Related papers: Quantifier-free induction for lists

The uncountability of the reals was first established by Cantor in what was later heralded as the first paper on set theory. Since the latter constitutes the official foundations of mathematics, the logical study of the uncountability of…

We present the first complete axiomatisation for quantifier-free separation logic. The logic is equipped with the standard concrete heaplet semantics and the proof system has no external feature such as nominals/labels. It is not possible…

Prompt-injected memory can improve reasoning without updating model weights, but it also creates a control problem: retrieved content helps only when it is applied in the right state. We study this problem in a strict training-free setting…

We give a rational form of a generic two-dimensional "quad" map, containing the so-called $Q_4$ case, but whose coefficients are free. Its integrability is proved using the calculation of algebraic entropy.

We analyze why low-speed sensorless control of the IM is intrinsically difficult, and what is gained by signal injection. The explanation relies on the control-theoretic concept of observability applied to a general model of the saturated…

In applications where categorical labels follow a natural hierarchy, classification methods that exploit the label structure often outperform those that do not. Un-fortunately, the majority of classification datasets do not come…

The issue of non-perturbative background independent quantization of matrix models is addressed. The analysis is carried out by considering a simple matrix model which is a matrix extension of ordinary mechanics reduced to 0 dimension. It…

We consider the problem of estimating the class prior in an unlabeled dataset. Under the assumption that an additional labeled dataset is available, the class prior can be estimated by fitting a mixture of class-wise data distributions to…

Concept Bottleneck Models (CBMs) map dense feature representations into human-interpretable concepts which are then combined linearly to make a prediction. However, modern CBMs rely on the CLIP model to obtain image-concept annotations, and…

Elimination of quantifiers is shown to fail dramatically for a group of well-known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds. Furthermore, it is suggested that only by…

We consider the algebras generated by observables in quantum field theory localized in regions in the null plane. For a scalar free field theory, we show that the one-particle structure can be decomposed into a continuous direct integral of…

We present a heuristic based algorithm to induce \textit{nonmonotonic} logic programs that will explain the behavior of XGBoost trained classifiers. We use the technique based on the LIME approach to locally select the most important…

Continual Learning (CL) involves training a machine learning model in a sequential manner to learn new information while retaining previously learned tasks without the presence of previous training data. Although there has been significant…

We present a combination of raising, explicit variable dependency representation, the liberalized delta-rule, and preservation of solutions for first-order deductive theorem proving. Our main motivation is to provide the foundation for our…

The important recent book by G. Schurz appreciates that the no-free-lunch theorems (NFL) have major implications for the problem of (meta) induction. Here I review the NFL theorems, emphasizing that they do not only concern the case where…

Let $U$ be a Lie ideal of a 2-torsion free prime $\Gamma $-ring $M$ such that $u\alpha u\in U$ for all $u\in U$ and $\alpha \in\Gamma $. If $T:M\rightarrow M$ is an additive mapping satifying the relation $T(u\alpha u)=T(u)\alpha u$ for all…

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…

The use of flexible machine-learning (ML) models to generate imputations of missing data within the framework of Multiple Imputation (MI) has recently gained traction, particularly in observational settings. For randomised controlled trials…

In this article we introduce the operations of insertion and deletion working in a random-context and semi-conditional manner. We show that the conditional use of rules strictly increase the computational power. In the case of…