Neuro-Symbolic Artificial Intelligence (NeSy AI) has emerged as a promising direction for integrating neural learning with symbolic reasoning. Typically, in the probabilistic variant of such systems, a neural network first extracts a set of symbols from sub-symbolic input, which are then used by a symbolic component to reason in a probabilistic manner towards answering a query. In this work, we address the problem of formally verifying the robustness of such NeSy probabilistic reasoning systems, therefore paving the way for their safe deployment in critical domains. We analyze the complexity of solving this problem exactly, and show that a decision version of the core computation is $\mathrm{NP}^{\mathrm{PP}}$-complete. In the face of this result, we propose the first approach for approximate, relaxation-based verification of probabilistic NeSy systems. We demonstrate experimentally on a standard NeSy benchmark that the proposed method scales exponentially better than solver-based solutions and apply our technique to a real-world autonomous driving domain, where we verify a safety property under large input dimensionalities.

Complex Event Recognition (CER) systems detect event occurrences in streaming input using predefined event patterns. Techniques that learn event patterns from data are highly desirable in CER. Since such patterns are typically represented by symbolic automata, we propose a family of such automata where the transition-enabling conditions are defined by Answer Set Programming (ASP) rules, and which, thanks to the strong connections of ASP to symbolic learning, are learnable from data. We present such a learning approach in ASP, capable of jointly learning the structure of an automaton, while synthesizing the transition guards from building-block predicates, and a scalable, incremental version thereof that progressively revises models learnt from mini-batches using Monte Carlo Tree Search. We evaluate our approach on three CER datasets and empirically demonstrate its efficacy.

Abstract Complex Event Recognition (CER) systems detect event occurrences in streaming time-stamped input using predefined event patterns. Logic-based approaches are of special interest in CER, since, via Statistical Relational AI, they combine uncertainty-resilient reasoning with time and change, with machine learning, thus alleviating the cost of manual event pattern authoring. We present a system based on Answer Set Programming (ASP), capable of probabilistic reasoning with complex event patterns in the form of weighted rules in the Event Calculus, whose structure and weights are learnt online. We compare our ASP-based implementation with a Markov Logic-based one and with a number of state-of-the-art batch learning algorithms on CER data sets for activity recognition, maritime surveillance and fleet management. Our results demonstrate the superiority of our novel approach, both in terms of efficiency and predictive performance. This paper is under consideration for publication in Theory and Practice of Logic Programming (TPLP).

Complex Event Recognition (CER) systems detect event occurrences in streaming time-stamped input using predefined event patterns. Logic-based approaches are of special interest in CER, since, via Statistical Relational AI, they combine uncertainty-resilient reasoning with time and change, with machine learning, thus alleviating the cost of manual event pattern authoring. We present WOLED, a system based on Answer Set Programming (ASP), capable of probabilistic reasoning with complex event patterns in the form of weighted rules in the Event Calculus, whose structure and weights are learnt online. We compare our ASP-based implementation with a Markov Logic-based one and with a crisp version of the algorithm that learns unweighted rules, on CER datasets for activity recognition, maritime surveillance and fleet management. Our results demonstrate the superiority of our novel implementation, both in terms of efficiency and predictive performance.

In the recent years research on dynamic social network has increased, which is also due to the availability of data sets from streaming media. Modeling a network's dynamic behaviour can be performed at the level of communities, which represent their mesoscale structure. Communities arise as a result of user to user interaction. In the current work we aim to predict the evolution of communities, i.e. to predict their future form. While this problem has been studied in the past as a supervised learning problem with a variety of classifiers, the problem is that the "knowledge" of a classifier is opaque and consequently incomprehensible to a human. Thus we have employed first order logic, and in particular the event calculus to represent the communities and their evolution. We addressed the problem of predicting the evolution as an online Inductive Logic Programming problem (ILP), where the issue is to learn first order logical clauses that associate evolutionary events, and particular Growth, Shrinkage, Continuation and Dissolution to lower level events. The lower level events are features that represent the structural and temporal characteristics of communities. Experiments have been performed on a real life data set form the Mathematics StackExchange forum, with the OLED framework for ILP. In doing so we have produced clauses that model both short term and long term correlations.

Abstract Systems for symbolic event recognition infer occurrences of events in time using a set of event definitions in the form of first-order rules. The Event Calculus is a temporal logic that has been used as a basis in event recognition applications, providing among others, direct connections to machine learning, via Inductive Logic Programming (ILP). We present an ILP system for online learning of Event Calculus theories. To allow for a single-pass learning strategy, we use the Hoeffding bound for evaluating clauses on a subset of the input stream. We employ a decoupling scheme of the Event Calculus axioms during the learning process, that allows to learn each clause in isolation. Moreover, we use abductive-inductive logic programming techniques to handle unobserved target predicates. We evaluate our approach on an activity recognition application and compare it to a number of batch learning techniques. We obtain results of comparable predicative accuracy with significant speed-ups in training time. We also outperform hand-crafted rules and match the performance of a sound incremental learner that can only operate on noise-free datasets.

We present a system that combines intelligent online tracking with complex event recognition against streaming positions relayed from numerous vessels. Given the vital importance of maritime safety to the environment, the economy, and in national security, our sys-tem leverages the real-time acquisition of vessel activity with ge-ographical and other static information. Thus, it can offer timely notification in emergency situations, such as intrusion into marine preservation areas, loitering, and unsafe sailing. Thanks to a mobil-ity tracking module, evolving trajectories generated by massive po-sitional updates can be compressed online into concise, but reliable synopses per ship, retaining only salient motion features within a sliding window. These features are exploited by a complex event recognition module that detects suspicious situations of interest to maritime authorities. We conducted a comprehensive empirical validation against a real dataset of traces collected from thousands of vessels. Our results confirm the scalability and approximation accuracy of the proposed system, and thus demonstrate its poten-tial for effective, real-time maritime monitoring. 1.