Related papers: A program for the full axiom of choice
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
This paper develops an operational semantics for a release-acquire fragment of the C11 memory model with relaxed accesses. We show that the semantics is both sound and complete with respect to the axiomatic model. The semantics relies on a…
The asynchronous computability theorem (ACT) uses concepts from combinatorial topology to characterize which tasks have wait-free solutions in read-write memory. A task can be expressed as a relation between two chromatic simplicial…
Automatic differentiation (AD) aims to compute derivatives of user-defined functions, but in Turing-complete languages, this simple specification does not fully capture AD's behavior: AD sometimes disagrees with the true derivative of a…
We study computable probably approximately correct (CPAC) learning, where learners are required to be computable functions. It had been previously observed that the Fundamental Theorem of Statistical Learning, which characterizes PAC…
Dummett's logic LC is intuitionistic logic extended with Dummett's axiom: for every two statements the first implies the second or the second implies the first. We present a natural deduction and a Curry-Howard correspondence for…
Answer-set programming (ASP) has emerged recently as a viable programming paradigm. We describe here an ASP system, DATALOG with constraints or DC, based on non-monotonic logic. Informally, DC theories consist of propositional clauses…
The standard axioms of set theory, the Zermelo-Fraenkel axioms (ZFC), do not suffice to answer all questions in mathematics. While this follows abstractly from Kurt G\"odel's famous incompleteness theorems, we nowadays know numerous…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
Reasoning about program correctness has been a central topic in static analysis for many years, with Hoare logic (HL) playing an important role. The key notions in HL are partial and total correctness. Both require that program executions…
Solving a decision theory problem usually involves finding the actions, among a set of possible ones, which optimize the expected reward, possibly accounting for the uncertainty of the environment. In this paper, we introduce the…
We propose a probabilistic Hoare logic aHL based on the union bound, a tool from basic probability theory. While the union bound is simple, it is an extremely common tool for analyzing randomized algorithms. In formal verification terms,…
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
We discuss the computational complexity and feasibility properties of scenario based techniques for uncertain optimization programs. We consider different solution alternatives ranging from the standard scenario approach to recursive…
It is well known that many theorems in recursion theory can be "relativized". This means that they remain true if partial recursive functions are replaced by functions that are partial recursive relative to some fixed oracle set. Uspensky…
Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…
The Curry-Howard correspondence is often described as relating proofs (in intutionistic natural deduction) to programs (terms in simply-typed lambda calculus). However this narrative is hardly a perfect fit, due to the computational content…
Most work on computational complexity is concerned with time. However this course will try to show that program-size complexity, which measures algorithmic information, is of much greater philosophical significance. I'll discuss how one can…
In this paper, we present a Hoare-style logic for reasoning about quantum programs with classical variables. Our approach offers several improvements over previous work: (1) Enhanced expressivity of the programming language: Our logic…