Related papers: Rewriting and Inductive Reasoning
In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not…
In a previous work, the first author extended to higher-order rewriting and dependent types the use of size annotations in types, a termination proof technique called type or size based termination and initially developed for ML-like…
Listwise reranking utilizing Large Language Models (LLMs) has achieved state-of-the-art retrieval effectiveness. Recently, reasoning-enhanced models have further pushed these boundaries by employing Chain-of-Thought (CoT) to perform deep…
This paper proposes an iterative inference algorithm for multi-hop explanation regeneration, that retrieves relevant factual evidence in the form of text snippets, given a natural language question and its answer. Combining multiple sources…
A central computational task in database theory, finite model theory, and computer science at large is the evaluation of a first-order sentence on a finite structure. In the context of this task, the \emph{width} of a sentence, defined as…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Learning rich and compact representations is an open topic in many fields such as object recognition or image retrieval. Deep neural networks have made a major breakthrough during the last few years for these tasks but their representations…
Large language models have demonstrated impressive reasoning capabilities but are inherently limited by their knowledge reservoir. Retrieval-augmented reasoning mitigates this limitation by allowing LLMs to query external resources, but…
We focus on the task of reasoning over paragraph effects in situation, which requires a model to understand the cause and effect described in a background paragraph, and apply the knowledge to a novel situation. Existing works ignore the…
We develop a rewriting theory suitable for diagrammatic algebras and lay down the foundations of a systematic study of their higher structures. In this paper, we focus on the question of finding bases. As an application, we give the first…
We present a unified deductive verification framework for first-order temporal properties based on well-founded rankings, where verification conditions are discharged using SMT solvers. To that end, we introduce a novel reduction from…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories. With some new results, we characterise a subclass of equational theories for which…
Large Reasoning Models (LRMs) often suffer from overthinking, generating verbose reasoning traces that compromise both computational efficiency and interpretability. Unlike prior efforts that rely on global length-based rewards, we propose…
We explore the Collatz conjecture and its variants through the lens of termination of string rewriting. We construct a rewriting system that simulates the iterated application of the Collatz function on strings corresponding to mixed…
Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
Transition Algebra (TA) is a type of infinite logic introduced to discuss rewriting systems. The natural deductive proof systems already introduced in TA satisfy completeness for countable signatures. However, it lacks compactness, making…
We consider the problem of automatically generating longer stories of over two thousand words. Compared to prior work on shorter stories, long-range plot coherence and relevance are more central challenges here. We propose the Recursive…
Reranking, the process of refining the output of a first-stage retriever, is often considered computationally expensive, especially with Large Language Models. Borrowing from recent advances in document compression for RAG, we reduce the…