相关论文: Simple Type Theory with Undefinedness, Quotation, …

A new attempt is demonstrated that QFTs can be UV finite if they are viewed as the low energy effective theories of a fundamental underlying theory (that is complete and well-defined in all respects) according to the modern standard point…

Given a semisimple stable autonomous tensor category over a field $K$, to any group presentation with finite number of generators we associate an element $Q(P)\in K$ invariant under the Andrews-Curtis moves. We show that in fact, this is…

Quantities are essential in documents to describe factual information. They are ubiquitous in application domains such as finance, business, medicine, and science in general. Compared to other information extraction approaches,…

A quotient construction defines an abstract type from a concrete type, using an equivalence relation to identify elements of the concrete type that are to be regarded as indistinguishable. The elements of a quotient type are…

Quantifying uncertainty of machine learning model predictions is essential for reliable decision-making, especially in safety-critical applications. Recently, uncertainty quantification (UQ) theory has advanced significantly, building on a…

This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for…

We propose an abstract notion of a type theory to unify the semantics of various type theories including Martin-L\"{o}f type theory, two-level type theory and cubical type theory. We establish basic results in the semantics of type theory:…

Thanks to information extraction and semantic Web efforts, search on unstructured text is increasingly refined using semantic annotations and structured knowledge bases. However, most users cannot become familiar with the schema of…

Analysability of finite $U$-rank types are explored both in general and in the theory $\mathrm{DCF}_0$. The well-known fact that the equation $\delta(\mathrm{log}\delta x)=0$ is analysable in but not almost internal to the constants is…

We introduce a type and effect system, for an imperative object calculus, which infers "sharing" possibly introduced by the evaluation of an expression, represented as an equivalence relation among its free variables. This direct…

We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the…

Uncertainty Quantification (UQ) is an essential step in computational model validation because assessment of the model accuracy requires a concrete, quantifiable measure of uncertainty in the model predictions. The concept of UQ in the…

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…

There is an increasing need to integrate model-agnostic explanation techniques with concept-based approaches, as the former can explain models across different architectures while the latter makes explanations more faithful and…

Evaluation of QA systems is very challenging and expensive, with the most reliable approach being human annotations of correctness of answers for questions. Recent works (AVA, BEM) have shown that transformer LM encoder based similarity…

This paper presents an elementary introduction to Consistent Quantum Theory (CQT), as developed by Griffiths and others over the past 25 years. The theory is a version of orthodox(Copenhagen) quantum mechanics, based on the notion that the…

There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B)…

We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$…

In this paper, using definability of types over indiscernible sequences as a template, we study a property of formulas and theories called "uniform definability of types over finite sets" (UDTFS). We explore UDTFS and show how it relates to…

Propositional type theory, first studied by Henkin, is the restriction of simple type theory to a single base type that is interpreted as the set of the two truth values. We show that two constants (falsity and implication) suffice for…