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Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that…
Modern machine learning pipelines are built on numerical algorithms. Reliable numerical methods are thus a prerequisite for trustworthy machine learning and cyber-physical systems. Therefore, we contribute a framework for verified numerical…
Model execution allows us to prototype and analyse software engineering models by stepping through their possible behaviours, using techniques like animation and simulation. On the other hand, deductive verification allows us to construct…
Transformers have demonstrated exceptional in-context learning (ICL) capabilities, enabling applications across natural language processing, computer vision, and sequential decision-making. In reinforcement learning, ICL reframes learning…
Recently deep reinforcement learning has achieved tremendous success in wide ranges of applications. However, it notoriously lacks data-efficiency and interpretability. Data-efficiency is important as interacting with the environment is…
Software tools of Automated Reasoning are too sophisticated for general use in mathematics education and respective reasoning, while Lucas-Interpretation provides a general concept for integrating such tools into educational software with…
Bilingual mathematical problem solving needs a clear link between language reasoning and symbolic calculation. Large language models often handle language well but are weak in accurate computation. This paper presents HERALD (Hybrid…
We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…
Proof engineering efforts using interactive theorem proving have yielded several impressive projects in software systems and mathematics. A key obstacle to such efforts is the requirement that the domain expert is also an expert in the…
Large Language Models (LLMs) are reported to hold undesirable attestation bias on inference tasks: when asked to predict if a premise P entails a hypothesis H, instead of considering H's conditional truthfulness entailed by P, LLMs tend to…
The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration…
Intrinsic definitional interpreters, definitional interpreters that operate on typing derivations instead of abstract syntax trees, have recently been studied as a promising methodology for defining dynamic semantics of programming…
Natural language is one of the most intuitive ways to express human intent. However, translating instructions and commands towards robotic motion generation and deployment in the real world is far from being an easy task. The challenge of…
Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an…
Large language models (LLMs) often struggle with mathematical problems that require exact computation or multi-step algebraic reasoning. Tool-integrated reasoning (TIR) offers a promising solution by leveraging external tools such as code…
Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…
Automated theorem provers are now commonly used within interactive theorem provers to discharge an increasingly large number of proof obligations. To maintain the trustworthiness of a proof, the automatically found proof must be verified…
Many automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter when translating monomorphic to…
In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…
We present simple new Hoare logics and refinement calculi for hybrid systems in the style of differential dynamic logic. (Refinement) Kleene algebra with tests is used for reasoning about the program structure and generating verification…