Related papers: Probabilistic Relational Reasoning via Metrics
Program sensitivity measures the distance between the outputs of a program when run on two related inputs. This notion, which plays a key role in areas such as data privacy and optimization, has been the focus of several program analysis…
Language support for differentially-private programming is both crucial and delicate. While elaborate program logics can be very expressive, type-system based approaches using linear types tend to be more lightweight and amenable to…
Program sensitivity measures how robust a program is to small changes in its input, and is a fundamental notion in domains ranging from differential privacy to cyber-physical systems. A natural way to formalize program sensitivity is in…
Curators of sensitive datasets sometimes need to know whether queries against the data are differentially private [Dwork et al. 2006]. Two sorts of logics have been proposed for checking this property: (1) type systems and other static…
Differential privacy is a modern approach in privacy-preserving data analysis to control the amount of information that can be inferred about an individual by querying a database. The most common techniques are based on the introduction of…
In this paper, we introduce a fundamental framework to create a bridge between Probability Theory and Fuzzy Logic. Indeed, our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy…
Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…
Information Retrieval systems can be improved by exploiting context information such as user and document features. This article presents a model based on overlapping probabilistic or fuzzy clusters for such features. The model is applied…
The fuzzy modality `probably` is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is…
In this work, we first define relations on the fuzzy parametrized soft sets and study their properties. We also give a decision making method based on these relations. In approximate reasoning, relations on the fuzzy parametrized soft sets…
A fuzzer provides randomly generated inputs to a targeted software to expose erroneous behavior. To efficiently detect defects, generated inputs should conform to the structure of the input format and thus, grammars can be used to generate…
Relational properties describe multiple runs of one or more programs. They characterize many useful notions of security, program refinement, and equivalence for programs with diverse computational effects, and they have received much…
Humans often communicate by using imprecise language, suggesting that fuzzy concepts with unclear boundaries are prevalent in language use. In this paper, we test the extent to which models trained to capture the distributional statistics…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
We introduce a general model for the local obfuscation of probability distributions by probabilistic perturbation, e.g., by adding differentially private noise, and investigate its theoretical properties. Specifically, we relax a notion of…
In this paper we present a propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is…
We present a framework to formally describe probabilistic system behavior and symbolically reason about it. In particular we aim at reasoning about possible failures and fault tolerance. We regard systems which are composed of different…
In dealing with veracity of data analytics, fuzzy methods are more and more relying on probabilistic and statistical techniques to underpin their applicability. Conversely, standard statistical models usually disregard to take into account…
We develop a method to incrementally construct programming languages. Our approach is categorical: each layer of the language is described as a monad. Our method either (i) concretely builds a distributive law between two monads, i.e.…
In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category…