Related papers: Isabelle's Metalogic: Formalization and Proof Chec…
We describe a natural deduction formalization of intuitionistic and classical propositional logic in the Isabelle/Pure framework. In contrast to earlier work, where we explored the pedagogical benefits of using a deep embedding approach to…
In Isabelle/HOL, declarative proofs written in the Isar language are widely appreciated for their readability and robustness. However, some users may prefer writing procedural "apply-style" proof scripts since they enable rapid exploration…
Isabelle/HOL augments classical higher-order logic with ad-hoc overloading of constant definitions---that is, one constant may have several definitions for non-overlapping types. In this paper, we present a mechanised proof that HOL with…
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…
Implementing a complex concept as an executable model in a strongly typed, purely functional language hits a sweet spot between mere simulation and formal specification. For research and education it is often desirable to enrich the…
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…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
We formalize the theory of forcing in the set theory framework of Isabelle/ZF. Under the assumption of the existence of a countable transitive model of ZFC, we construct a proper generic extension and show that the latter also satisfies…
Consensus protocols are crucial for a blockchain system as they are what allow agreement between the system's nodes in a potentially adversarial environment. For this reason, it is paramount to ensure their correct design and implementation…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
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…
Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical theory (inspired by ideas of Ernst…
Formal theorem proving, a field at the intersection of mathematics and computer science, has seen renewed interest with advancements in large language models (LLMs). This paper introduces SubgoalXL, a novel approach that synergizes…
We report on our formalization of matrix-interpretation in Isabelle/HOL. Matrices are required to certify termination proofs and we wish to utilize them for complexity proofs, too. For the latter aim, only basic methods have already been…
The Isabelle Archive of Formal Proofs has grown to a significant size in the past years. It makes up for an impressive body of research, which enables a number of statistical approaches to various aspects in theorem proving, and has not yet…
In this Masters thesis we present an implementation of a fragment of "book HoTT" as an object logic for the interactive proof assistant Isabelle. We also give a mathematical description of the underlying theory of the Isabelle/Pure logical…
We report on the mechanization of (preference-based) conditional normative reasoning. Our focus is on Aqvist's system E for conditional obligation, and its extensions. Our mechanization is achieved via a shallow semantical embedding in…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
In this paper, we propose the use of interactive theorem proving for explainable machine learning. After presenting our proposition, we illustrate it on the dedicated application of explaining security attacks using the Isabelle…
Interactive theorem provers are complex systems that require sophisticated platform efforts - and hence systems programming environments - to manage effectively. The Isabelle platform exemplifies this with its Isabelle/Scala systems…