Autonomous cyber-physical systems like robots and self-driving cars could greatly benefit from using formal methods to reason reliably about their control decisions. However, before a problem can be solved it needs to be stated. This requires writing a formal physics model of the cyber-physical system, which is a complex task that traditionally requires human expertise and becomes a bottleneck. This paper experimentally studies whether Large Language Models (LLMs) can automate the formalization process. A 20 problem benchmark suite is designed drawing from undergraduate level physics kinematics problems. In each problem, the LLM is provided with a natural language description of the objects' motion and must produce a model in differential game logic (dGL). The model is (1) syntax checked and iteratively refined based on parser feedback, and (2) semantically evaluated by checking whether symbolically executing the dGL formula recovers the solution to the original physics problem. A success rate of 70% (best over 5 samples) is achieved. We analyze failing cases, identifying directions for future improvement. This provides a first quantitative baseline for LLM-based autoformalization from natural language to a hybrid games logic with continuous dynamics.

This perspective piece calls for the study of the new field of Intersymbolic AI, by which we mean the combination of symbolic AI, whose building blocks have inherent significance/meaning, with subsymbolic AI, whose entirety creates significance/effect despite the fact that individual building blocks escape meaning. Canonical kinds of symbolic AI are logic, games and planning. Canonical kinds of subsymbolic AI are (un)supervised machine and reinforcement learning. Intersymbolic AI interlinks the worlds of symbolic AI with its compositional symbolic significance and meaning and of subsymbolic AI with its summative significance or effect to enable culminations of insights from both worlds by going between and across symbolic AI insights with subsymbolic AI techniques that are being helped by symbolic AI principles. For example, Intersymbolic AI may start with symbolic AI to understand a dynamic system, continue with subsymbolic AI to learn its control, and end with symbolic AI to safely use the outcome of the learned subsymbolic AI controller in the dynamic system. Intersymbolic AI combines both symbolic and subsymbolic AI to increase the effectiveness of AI compared to either kind of AI alone, in much the same way that the combination of both conscious and subconscious thought increases the effectiveness of human thought compared to either kind of thought alone. Some successful contributions to the Intersymbolic AI paradigm are surveyed here but many more are considered possible by advancing Intersymbolic AI.

Deep reinforcement learning algorithms (Sutton & Barto, 1998) are effective at learning, often from raw sensor inputs, control policies that optimize for a quantitative reward signal. Learning these policies can require experiencing millions of unsafe actions. Even if a safe policy is finally learned - which will happen only if the reward signal reflects all relevant safety priorities - providing a purely statistical guarantee that the optimal policy is safe requires an unrealistic amount of training data (Kalra & Paddock, 2016). The difficulty of establishing the safety of these algorithms makes it difficult to justify the use of reinforcement learning in safety-critical domains where industry standards demand strong evidence of safety prior to deployment (ISO-26262, 2011). Formal verification provides a rigorous way of establishing safety for traditional control systems (Clarke et al., 2018). The problem of providing formal guarantees in RL is called formally constrained reinforcement learning (FCRL).

The desire to use reinforcement learning in safety-critical settings has inspired a recent interest in formal methods for learning algorithms. Existing formal methods for learning and optimization primarily consider the problem of constrained learning or constrained optimization. Given a single correct model and associated safety constraint, these approaches guarantee efficient learning while provably avoiding behaviors outside the safety constraint. Acting well given an accurate environmental model is an important pre-requisite for safe learning, but is ultimately insufficient for systems that operate in complex heterogeneous environments. This paper introduces verification-preserving model updates, the first approach toward obtaining formal safety guarantees for reinforcement learning in settings where multiple environmental models must be taken into account. Through a combination of design-time model updates and runtime model falsification, we provide a first approach toward obtaining formal safety proofs for autonomous systems acting in heterogeneous environments.

Over the last few decades, the unprecedented pace of technological progress has allowed us to upgrade and modernize much of our infrastructure and solve many long-standing logistical problems. For example, Babylon Health's AI-driven smartphone app is helping assess and prioritize 1.2 million patients in North London, electronic transfers allow us to instantly send money nearly anywhere in the world, and, over the last 20 years, GPS has revolutionized how we navigate, how we track and ship goods, and how we regulate traffic. However, exponential growth comes with its own set of hurdles that must be navigated. The foremost issue is that it's exceedingly difficult to predict how various technologies will evolve. As a result, it becomes challenging to plan for the future and ensure that the necessary safety features are in place.

Formal verification provides a high degree of confidence in safe system operation, but only if reality matches the verified model. Although a good model will be accurate most of the time, even the best models are incomplete. This is especially true in Cyber-Physical Systems because high-fidelity physical models of systems are expensive to develop and often intractable to verify. Conversely, reinforcement learning-based controllers are lauded for their flexibility in unmodeled environments, but do not provide guarantees of safe operation. This paper presents an approach for provably safe learning that provides the best of both worlds: the exploration and optimization capabilities of learning along with the safety guarantees of formal verification. Our main insight is that formal verification combined with verified runtime monitoring can ensure the safety of a learning agent. Verification results are preserved whenever learning agents limit exploration within the confounds of verified control choices as long as observed reality comports with the model used for off-line verification. When a model violation is detected, the agent abandons efficiency and instead attempts to learn a control strategy that guides the agent to a modeled portion of the state space. We prove that our approach toward incorporating knowledge about safe control into learning systems preserves safety guarantees, and demonstrate that we retain the empirical performance benefits provided by reinforcement learning. We also explore various points in the design space for these justified speculative controllers in a simple model of adaptive cruise control model for autonomous cars.

Two self-driving cars are headed down the highway when the lead car decides to speed up to avoid being rear-ended by the second. That car, in turn, slows down to avoid hitting the first. Then a third car suddenly comes between the two, prompting the slower car to change lanes to avoid and accident. The problem: There are cars in the lanes on either side of it. What's an autonomous car to do?