Related papers: The Boyer-Moore Waterfall Model Revisited

In this preliminary work, we propose to use a polynomial approach in order to study the stability of switched systems. The proposed strategy is based on the Bernstein interpolation method that may transform a switched system into a…

Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…

In logical reasoning, it is often the case that only some of a collection of assumptions are needed to reach a conclusion. A strengthening lemma is an assertion that a given conclusion is independent in this sense of a particular…

Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…

We introduce an ensemble learning post-processing methodology for probabilistic hydrological modelling. This methodology generates numerous point predictions by applying a single hydrological model, yet with different parameter values drawn…

This comprehensive survey examines Lean 4, a state-of-the-art interactive theorem prover and functional programming language. We analyze its architectural design, type system, metaprogramming capabilities, and practical applications in…

We propose an incremental approach for safety proofs that decomposes a proof with a complex inductive invariant into a sequence of simpler proof steps. Our proof system combines rules for (i) forward reasoning using inductive invariants,…

The most effective techniques to detect LLM-generated text rely on inserting a detectable signature -- or watermark -- during the model's decoding process. Most existing watermarking methods require access to the underlying LLM's logits,…

Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further…

Hierarchical proof trees (hiproofs for short) add structure to ordinary proof trees, by allowing portions of trees to be hierarchically nested. The additional structure can be used to abstract away from details, or to label particular…

Existing watermarking methods for large language models (LLMs) mainly embed watermark by adjusting the token sampling prediction or post-processing, lacking intrinsic coupling with LLMs, which may significantly reduce the semantic quality…

We introduce our implementation in HOL Light of the metatheory for G\"odel-L\"ob provability logic (GL), covering soundness and completeness w.r.t. possible world semantics and featuring a prototype of a theorem prover for GL itself. The…

Proof engineering is notoriously labor-intensive: proofs that are straightforward on paper often require lengthy scripts in theorem provers. Recent advances in large language models (LLMs) create new opportunities for proof automation:…

Robotic cell injection is used for automatically delivering substances into a cell and is an integral component of drug development, genetic engineering and many other areas of cell biology. Traditionally, the correctness of functionality…

We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original…

With the rapid proliferation of generative models, such as diffusion models, digital watermarking has emerged as a crucial solution for identifying AI-generated images. Modern post-hoc watermarking schemes use neural networks to achieve an…

We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus. The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP…

In this paper, we present a visual analytics tool for enabling hypothesis-based evaluation of machine learning (ML) models. We describe a novel ML-testing framework that combines the traditional statistical hypothesis testing (commonly used…

Tool-Integrated Reasoning (TIR) enables large language models (LLMs) to improve their internal reasoning ability by integrating external tools. However, models employing TIR often display suboptimal behaviors, such as insufficient or…

For AI systems to garner widespread public acceptance, we must develop methods capable of explaining the decisions of black-box models such as neural networks. In this work, we identify two issues of current explanatory methods. First, we…