Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective

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.Comment: Updated version, draft of accepted IJCAI2020 Survey Pape

Parameter Learning of Logic Programs for Symbolic-Statistical Modeling

We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, that runs for a class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have been developed independently in each research field. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can significantly outperform the Inside-Outside algorithm

Compositional Set Invariance in Network Systems with Assume-Guarantee Contracts

This paper presents an assume-guarantee reasoning approach to the computation of robust invariant sets for network systems. Parameterized signal temporal logic (pSTL) is used to formally describe the behaviors of the subsystems, which we use as the template for the contract. We show that set invariance can be proved with a valid assume-guarantee contract by reasoning about individual subsystems. If a valid assume-guarantee contract with monotonic pSTL template is known, it can be further refined by value iteration. When such a contract is not known, an epigraph method is proposed to solve for a contract that is valid, ---an approach that has linear complexity for a sparse network. A microgrid example is used to demonstrate the proposed method. The simulation result shows that together with control barrier functions, the states of all the subsystems can be bounded inside the individual robust invariant sets.Comment: Submitted to 2019 American Control Conferenc

Parameterized Compilation Lower Bounds for Restricted CNF-formulas

We show unconditional parameterized lower bounds in the area of knowledge compilation, more specifically on the size of circuits in decomposable negation normal form (DNNF) that encode CNF-formulas restricted by several graph width measures. In particular, we show that - there are CNF formulas of size $n$ and modular incidence treewidth $k$ whose smallest DNNF-encoding has size $n^{\Omega(k)}$, and - there are CNF formulas of size $n$ and incidence neighborhood diversity $k$ whose smallest DNNF-encoding has size $n^{\Omega(\sqrt{k})}$. These results complement recent upper bounds for compiling CNF into DNNF and strengthen---quantitatively and qualitatively---known conditional low\-er bounds for cliquewidth. Moreover, they show that, unlike for many graph problems, the parameters considered here behave significantly differently from treewidth

COST Action IC 1402 ArVI: Runtime Verification Beyond Monitoring -- Activity Report of Working Group 1

This report presents the activities of the first working group of the COST Action ArVI, Runtime Verification beyond Monitoring. The report aims to provide an overview of some of the major core aspects involved in Runtime Verification. Runtime Verification is the field of research dedicated to the analysis of system executions. It is often seen as a discipline that studies how a system run satisfies or violates correctness properties. The report exposes a taxonomy of Runtime Verification (RV) presenting the terminology involved with the main concepts of the field. The report also develops the concept of instrumentation, the various ways to instrument systems, and the fundamental role of instrumentation in designing an RV framework. We also discuss how RV interplays with other verification techniques such as model-checking, deductive verification, model learning, testing, and runtime assertion checking. Finally, we propose challenges in monitoring quantitative and statistical data beyond detecting property violation

Techniques for automated parameter estimation in computational models of probabilistic systems

The main contribution of this dissertation is the design of two new algorithms for automatically synthesizing values of numerical parameters of computational models of complex stochastic systems such that the resultant model meets user-specified behavioral specifications. These algorithms are designed to operate on probabilistic systems – systems that, in general, behave differently under identical conditions. The algorithms work using an approach that combines formal verification and mathematical optimization to explore a model\u27s parameter space. The problem of determining whether a model instantiated with a given set of parameter values satisfies the desired specification is first defined using formal verification terminology, and then reformulated in terms of statistical hypothesis testing. Parameter space exploration involves determining the outcome of the hypothesis testing query for each parameter point and is guided using simulated annealing. The first algorithm uses the sequential probability ratio test (SPRT) to solve the hypothesis testing problems, whereas the second algorithm uses an approach based on Bayesian statistical model checking (BSMC). The SPRT-based parameter synthesis algorithm was used to validate that a given model of glucose-insulin metabolism has the capability of representing diabetic behavior by synthesizing values of three parameters that ensure that the glucose-insulin subsystem spends at least 20 minutes in a diabetic scenario. The BSMC-based algorithm was used to discover the values of parameters in a physiological model of the acute inflammatory response that guarantee a set of desired clinical outcomes. These two applications demonstrate how our algorithms use formal verification, statistical hypothesis testing and mathematical optimization to automatically synthesize parameters of complex probabilistic models in order to meet user-specified behavioral propertie

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

Systems and Methods for Inducing Effects in a Signal

A system for inducing an effect in a raw audio signal comprises a computing device for receiving a first audio signal and a second audio signal from a signal source, and the second audio signal comprises the first audio signal induced with an effect. The system further comprises logic that parameterizes the effect in the second audio signal into an artificial neural network (ANN)

Content-based Video Retrieval by Integrating Spatio-Temporal and Stochastic Recognition of Events

As amounts of publicly available video data grow the need to query this data efficiently becomes significant. Consequently content-based retrieval of video data turns out to be a challenging and important problem. We address the specific aspect of inferring semantics automatically from raw video data. In particular, we introduce a new video data model that supports the integrated use of two different approaches for mapping low-level features to high-level concepts. Firstly, the model is extended with a rule-based approach that supports spatio-temporal formalization of high-level concepts, and then with a stochastic approach. Furthermore, results on real tennis video data are presented, demonstrating the validity of both approaches, as well us advantages of their integrated us