Set-valued Variables Research Articles

Integrating Logic Rules with Everything Else, Seamlessly

AbstractThis paper presents a language, Alda, that supports all of logic rules, sets, functions, updates, and objects as seamlessly integrated built-ins. The key idea is to support predicates in rules as set-valued variables that can be used and updated in any scope, and support queries using rules as either explicit or implicit automatic calls to an inference function. We have defined a formal semantics of the language, implemented a prototype compiler that builds on an object-oriented language that supports concurrent and distributed programming and on an efficient logic rule system, and successfully used the language and implementation on benchmarks and problems from a wide variety of application domains. We describe the compilation method and results of experimental evaluation.

Range-Only SLAM With Occupancy Maps: A Set-Membership Approach

This paper proposes a new set-membership approach to solve range-only simultaneous localization and mapping (SLAM) problems in the case where the map is described by an arbitrary occupancy set (i.e., we do not assume that the map is composed of segments, punctual marks, etc.). The principle is to transform the SLAM problem into a hybrid constraint satisfaction problem (CSP), where the variables can either be real numbers, vectors, trajectories, or subsets of \BBR <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> . An extension of existing constraint propagation methods is then proposed to solve hybrid CSPs involving set-valued variables. A simulated test case is then proposed to show the feasibility of the approach.

Representing uncertainty on set-valued variables using belief functions

A formalism is proposed for representing uncertain information on set-valued variables using the formalism of belief functions. A set-valued variable X on a domain Ω is a variable taking zero, one or several values in Ω. While defining mass functions on the frame 2 2 Ω is usually not feasible because of the double-exponential complexity involved, we propose an approach based on a definition of a restricted family of subsets of 2 Ω that is closed under intersection and has a lattice structure. Using recent results about belief functions on lattices, we show that most notions from Dempster–Shafer theory can be transposed to that particular lattice, making it possible to express rich knowledge about X with only limited additional complexity as compared to the single-valued case. An application to multi-label classification (in which each learning instance can belong to several classes simultaneously) is demonstrated.

Stochastic nagumo's viability theorem

This paper is devoted to viability of random set-valued variables by stochastic differential equations, characterized in terms of stochastic tangent sets to random set-valued variables

Random sets and fuzzy interval analysis

Abstract A general expression of function with random set-valued arguments is stated, which encompasses Zadeh's extension principle as well as functions of random variables, and interval analysis. A monotonicity property is derived for algebraic operations performed between random set-valued variables. This property extends the monotonicity of functions with set-valued arguments, in the sense of inclusion. The application of this result to the approximate calculation of functions of random variables is suggested and illustrated by an example.