Related papers: Quantitative Strongest Post
We present a novel \emph{weakest pre calculus} for \emph{reasoning about quantitative hyperproperties} over \emph{nondeterministic and probabilistic} programs. Whereas existing calculi allow reasoning about the expected value that a…
In this article we investigate the relationships between the classical notions of weakest precondition and weakest liberal precondition, and provide several results, namely that in general, weakest liberal precondition is neither stronger…
We present quantitative separation logic ($\mathsf{QSL}$). In contrast to classical separation logic, $\mathsf{QSL}$ employs quantities which evaluate to real numbers instead of predicates which evaluate to Boolean values. The connectives…
We present a weakest-precondition-style calculus for reasoning about the expected values (pre-expectations) of \emph{mixed-sign unbounded} random variables after execution of a probabilistic program. The semantics of a while-loop is…
This paper presents a wp-style calculus for obtaining bounds on the expected run-time of probabilistic programs. Its application includes determining the (possibly infinite) expected termination time of a probabilistic program and proving…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about…
We study weighted programming, a programming paradigm for specifying mathematical models. More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic…
The large overhead imposed by quantum error correction is a critical challenge to the realization of quantum computers, and motivates searching for alternative error correcting codes and fault-tolerant circuit constructions. Postselection…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…
Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
We present a unified logical framework for representing and reasoning about both probability quantitative and qualitative preferences in probability answer set programming, called probability answer set optimization programs. The proposed…
We study the problem of assessing the robustness of counterfactual explanations for deep learning models. We focus on $\textit{plausible model shifts}$ altering model parameters and propose a novel framework to reason about the robustness…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
Computational interpretations of linear logic allow static control of memory resources: the data produced by the program are endowed through its type with attributes that determine its life cycle, and guarantee safe deallocation. The use of…
We develop a notion of predicate transformer and, in particular, the weakest precondition, appropriate for quantum computation. We show that there is a Stone-type duality between the usual state-transformer semantics and the weakest…
Refinement calculus provides a structured framework for the progressive and modular development of programs, ensuring their correctness throughout the refinement process. This paper introduces a refinement calculus tailored for quantum…
We present a variant of the quantum relational Hoare logic from (Unruh, POPL 2019) that allows us to use "expectations" in pre- and postconditions. That is, when reasoning about pairs of programs, our logic allows us to quantitatively…