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We present a new software tool for teaching logic based on natural deduction. Its proof system is formalized in the proof assistant Isabelle such that its definition is very precise. Soundness of the formalization has been proved in…
Integer Linear Programming (ILP) provides a viable mechanism to encode explicit and controllable assumptions about explainable multi-hop inference with natural language. However, an ILP formulation is non-differentiable and cannot be…
This paper presents INPROVF, an automatic framework that combines large language models (LLMs) and formal methods to speed up the repair process of high-level robot controllers. Previous approaches based solely on formal methods are…
We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an…
Students in programming languages and formal logic courses often struggle with constructing rule-based derivation trees due to the complexity of applying inference rules, the lack of immediate feedback, and the manual effort required for…
In this paper we present the verification of an imperative implementation of the ubiquitous B+-tree data structure in the interactive theorem prover Isabelle/HOL. The implementation supports membership test, insertion and range queries with…
We provide simple equational principles for deriving rely-guarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution…
Bhat et al. developed an inductive compiler that computes density functions for probability spaces described by programs in a simple probabilistic functional language. In this work, we implement such a compiler for a modified version of…
Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications. However, their ability to generate…
Reinforcement learning has seen wide success in finetuning large language models to better align with instructions via human feedback. The so-called algorithm, Reinforcement Learning with Human Feedback (RLHF) demonstrates impressive…
We formally introduce IsaVODEs (Isabelle verification with Ordinary Differential Equations), a framework for the verification of cyber-physical systems. We describe the semantic foundations of the framework's formalisation in the…
Interactive Theorem Provers (ITPs) are an indispensable tool in the arsenal of formal method experts as a platform for construction and (formal) verification of proofs. The complexity of the proofs in conjunction with the level of expertise…
Machine-learning automation tools, ranging from humble grid-search to hyperopt, auto-sklearn, and TPOT, help explore large search spaces of possible pipelines. Unfortunately, each of these tools has a different syntax for specifying its…
Large Language Models (LLMs), particularly smaller variants, still struggle with complex reasoning tasks. While inference-time prompting can guide reasoning, existing methods often rely on sequential queries. Ensemble approaches offer a…
This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization…
We formally specified the type system and operational semantics of LOOPw with Ott and Isabelle/HOL proof assistant. Moreover, both the type system and the semantics of LOOPw have been tested using Isabelle/HOL program extraction facility…
Using Isabelle/HOL, we verify a union-find data structure with an explain operation due to Nieuwenhuis and Oliveras. We devise a simpler, more naive version of the explain operation whose soundness and completeness is easy to verify. Then,…
Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to…
The heterogeneous nature of the logical foundations used in different interactive proof assistant libraries has rendered discovery of similar mathematical concepts among them difficult. In this paper, we compare a previously proposed…
High-frequency inductive power transfer (IPT) has garnered significant attention in recent years due to its long transmission distance and high efficiency. The inductance values L and quality factors Q of the transmitting and receiving…