Related papers: Rewriting and Inductive Reasoning
Large Reasoning Models (LRMs) often suffer from overthinking, generating unnecessarily long reasoning chains even for simple tasks. This leads to substantial computational overhead with limited performance gain, primarily due to redundant…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
When proving theorems from large sets of logical assertions, it can be helpful to restrict the search for a proof to those assertions that are relevant, that is, closely related to the theorem in some sense. For example, in the Watson…
Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity.…
We explore a new language model inversion problem under strict black-box, zero-shot, and limited data conditions. We propose a novel training-free framework that reconstructs prompts using only a limited number of text outputs from a…
Reverse thinking plays a crucial role in human reasoning. Humans can reason not only from a problem to a solution but also in reverse, i.e., start from the solution and reason towards the problem. This often enhances overall reasoning…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
Supervised fine-tuning enhances the problem-solving abilities of language models across various mathematical reasoning tasks. To maximize such benefits, existing research focuses on broadening the training set with various data augmentation…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
Sentence compression reduces the length of text by removing non-essential content while preserving important facts and grammaticality. Unsupervised objective driven methods for sentence compression can be used to create customized models…
To understand cognitive reasoning in the brain, it has been proposed that symbols and compositions of symbols are represented by activity patterns (vectors) in a large population of neurons. Formal models implementing this idea [Plate…
This paper presents Abduction and Argumentation as two principled forms for reasoning, and fleshes out the fundamental role that they can play within Machine Learning. It reviews the state-of-the-art work over the past few decades on the…
We present a modification of the superposition calculus that is meant to generate explanations why a set of clauses is satisfiable. This process is related to abductive reasoning, and the explanations generated are clauses constructed over…
In traditional rewriting theory, one studies a set of terms up to a set of rewriting relations. In algebraic rewriting, one instead studies a vector space of terms, up to a vector space of relations. Strikingly, although both theories are…
We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…
The decoding algorithm is critical for open-ended text generation, transforming latent representations into coherent and meaningful outputs. This paper investigates the self-reinforcement effect in text generation and the effectiveness of a…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
We generalize several propositional preprocessing techniques to higher-order logic, building on existing first-order generalizations. These techniques eliminate literals, clauses, or predicate symbols from the problem, with the aim of…
Reinforcement learning-based retrieval-augmented generation (RAG) methods enhance the reasoning abilities of large language models (LLMs). However, most rely only on final-answer rewards, overlooking intermediate reasoning quality. This…