Related papers: Uniform Realizability Interpretations
We introduce a notion of realizability with ordinal Turing machines based on recognizability rather than computability, i.e., the ability to uniquely identify an object. We show that the arising concept of $r$-realizabilty has the property…
I propose a new class of interpretations, {\it real world interpretations}, of the quantum theory of closed systems. These interpretations postulate a preferred factorization of Hilbert space and preferred projective measurements on one…
Estimating uncertainty is at the core of performing scientific measurements in HEP: a measurement is not useful without an estimate of its uncertainty. The goal of uncertainty quantification (UQ) is inextricably linked to the question, "how…
We formalize a novel modeling framework for achieving interpretability in deep learning, anchored in the principle of inference equivariance. While the direct verification of interpretability scales exponentially with the number of…
With dramatic improvements in optimization software, the solution of large-scale problems that seemed intractable decades ago are now a routine task. This puts even more real-world applications into the reach of optimizers. At the same…
We give a new presentation of interactive realizability with a more explicit syntax. Interactive realizability is a realizability semantics that extends the Curry-Howard correspondence to (sub-)classical logic, more precisely to first-order…
We provide a new realisability model based on orthogonality for the multiplicative fragment of linear logic, both in presence of generalised axioms (MLL*) and in the standard case (MLL). The novelty is the definition of cut elimination for…
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment of first-order logic to contexts involving relations of arity greater than two. Quantifiers in this…
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…
In Hayashi and Leigh (2024), the authors formulate classical number realisability for first-order arithmetic and a corresponding axiomatic system based on Krivine's classical realisability interpretation. This paper presents a…
We show that no total functional can uniformly transform $\Pi_1$ primality into explicit $\Sigma_1$ witnesses without violating normalization in $\mathsf{HA}$. The argument proceeds through three complementary translations: a geometric…
We present new results on finite satisfiability of logics with counting and arithmetic. One result is a tight bound on the complexity of satisfiability of logics with so-called local Presburger quantifiers, which sum over neighbors of a…
Wallace (2022) has recently argued that a number of popular approaches to the measurement problem can't be fully extended to relativistic quantum mechanics and quantum field theory; Wallace thus contends that as things currently stand, only…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…
The increasing adoption of machine learning tools has led to calls for accountability via model interpretability. But what does it mean for a machine learning model to be interpretable by humans, and how can this be assessed? We focus on…
This paper argues that interpretability research in Artificial Intelligence (AI) is fundamentally ill-posed as existing definitions of interpretability fail to describe how interpretability can be formally tested or designed for. We posit…
During the last twenty years or so a wide range of realizability interpretations of classical analysis have been developed. In many cases, these are achieved by extending the base interpreting system of primitive recursive functionals with…
For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While…
In this paper, we present a general realizability semantics for the simply typed $\lambda\mu$-calculus. Then, based on this semantics, we derive both weak and strong normalization results for two versions of the $\lambda\mu$-calculus…
Algorithmic interpretability is necessary to build trust, ensure fairness, and track accountability. However, there is no existing formal measurement method for algorithmic interpretability. In this work, we build upon programming language…