Related papers: Interpolation in model theory
We introduce Craig interpolation and related notions such as uniform interpolation, Beth definability, and theory decomposition in classical propositional logic. We present four approaches to computing interpolants: via quantifier…
This paper develops a general methodology to connect propositional and first-order interpolation. In fact, the existence of suitable skolemizations and of Herbrand expansions together with a propositional interpolant suffice to construct a…
Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…
We review a few results concerning interpolation of monotone functions on infinite lattices, emphasizing the role of set-theoretic considerations. We also discuss a few open problems.
This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric…
This chapter provides a comprehensive overview of proof-theoretic methods for establishing interpolation properties across a range of logics, including classical, intuitionistic, modal, and substructural logics. Central to the discussion…
This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…
We consider interpolation from the viewpoint of fully automated theorem proving in first-order logic as a general core technique for mechanized knowledge processing. For Craig interpolation, our focus is on the two-stage approach, where…
This chapter surveys some of the main results on interpolation in several of the most prominent families of non-classical logics. Special attention is given to the distinction between the two most commonly studied variants of…
Craig interpolation is a widespread method in verification, with important applications such as Predicate Abstraction, CounterExample Guided Abstraction Refinement and Lazy Abstraction With Interpolants. Most state-of-the-art model checking…
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
In this paper we study interpolation in local extensions of a base theory. We identify situations in which it is possible to obtain interpolants in a hierarchical manner, by using a prover and a procedure for generating interpolants in the…
Social abstract argumentation is a principled way to assign values to conflicting (weighted) arguments. In this note we discuss the important property of the uniqueness of the model.
In this paper, we investigate the extrapolation capabilities of implicit deep learning models in handling unobserved data, where traditional deep neural networks may falter. Implicit models, distinguished by their adaptability in layer…
We present a method for extracting general modules for ontologies formulated in the description logic ALC. A module for an ontology is an ideally substantially smaller ontology that preserves all entailments for a user-specified set of…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…
In this article, a model-theoretic approach is proposed to prove that the first-order G\"odel logic, $\mathbf{G}$, as well as its extension $\mathbf{G}^\Delta$ associated with first-order relational languages enjoy the Craig interpolation…