Neural-symbolic learning for knowledge base completion

A query answering task computes the prediction scores of ground queries inferred from a Knowledge Base (KB). Traditional symbolic-based methods solve this task using ‘exact’ provers. However, they are not very scalable and difficult to apply to current large KBs. Sub-symbolic methods have recently been proposed to address this problem. They require to be trained to learn the semantics of the symbolic representation and use it to make predictions about query answering. Such predictions may rely upon unknown rules over the given KB. Not all proposed sub-symbolic systems are capable of inducing rules from the KB; and even more challenging is the learning of rules that are human interpretable. Some approaches, e.g., those based on a Neural Theorem Prover (NTP), are able to address this problem but with limited scalability and expressivity of the rules that they can induce. We take inspiration from the NTP framework and propose three sub-symbolic architectures that solve the query answering task in a scalable manner while supporting the induction of more expressive rules. Two of these architectures, called Topical NTP (TNTP) and Topic-Subdomain NTP (TSNTP), address the scalability aspect. Trained representations of predicates and constants are clustered and the soft-unification of the backward chaining proof procedure that they use is controlled by these clusters. The third architecture, called Negation-as-Failure TSNTP (NAF TSNTP), addresses the expressivity of the induced rules by supporting the learning of rules with negation-as-failure. All these architectures make use of additional hyperparameters that encourage the learning of induced rules during training. Each architecture is evaluated over benchmark datasets with increased complexity in size of the KB, number of predicates and constants present in the KB, and level of incompleteness of the KB with respect to test sets. The evaluation measures the accuracy of query answering prediction and computational time. The former uses two key metrics, AUC_PR and HITS, adopted also by existing sub-symbolic systems that solve the same task, whereas the computational time is in terms of CPU training time. The evaluation performance of our systems is compared against that of existing state-of-the-art sub-symbolic systems, showing that our approaches are indeed in most cases more accurate in solving query answering tasks, whilst being more efficient in computational time. The increased accuracy in some tasks is specifically due to the learning of more expressive rules, thus demonstrating the importance of increased expressivity in rule induction.Open Acces

Principles of Security and Trust

This open access book constitutes the proceedings of the 8th International Conference on Principles of Security and Trust, POST 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 10 papers presented in this volume were carefully reviewed and selected from 27 submissions. They deal with theoretical and foundational aspects of security and trust, including on new theoretical results, practical applications of existing foundational ideas, and innovative approaches stimulated by pressing practical problems

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Principles of Security and Trust

This open access book constitutes the proceedings of the 8th International Conference on Principles of Security and Trust, POST 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 10 papers presented in this volume were carefully reviewed and selected from 27 submissions. They deal with theoretical and foundational aspects of security and trust, including on new theoretical results, practical applications of existing foundational ideas, and innovative approaches stimulated by pressing practical problems

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4

Perspectives on adaptive dynamical systems

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges, and give perspectives on future research directions, looking to inspire interdisciplinary approaches.Comment: 46 pages, 9 figure

Perspectives on adaptive dynamical systems

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches

Second Generation General System Theory: Perspectives in Philosophy and Approaches in Complex Systems

Following the classical work of Norbert Wiener, Ross Ashby, Ludwig von Bertalanffy and many others, the concept of System has been elaborated in different disciplinary fields, allowing interdisciplinary approaches in areas such as Physics, Biology, Chemistry, Cognitive Science, Economics, Engineering, Social Sciences, Mathematics, Medicine, Artificial Intelligence, and Philosophy. The new challenge of Complexity and Emergence has made the concept of System even more relevant to the study of problems with high contextuality. This Special Issue focuses on the nature of new problems arising from the study and modelling of complexity, their eventual common aspects, properties and approaches—already partially considered by different disciplines—as well as focusing on new, possibly unitary, theoretical frameworks. This Special Issue aims to introduce fresh impetus into systems research when the possible detection and correction of mistakes require the development of new knowledge. This book contains contributions presenting new approaches and results, problems and proposals. The context is an interdisciplinary framework dealing, in order, with electronic engineering problems; the problem of the observer; transdisciplinarity; problems of organised complexity; theoretical incompleteness; design of digital systems in a user-centred way; reaction networks as a framework for systems modelling; emergence of a stable system in reaction networks; emergence at the fundamental systems level; behavioural realization of memoryless functions