In this paper, we introduce the  probabilistic normed groups. Among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. We also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.

We define strong monads of continuous (lower, upper) previsions, and of forks, modeling both probabilistic and non-deterministic choice. This is an elegant alternative to recent proposals by Mislove, Tix, Keimel, and Plotkin. We show that our monads are sound and complete, in the sense that they model exactly the interaction between probabilistic and (demonic, angelic, chaotic) choice.

Bayesian networks provide a probabilistic seman­ tics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the conclusions are much weaker than those computed from complete probability distributions, they are still valuable for suggesting potential actions, eliminating o...

Existing relational learning approaches usually work on complete relational data, but real-world data are often incomplete. This paper proposes the MGDA approach to learn structures of probabilistic relational model (PRM) from incomplete relational data. The missing values are filled in randomly at first, and a maximum likelihood tree (MLT) is generated from the complete data sample. Then, Gibb...

The Inference problem in probabilistic or Bayesian networks—given a probabilistic network and a joint value assignment to a subset of its variables, compute the posterior probability of that assignment—is arguably the canonical computational problem related to such networks. Since it has been proven NP-hard by Cooper in 1990 [2], a number of complexity results have been obtained for the inferen...

We analyze a classical generalized probabilistic satisfiability problem (GGenPSAT) which consists in deciding the satisfiability of Boolean combinations of linear inequalities involving probabilities of classical propositional formulas. GGenPSAT coincides precisely with the satisfiability problem of the probabilistic logic of Fagin et al. and was proved to be NP-complete. Here, we present a pol...

The main goal of this work is to present the proof-theoretical and model-theoretical approach to a probabilistic logic which allows reasoning about temporal information. We extend both the language of linear time logic and the language of probabilistic logic, allowing statements like “A will always hold”and “the probability that A will hold in next moment is at least the probability that B will...

The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton A, are there words accepted by A with probability arbitrarily close to 1? This problem was proved undecidable recently. We sharpen this result, showing that the undecidability holds even if the probabilistic automata have only one probabilistic transition. Our main contributio...

Probabilistic programming languages (PPLs) provide users a clean syntax for concisely representing probabilistic processes and easy access to sophisticated built-in inference algorithms. Unfortunately, writing a PPL program by hand can be difficult for non-experts, requiring extensive knowledge of statistics and deep insights into the data. To make the modeling process easier, we have created a...

We study the problem of exchanging probabilistic data between ontology-based probabilistic databases. The probabilities of the probabilistic source databases are compactly encoded via Boolean formulas with the variables adhering to the dependencies imposed by a Bayesian network, which are closely related to the management of provenance. For the ontologies and the ontology mappings, we consider ...