This thesis studies the single-use restriction for register automata and transducers over infinite alphabets. The restriction requires that a read-access to a register should have the side effect of destroying its contents. This constraint results in robust classes of languages and transductions. For automata models, we show that one-way register automata, two-way register automata, and orbit-finite monoids have the same expressive power. For transducer models, we show that single-use Mealy machines and single-use two-way transducers admit versions of the Krohn-Rhodes decomposition theorem. Moreover, single-use Mealy machines are equivalent to an algebraic model called local algebraic semigroup transductions. Additionally, we show that single-use two-way transducers are equivalent to single-use streaming string transducers (SSTs) over infinite alphabets and to regular list functions with atoms. Compared with the previous work arXiv:1907.10504, this thesis offers a coherent narrative on the single-use restriction. We introduce an abstract notion of single-use functions and use them to define all the discussed single-use models. We also introduce and study the algebraic models of local semigroup transduction and local rational semigroup transduction.

In this chapter, we are interested in formalizing the reasoning of a single agent who can make observations on a dynamic system and considers actions to perform on it. Reasoning about action and change is among the first issues addressed within Artificial Intelligence (AI); especially, it was the subject of the seminal article by McCarthy and Hayes [1969]. Research in this area has been very productive until the late 1990s. Among other things, solutions to the various problems to be faced when dealing with action representation were put forward and a classification of action languages according to their expressive power was undertaken. Moreover, much progress towards the automatization of reasoning about action and change was made, for example through the design and the evaluation of algorithms implementing the reasoning processes of the main action languages and the investigation of the computational complexity of such processes. The reasons why an agent may wish to act in order to modify the current state of a dynamic system or to learn more about it are numerous.

In this work, we prove over 3000 previously ATP-unproved Mizar/MPTP problems by using several ATP and AI methods, raising the number of ATP-solved Mizar problems from 75\% to above 80\%. First, we start to experiment with the cvc5 SMT solver which uses several instantiation-based heuristics that differ from the superposition-based systems, that were previously applied to Mizar,and add many new solutions. Then we use automated strategy invention to develop cvc5 strategies that largely improve cvc5's performance on the hard problems. In particular, the best invented strategy solves over 14\% more problems than the best previously available cvc5 strategy. We also show that different clausification methods have a high impact on such instantiation-based methods, again producing many new solutions. In total, the methods solve 3021 (21.3\%) of the 14163 previously unsolved hard Mizar problems. This is a new milestone over the Mizar large-theory benchmark and a large strengthening of the hammer methods for Mizar.

In order to ensure autonomous vehicles are safe for on-road deployment, simulation-based testing has become an integral complement to on-road testing. The rise in simulation testing and validation reflects a growing need to verify that AV behavior is consistent with desired outcomes even in edge case scenarios $-$ which may seldom or never appear in on-road testing data. This raises a critical question: to what extent are AV failures in simulation consistent with data collected from real-world testing? As a result of the gap between simulated and real sensor data (sim-to-real gap), failures in simulation can either be spurious (simulation- or simulator-specific issues) or relevant (safety-critical AV system issues). One possible method for validating if simulated time series failures are consistent with real world time series sensor data could involve retrieving instances of the failure scenario from a real-world time series dataset, in order to understand AV performance in these scenarios. Adopting this strategy, we propose a formal definition of what constitutes a match between a real-world labeled time series data item and a simulated scenario written from a fragment of the Scenic probabilistic programming language for simulation generation. With this definition of a match, we develop a querying algorithm that identifies the subset of a labeled time series dataset matching a given scenario. To allow this approach to be used to verify the safety of other cyber-physical systems (CPS), we present a definition and algorithm for matching scalable beyond the autonomous vehicles domain. Experiments demonstrate the precision and scalability of the algorithm for a set of challenging and uncommon time series scenarios identified from the nuScenes autonomous driving dataset. We include a full system implementation of the querying algorithm freely available for use across a wide range of CPS.

The process of developing theories and models and testing them with experiments is fundamental to the scientific method. Automating the entire scientific method then requires not only automation of the induction of theories from data, but also experimentation from design to implementation. This is the idea behind a robot scientist -- a coupled system of AI and laboratory robotics that has agency to test hypotheses with real-world experiments. In this chapter we explore some of the fundamentals of robot scientists in the philosophy of science. We also map the activities of a robot scientist to machine learning paradigms, and argue that the scientific method shares an analogy with active learning. We demonstrate these concepts using examples from previous robot scientists, and also from Genesis: a next generation robot scientist designed for research in systems biology, comprising a micro-fluidic system with 1000 computer-controlled micro-bioreactors and interpretable models based in controlled vocabularies and logic.

We introduce LLM-ARC, a neuro-symbolic framework designed to enhance the logical reasoning capabilities of Large Language Models (LLMs), by combining them with an Automated Reasoning Critic (ARC). LLM-ARC employs an Actor-Critic method where the LLM Actor generates declarative logic programs along with tests for semantic correctness, while the Automated Reasoning Critic evaluates the code, runs the tests and provides feedback on test failures for iterative refinement. Implemented using Answer Set Programming (ASP), LLM-ARC achieves a new state-of-the-art accuracy of 88.32% on the FOLIO benchmark which tests complex logical reasoning capabilities. Our experiments demonstrate significant improvements over LLM-only baselines, highlighting the importance of logic test generation and iterative self-refinement. We achieve our best result using a fully automated self-supervised training loop where the Actor is trained on end-to-end dialog traces with Critic feedback. We discuss potential enhancements and provide a detailed error analysis, showcasing the robustness and efficacy of LLM-ARC for complex natural language reasoning tasks.

Developing autonomous decision-making requires safety assurance. Agent programming languages like AgentSpeak and Gwendolen provide tools for programming autonomous decision-making. However, despite numerous efforts to apply model checking to these languages, challenges persist such as a faithful semantic mapping between agent programs and the generated models, efficient model generation, and efficient model checking. As an extension of the agent programming language GOAL, vGOAL has been proposed to formally specify autonomous decisions with an emphasis on safety. This paper tackles the mentioned challenges through two automated model-checking processes for vGOAL: one for Computation Tree Logic and another for Probabilistic Computation Tree Logic. Compared with the existing model-checking approaches of agent programming languages, it has three main advantages. First, it efficiently performs automated model-checking analysis for a given vGOAL specification, including efficiently generating input models for NuSMV and Storm and leveraging these efficient model checkers. Second, the semantic equivalence is established for both nondeterministic models and probabilistic models of vGOAL: from vGOAL to transition systems or DTMCs. Third, an algorithm is proposed for efficiently detecting errors, which is particularly useful for vGOAL specifications that describe complex scenarios. Validation and experiments in a real-world autonomous logistic system with three autonomous mobile robots illustrate both the efficiency and practical usability of the automated CTL and PCTL model-checking process for vGOAL.

With large language models, robots can understand language more flexibly and more capable than ever before. This survey reviews and situates recent literature into a spectrum with two poles: 1) mapping between language and some manually defined formal representation of meaning, and 2) mapping between language and high-dimensional vector spaces that translate directly to low-level robot policy. Using a formal representation allows the meaning of the language to be precisely represented, limits the size of the learning problem, and leads to a framework for interpretability and formal safety guarantees. Methods that embed language and perceptual data into high-dimensional spaces avoid this manually specified symbolic structure and thus have the potential to be more general when fed enough data but require more data and computing to train. We discuss the benefits and tradeoffs of each approach and finish by providing directions for future work that achieves the best of both worlds.

We describe the methods and technologies underlying the application Grants4Companies. The application uses a logic-based expert system to display a list of business grants suitable for the logged-in business. To evaluate suitability of the grants, formal representations of their conditions are evaluated against properties of the business, taken from the registers of the Austrian public administration. The logical language for the representations of the grant conditions is based on S-expressions. We further describe a Proof of Concept implementation of reasoning over the formalised grant conditions. The proof of concept is implemented in Common Lisp and interfaces with a reasoning engine implemented in Scryer Prolog. The application has recently gone live and is provided as part of the Business Service Portal by the Austrian Federal Ministry of Finance.

Solving Olympiad-level mathematical problems represents a significant advancement in machine intelligence and automated reasoning. Current machine learning methods, however, struggle to solve Olympiad-level problems beyond Euclidean plane geometry due to a lack of large-scale, high-quality datasets. The challenge is even greater in algebraic systems, which involve infinite reasoning spaces within finite conditions. To address these issues, we propose AIPS, an Algebraic Inequality Proving System capable of autonomously generating complex inequality theorems and effectively solving Olympiad-level inequality problems without requiring human demonstrations. During proof search in a mixed reasoning manner, a value curriculum learning strategy on generated datasets is implemented to improve proving performance, demonstrating strong mathematical intuitions. On a test set of 20 International Mathematical Olympiad-level inequality problems, AIPS successfully solved 10, outperforming state-of-the-art methods. Furthermore, AIPS automatically generated a vast array of non-trivial theorems without human intervention, some of which have been evaluated by professional contestants and deemed to reach the level of the International Mathematical Olympiad. Notably, one theorem was selected as a competition problem in a major city 2024 Mathematical Olympiad.