risc.jku.at/conferences/adg2021).

Graphs can represent relational information among entities and graph structures are widely used in many intelligent tasks such as search, recommendation, and question answering. However, most of the graph-structured data in practice suffers from incompleteness, and thus link prediction becomes an important research problem. Though many models are proposed for link prediction, the following two problems are still less explored: (1) Most methods model each link independently without making use of the rich information from relevant links, and (2) existing models are mostly designed based on associative learning and do not take reasoning into consideration. With these concerns, in this paper, we propose Graph Collaborative Reasoning (GCR), which can use the neighbor link information for relational reasoning on graphs from logical reasoning perspectives. We provide a simple approach to translate a graph structure into logical expressions, so that the link prediction task can be converted into a neural logic reasoning problem. We apply logical constrained neural modules to build the network architecture according to the logical expression and use back propagation to efficiently learn the model parameters, which bridges differentiable learning and symbolic reasoning in a unified architecture. To show the effectiveness of our work, we conduct experiments on graph-related tasks such as link prediction and recommendation based on commonly used benchmark datasets, and our graph collaborative reasoning approach achieves state-of-the-art performance.

Over the last couple of decades, there has been a considerable effort devoted to the problem of updating logic programs under the stable model semantics (a.k.a. answer-set programs) or, in other words, the problem of characterising the result of bringing up-to-date a logic program when the world it describes changes. Whereas the state-of-the-art approaches are guided by the same basic intuitions and aspirations as belief updates in the context of classical logic, they build upon fundamentally different principles and methods, which have prevented a unifying framework that could embrace both belief and rule updates. In this paper, we will overview some of the main approaches and results related to answer-set programming updates, while pointing out some of the main challenges that research in this topic has faced.

We propose an efficient interpretable neuro-symbolic model to solve Inductive Logic Programming (ILP) problems. In this model, which is built from a set of meta-rules organised in a hierarchical structure, first-order rules are invented by learning embeddings to match facts and body predicates of a meta-rule. To instantiate it, we specifically design an expressive set of generic meta-rules, and demonstrate they generate a consequent fragment of Horn clauses. During training, we inject a controlled \pw{Gumbel} noise to avoid local optima and employ interpretability-regularization term to further guide the convergence to interpretable rules. We empirically validate our model on various tasks (ILP, visual genome, reinforcement learning) against several state-of-the-art methods.

Is knowledge definable as justified true belief ("JTB")? We argue that one can legitimately answer positively or negatively, depending on whether or not one's true belief is justified by what we call adequate reasons. To facilitate our argument we introduce a simple propositional logic of reason-based belief, and give an axiomatic characterization of the notion of adequacy for reasons. We show that this logic is sufficiently flexible to accommodate various useful features, including quantification over reasons. We use our framework to contrast two notions of JTB: one internalist, the other externalist. We argue that Gettier cases essentially challenge the internalist notion but not the externalist one. Our approach commits us to a form of infallibilism about knowledge, but it also leaves us with a puzzle, namely whether knowledge involves the possession of only adequate reasons, or leaves room for some inadequate reasons. We favor the latter position, which reflects a milder and more realistic version of infallibilism.