Visual question answering (VQA) has been gaining a lot of traction in the machine learning community in the recent years due to the challenges posed in understanding information coming from multiple modalities (i.e., images, language). In VQA, a series of questions are posed based on a set of images and the task at hand is to arrive at the answer. To achieve this, we take a symbolic reasoning based approach using the framework of formal logic. The image and the questions are converted into symbolic representations on which explicit reasoning is performed. We propose a formal logic framework where (i) images are converted to logical background facts with the help of scene graphs, (ii) the questions are translated to first-order predicate logic clauses using a transformer based deep learning model, and (iii) perform satisfiability checks, by using the background knowledge and the grounding of predicate clauses, to obtain the answer. Our proposed method is highly interpretable and each step in the pipeline can be easily analyzed by a human. We validate our approach on the CLEVR and the GQA dataset. We achieve near perfect accuracy of 99.6% on the CLEVR dataset comparable to the state of art models, showcasing that formal logic is a viable tool to tackle visual question answering. Our model is also data efficient, achieving 99.1% accuracy on CLEVR dataset when trained on just 10% of the training data.

We propose two new doxastic extensions of fuzzy \L ukasiewicz logic in which their semantics are Kripke-based with both fuzzy atomic propositions and fuzzy accessibility relations. A class of these extensions is equipped with uninformed belief operator, and the other class is based on a new notion of skeptical belief. We model a fuzzy version of muddy children problem and a CPA-security experiment using uniformed belief and skeptical belief, respectively. Moreover, we prove soundness and completeness for both of these belief extensions.

A shallow semantical embedding for public announcement logic with relativized common knowledge is presented. This embedding enables the first-time automation of this logic with off-the-shelf theorem provers for classical higher-order logic. It is demonstrated (i) how meta-theoretical studies can be automated this way, and (ii) how non-trivial reasoning in the target logic (public announcement logic), required e.g. to obtain a convincing encoding and automation of the wise men puzzle, can be realized. Key to the presented semantical embedding is that evaluation domains are modeled explicitly and treated as an additional parameter in the encodings of the constituents of the embedded target logic; in previous related works, e.g. on the embedding of normal modal logics, evaluation domains were implicitly shared between meta-logic and target logic. The work presented in this article constitutes an important addition to the pluralist LogiKEy knowledge engineering methodology, which enables experimentation with logics and their combinations, with general and domain knowledge, and with concrete use cases -- all at the same time.

The goal of program synthesis from examples is to find a computer program that is consistent with a given set of input-output examples. Most learning-based approaches try to find a program that satisfies all examples at once. Our work, by contrast, considers an approach that breaks the problem into two stages: (a) find programs that satisfy only one example, and (b) leverage these per-example solutions to yield a program that satisfies all examples. We introduce the Cross Aggregator neural network module based on a multi-head attention mechanism that learns to combine the cues present in these per-example solutions to synthesize a global solution. Evaluation across programs of different lengths and under two different experimental settings reveal that when given the same time budget, our technique significantly improves the success rate over PCCoder [32] and other ablation baselines.

Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL formulas for classifying traces; despite a growing interest of the research community, existing solutions suffer from two limitations: they do not scale beyond small formulas, and they may exhaust computational resources without returning any result. We introduce a new algorithm addressing both issues: our algorithm is able to construct formulas an order of magnitude larger than previous methods, and it is anytime, meaning that it in most cases successfully outputs a formula, albeit possibly not of minimal size. We evaluate the performances of our algorithm using an open source implementation against publicly available benchmarks.

The OSSU curriculum is a complete education in computer science using online materials. It's for those who want a proper, well-rounded grounding in concepts fundamental to all computing disciplines, and for those who have the discipline, will, and (most importantly!) good habits to obtain this education largely on their own, but with support from a worldwide community of fellow learners. It is designed according to the degree requirements of undergraduate computer science majors, minus general education (non-CS) requirements, as it is assumed most of the people following this curriculum are already educated outside the field of CS. The courses themselves are among the very best in the world, often coming from Harvard, Princeton, MIT, etc., but specifically chosen to meet the following criteria. When no course meets the above criteria, the coursework is supplemented with a book.

Runtime Verification is a lightweight formal verification technique. It is used to verify at runtime whether the system under analysis behaves as expected. The expected behaviour is usually formally specified by means of properties, which are used to automatically synthesise monitors. A monitor is a device that, given a sequence of events representing a system execution, returns a verdict symbolising the satisfaction or violation of the formal property. Properties that can (resp. cannot) be verified at runtime by a monitor are called monitorable and non-monitorable, respectively. In this paper, we revise the notion of monitorability from a practical perspective, where we show how non-monitorable properties can still be used to generate partial monitors, which can partially check the properties. Finally, we present the implications both from a theoretical and practical perspectives.

We consider the problem of automatically constructing computer programs from input-output examples. We investigate how to augment probabilistic and neural program synthesis methods with new search algorithms, proposing a framework called distribution-based search. Within this framework, we introduce two new search algorithms: Heap Search, an enumerative method, and SQRT Sampling, a probabilistic method. We prove certain optimality guarantees for both methods, show how they integrate with probabilistic and neural techniques, and demonstrate how they can operate at scale across parallel compute environments. Collectively these findings offer theoretical and applied studies of search algorithms for program synthesis that integrate with recent developments in machine-learned program synthesizers.

Goal-directed evaluation of Answer Set Programs is gaining traction thanks to its amenability to create AI systems that can, due to the evaluation mechanism used, generate explanations and justifications. s(CASP) is one of these systems and has been already used to write reasoning systems in several fields. It provides enhanced expressiveness w.r.t. other ASP systems due to its ability to use constraints, data structures, and unbound variables natively. However, the performance of existing s(CASP) implementations is not on par with other ASP systems: model consistency is checked once models have been generated, in keeping with the generate-and-test paradigm. In this work, we present a variation of the top-down evaluation strategy, termed Dynamic Consistency Checking, which interleaves model generation and consistency checking. This makes it possible to determine when a literal is not compatible with the denials associated to the global constraints in the program, prune the current execution branch, and choose a different alternative. This strategy is specially (but not exclusively) relevant in problems with a high combinatorial component. We have experimentally observed speedups of up to 90x w.r.t. the standard versions of s(CASP).

Autonomous systems are highly complex and present unique challenges for the application of formal methods. Autonomous systems act without human intervention, and are often embedded in a robotic system, so that they can interact with the real world. As such, they exhibit the properties of safety-critical, cyber-physical, hybrid, and real-time systems. This EPTCS volume contains the proceedings for the third workshop on Formal Methods for Autonomous Systems (FMAS 2021), which was held virtually on the 21st and 22nd of October 2021. Like the previous workshop, FMAS 2021 was an online, stand-alone event, as an adaptation to the ongoing COVID-19 restrictions. Despite the challenges this brought, we were determined to build on the success of the previous two FMAS workshops. The goal of FMAS is to bring together leading researchers who are tackling the unique challenges of autonomous systems using formal methods, to present recent and ongoing work. We are interested in the use of formal methods to specify, model, or verify autonomous and/or robotic systems; in whole or in part. We are also interested in successful industrial applications and potential future directions for this emerging application of formal methods.