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Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…
In this paper, for the first time in the literature, we study the stability of solutions of two classes of feasibility (i.e., split equality and split feasibility) problems by set-valued and variational analysis techniques. Our idea is to…
We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…
We introduce the problem of temporal coverability for realizability and synthesis. Namely, given a language of words that must be covered by a produced system, how to automatically produce such a system. We consider the case of coverability…
The idea of fully accepting statements when the evidence has rendered them probable enough faces a number of difficulties. We leave the interpretation of probability largely open, but attempt to suggest a contextual approach to full belief.…
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…
I think we can agree that dealing with uncertainty is not easy. Probability is the main tool for dealing with uncertainty, and we know there are many probability-related puzzles and paradoxes. Here I describe a rather idiosyncratic…
This paper addresses decision-aiding problems that involve multiple objectives and uncertain states of the world. Inspired by the capability approach, we focus on cases where a policy maker chooses an act that, combined with a state of the…
A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…
We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought;…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
A set X of partial words over a finite alphabet A is called unavoidable if every two-sided infinite word over A has a factor compatible with an element of X. Unlike the case of a set of words without holes, the problem of deciding whether…
We investigate the probabilistic feasibility of randomized solutions to two distinct classes of uncertain multi-agent optimization programs. We first assume that only the constraints of the program are affected by uncertainty, while the…
Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
Tournament solutions provide methods for selecting the "best" alternatives from a tournament and have found applications in a wide range of areas. Previous work has shown that several well-known tournament solutions almost never rule out…
While keyword query empowers ordinary users to search vast amount of data, the ambiguity of keyword query makes it difficult to effectively answer keyword queries, especially for short and vague keyword queries. To address this challenging…
Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on…