Related papers: Induction Models on \mathbb{N}
Recent work has shown that large pretrained Language Models (LMs) can not only perform remarkably well on a range of Natural Language Processing (NLP) tasks but also start improving on reasoning tasks such as arithmetic induction, symbolic…
Inductive definitions are an important form of knowledge. The logic FO(ID) is an extension of classical first-order logic FO with general non-monotone inductive definitions. Most existing proof systems for inductive definitions impose…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such…
We present a sequent-based deductive system for automatically proving entailments in separation logic by using mathematical induction. Our technique, called mutual explicit induction proof, is an instance of Noetherian induction.…
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
The theory of spin models intersects with condensed matter physics, complex systems, graph theory, combinatorial optimization, computational complexity and neural networks. Many ensuing applications rely on the fact that complicated spin…
In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time. In this paper, we introduce INT, an INequality Theorem proving benchmark, specifically designed to…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
One of the most basic functions of language is to refer to objects in a shared scene. Modeling reference with continuous representations is challenging because it requires individuation, i.e., tracking and distinguishing an arbitrary number…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
Reasoning is an important task for large language models (LLMs). Among all the reasoning paradigms, inductive reasoning is one of the fundamental types, which is characterized by its particular-to-general thinking process and the…
A key result in a 2004 paper by S. Arkhipov, R. Bezrukavnikov, and V. Ginzburg (ABG) gives an equivalence of the bounded derived category of finite dimensional modules for the principal block of a Lusztig quantum algebra at an $\ell^{th}$…
Sequence comparison is a basic task to capture similarities and differences between two or more sequences of symbols, with countless applications such as in computational biology. An alignment is a way to compare sequences, where a giving…
In the recent past, the reduction-based and the model-based methods to prove cut elimination have converged, so that they now appear just as two sides of the same coin. This paper details some of the steps of this transformation.
Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are…
We show that induction of covariant representations for C*-dynamical systems is natural in the sense that it gives a natural transformation between certain crossed-product functors. This involves setting up suitable categories of…
The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to…
We give an explicit criterion for the irreducibility of some induction products of evaluation modules of affine Hecke algebras of type A. This allows to describe the form of the singularities of the trigonometric R-matrix associated to any…
Researchers have derived many theoretical models for specifying users' insights as they interact with a visualization system. These representations are essential for understanding the insight discovery process, such as when inferring user…