Givenasignature , a (possiblyinfinite) set Z andrelation-decoders ,a soft-structureisatuple Z =( Z, ). Inordertoground andevaluate architecture 3. Figure 1 outlines S and DCretains embeddings show regions, DC, increasing appears performance.

Knowledge representation and reasoning in neural networks have been a long-standing endeavor which has attracted much attention recently. The principled integration of reasoning and learning in neural networks is a main objective of the area of neurosymbolic Artificial Intelligence (AI). In this chapter, a simple energy-based neurosymbolic AI system is described that can represent and reason formally about any propositional logic formula. This creates a powerful combination of learning from data and knowledge and logical reasoning. We start by positioning neurosymbolic AI in the context of the current AI landscape that is unsurprisingly dominated by Large Language Models (LLMs). We identify important challenges of data efficiency, fairness and safety of LLMs that might be addressed by neurosymbolic reasoning systems with formal reasoning capabilities. We then discuss the representation of logic by the specific energy-based system, including illustrative examples and empirical evaluation of the correspondence between logical reasoning and energy minimization using Restricted Boltzmann Machines (RBM). Learning from data and knowledge is also evaluated empirically and compared with a symbolic, neural and a neurosymbolic system. Results reported in this chapter in an accessible way are expected to reignite the research on the use of neural networks as massively-parallel models for logical reasoning and promote the principled integration of reasoning and learning in deep networks. We conclude the chapter with a discussion of the importance of positioning neurosymbolic AI within a broader framework of formal reasoning and accountability in AI, discussing the challenges for neurosynbolic AI to tackle the various known problems of reliability of deep learning.

Neural-symbolic integration aims to combine the connectionist subsymbolic with the logical symbolic approach to artificial intelligence. In this paper, we first define the answer set semantics of (boolean) neural nets and then introduce from first principles a class of neural logic programs and show that nets and programs are equivalent.

As Artificial Intelligence, and Deep Learning in particular, reach impressive results, it gains also unprecedented popularity not only in academics and industry but also in popular culture and society in general. This increasingly ubiquitous AI presence has arisen several concerns about its impacts on humanity and the planet, with some well-known scientists like Stephen Hawking having spoken concerns about AI's accountability [1]. Despite achieving outstanding results in Computer Vision, Natural Language Processing and Game Playing [2, 3], tasks in which AIs formerly have poor performance compared to humans, those concerns about AI triggered debates among research communities, including those discussed by Gary Marcus [4] and on AAAI-2020 debate with Geoffrey Hinton, Yoshua Bengio and Yann LeCun [5].

Despite the extensive investment and impressive recent progress at reasoning by similarity, deep learning continues to struggle with more complex forms of reasoning such as non-monotonic and commonsense reasoning. Non-monotonicity is a property of non-classical reasoning typically seen in commonsense reasoning, whereby a reasoning system is allowed (differently from classical logic) to jump to conclusions which may be retracted later, when new information becomes available. Neural-symbolic systems such as Logic Tensor Networks (LTN) have been shown to be effective at enabling deep neural networks to achieve reasoning capabilities. In this paper, we show that by combining a neural-symbolic system with methods from continual learning, LTN can obtain a higher level of accuracy when addressing non-monotonic reasoning tasks. Continual learning is added to LTNs by adopting a curriculum of learning from knowledge and data with recall. We call this process Continual Reasoning, a new methodology for the application of neural-symbolic systems to reasoning tasks. Continual Reasoning is applied to a prototypical non-monotonic reasoning problem as well as other reasoning examples. Experimentation is conducted to compare and analyze the effects that different curriculum choices may have on overall learning and reasoning results. Results indicate significant improvement on the prototypical non-monotonic reasoning problem and a promising outlook for the proposed approach on statistical relational learning examples.

After a year's hiatus, the AI Debate hosted by Gary Marcus and Vincent Boucher returned with a gaggle of AI thinkers, this time including policy types and scholars outside of the discipline of AI such as Noam Chomsky. After a one-year hiatus, the annual artificial intelligence debate organized by Montreal.ai Learn about the leading tech trends the world will lean into over the next 12 months and how they will affect your life and your job. The debate this year, AI Debate 3: The AGI Debate, as it's called, focused on the concept of artificial general intelligence, the notion of a machine capable of integrating a myriad of reasoning abilities approaching human levels. While the previous debate featured a number of AI scholars, Friday's meet-up drew participation by 16 participants from a much wider gamut of professional backgrounds. In addition to numerous computer scientists and AI luminaries, the program included legendary linguist and activist Noam Chomsky, computational neuroscientist Konrad Kording, and Canadian parliament member Michelle Rempel Garner. Also: AI's true goal may no longer be intelligence Marcus was once again joined by his co-host, Vincent Boucher of Montreal.ai. The debate ran longer than planned. The full 3.5 hours can be viewed on the YouTube page for the debate. The debate Web site is agidebate dot com. In addition, you may want to follow the hashtag #agidebate. NYU professor emeritus and AI gadfly Gary Marcus resumed his duties hosting the multi-scholar face-off. Marcus started things off with a slide show of a "very brief history of AI," tongue firmly in cheek. Marcus said that contrary to enthusiasm in the decade following the landmark ImageNet success, the "promise" of machines doing various things had not paid off. He featured reference to his own New Yorker article throwing cold water on the matter.

In recent years, there has been an increasing interest in exploiting logically specified background knowledge in order to obtain neural models (i) with a better performance, (ii) able to learn from less data, and/or (iii) guaranteed to be compliant with the background knowledge itself, e.g., for safety-critical applications. In this survey, we retrace such works and categorize them based on (i) the logical language that they use to express the background knowledge and (ii) the goals that they achieve.

We present a survey of ways in which domain-knowledge has been included when constructing models with neural networks. The inclusion of domain-knowledge is of special interest not just to constructing scientific assistants, but also, many other areas that involve understanding data using human-machine collaboration. In many such instances, machine-based model construction may benefit significantly from being provided with human-knowledge of the domain encoded in a sufficiently precise form. This paper examines two broad approaches to encode such knowledge--as logical and numerical constraints--and describes techniques and results obtained in several sub-categories under each of these approaches.

Current advances in Artificial Intelligence (AI) and Machine Learning (ML) have achieved unprecedented impact across research communities and industry. Nevertheless, concerns about trust, safety, interpretability and accountability of AI were raised by influential thinkers. Many have identified the need for well-founded knowledge representation and reasoning to be integrated with deep learning and for sound explainability. Neural-symbolic computing has been an active area of research for many years seeking to bring together robust learning in neural networks with reasoning and explainability via symbolic representations for network models. In this paper, we relate recent and early research results in neurosymbolic AI with the objective of identifying the key ingredients of the next wave of AI systems. We focus on research that integrates in a principled way neural network-based learning with symbolic knowledge representation and logical reasoning. The insights provided by 20 years of neural-symbolic computing are shown to shed new light onto the increasingly prominent role of trust, safety, interpretability and accountability of AI. We also identify promising directions and challenges for the next decade of AI research from the perspective of neural-symbolic systems.

Neural-symbolic computing has now become the subject of interest of both academic and industry research laboratories. Graph Neural Networks (GNN) have been widely used in relational and symbolic domains, with widespread application of GNNs in combinatorial optimization, constraint satisfaction, relational reasoning and other scientific domains. The need for improved explainability, interpretability and trust of AI systems in general demands principled methodologies, as suggested by neural-symbolic computing. In this paper, we review the state-of-the-art on the use of GNNs as a model of neural-symbolic computing. This includes the application of GNNs in several domains as well as its relationship to current developments in neural-symbolic computing.