相关论文: On the Herbrand Functional Interpretation

We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one…

Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and…

Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view, it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information of which instances…

Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we…

The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…

We model the process of human full interpretation of object images, namely the ability to identify and localize all semantic features and parts that are recognized by human observers. The task is approached by dividing the interpretation of…

In a series of papers, a many-minds interpretation of quantum theory has been developed. The aim in these papers is to present an explicit mathematical formalism which constitutes a complete theory compatible with relativistic quantum field…

Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…

We set up general machinery to study interpretations of fragments of theories. We then apply this to existential fragments of theories of fields, and especially of henselian valued fields. As an application we prove many-one reductions…

Counterfactual explanations have been argued to be one of the most intuitive forms of explanation. They are typically defined as a minimal set of edits on a given data sample that, when applied, changes the output of a model on that sample.…

It is well known that dependence logic captures the complexity class NP, and it has recently been shown that inclusion logic captures P on ordered models. These results demonstrate that team semantics offers interesting new possibilities…

The purpose of this article is threefold: Firstly, we propose some enhancements to the existing definition of 6-functor formalisms. Secondly, we systematically study the category of kernels, which is a certain 2-category attached to every…

The main aim of this paper is to promote a certain style of doing coinductive proofs, similar to inductive proofs as commonly done by mathematicians. For this purpose, we provide a reasonably direct justification for coinductive proofs…

We explain why the main conclusion of Bender et al, hep-th/0511229 [J. Phys. A 39 (2006) 1657] regarding the practical superiority of the non-Hermitian description of PT-symmetric quantum systems over their Hermitian description is not…

Classical semantics assumes that one can model reference, predication and quantification with respect to a fixed domain of precise referent objects. Non-logical terms and quantification are then interpreted directly in terms of elements and…

Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars $\mathbb{R}$ or $\mathbb{C}$ by a real or complex Dedekind complete unital…

We present a conceptual framework that unifies a variety of evaluation metrics for different structured prediction tasks (e.g. event and relation extraction, syntactic and semantic parsing). Our framework requires representing the outputs…

Functional Distributional Semantics is a framework that aims to learn, from text, semantic representations which can be interpreted in terms of truth. Here we make two contributions to this framework. The first is to show how a type of…

Prior works have demonstrated that implicit representations trained only for reconstruction tasks typically generate encodings that are not useful for semantic tasks. In this work, we propose a method that contextualises the encodings of…

We develop and investigate a general theory of representations of second-order functionals, based on a notion of a right comodule for a monad on the category of containers. We show how the notion of comodule representability naturally…