相关论文: Advanced Proof Viewing in ProofTool

Vector quantization has emerged as a powerful tool in large-scale multimodal models, unifying heterogeneous representations through discrete token encoding. However, its effectiveness hinges on robust codebook design. Current…

Why do modern language models, trained to do well on next-word prediction, appear to generate coherent documents and capture long-range structure? Here we show that next-token prediction is provably powerful for learning longer-range…

In our previous series of studies to investigate the role of evidential reasoning in the RUBRIC system for full-text document retrieval (Tong et al., 1985; Tong and Shapiro, 1985; Tong and Appelbaum, 1987), we identified the important role…

The aim of this thesis is to present an extension to the string graphs of Dixon, Duncan and Kissinger that allows the finite representation of certain infinite families of graphs and graph rewrite rules, and to demonstrate that a logic can…

We introduce a data structure that allows for efficient (probabilistic) presence proofs and non-probabilistic absence proofs in a bandwidth efficient and secure way. The Bloom tree combines the idea of Bloom filters with that of Merkle…

Typeclasses provide an elegant and effective way of managing ad-hoc polymorphism in both programming languages and interactive proof assistants. However, the increasingly sophisticated uses of typeclasses within proof assistants, especially…

Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…

The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…

We are living in the big data age: An ever increasing amount of data is being produced through data acquisition and computer simulations. While large scale analysis and simulations have received significant attention for cloud and…

Ren et al. recently introduced a method for aggregating multiple decision trees into a strong predictor by interpreting a path taken by a sample down each tree as a binary vector and performing linear regression on top of these vectors…

SAT provers are powerful tools for solving real-sized logic problems, but using them requires solid programming knowledge and may be seen w.r.t.\ logic like assembly language w.r.t.\ programming. Something like a high level language was…

We introduce a Three Tier Tree Calculus (3TC) that defines in a systematic way three tiers of tree structures underlying proof search in logic programming. We use 3TC to define a new -- structural -- version of resolution for logic…

Recent advances in large language models have demonstrated impressive capabilities in mathematical formalization. However, existing benchmarks focus on logical verification of declarative propositions, often neglecting the task of…

In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering…

We have developed a Prolog visualization system that is intended to support Prolog programming education. The system uses Logichart diagrams to visualize Prolog programs. The Logichart diagram is designed to visualize the Prolog execution…

This paper describes techniques for growing classification and regression trees designed to induce visually interpretable trees. This is achieved by penalizing splits that extend the subset of features used in a particular branch of the…

We demonstrate the inter-translatability of proofs between the most prominent sequent-based formalisms for G\"odel-L\"ob provability logic. In particular, we consider Sambin and Valentini's sequent system GLseq, Shamkanov's non-wellfounded…

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…

In this work, we present a visualisation tool that is able to process Coq proof scripts and generate a table representation of the contained proofs as $\LaTeX$ or PDF files. This tool has the aim to support both education and review…

Retrieval-based systems approximate access to a corpus by exposing only a truncated subset of available evidence. Even when relevant information exists in the corpus, truncation can prevent compatible evidence from co-occurring, leading to…