Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes’ theorem to complex problems. In the application of Bayesian networks, most of the work is related to probabilistic inferences. Any variable updating in any node of Bayesi...

We analyze different types of aggregation operators based on the use of probabilities, weighted averages (WAs) and generalized aggregation operators. We present the generalized probabilistic weighted averaging (GPWA) operator. It is a new aggregation operator that unifies the WA and the probability in the same formulation considering the degree of importance that each concept has in the analysi...

Ontologies play a central role in the development of the semantic web, as they provide precise definitions of shared terms in web resources. One important web ontology language is DAML+OIL; it has a formal semantics and a reasoning support through a mapping to the expressive description logic ! with the addition of inverse roles. In this paper, we present a probabilistic extension of ! , called...

In this paper we consider Milner's calculus CCS enriched by a probabilistic choice operator. The calculus is given operational semantics based on probabilistic transition systems. We deene operational notions of preorder and equivalence as prob-abilistic extensions of the simulation preorder and the bisimulation equivalence respectively. We extend existing category-theoretic techniques for solv...

We examine the computational complexity of testing and nding small plans in probabilistic planning domains with both at and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and looping plans, and partially ordered plans under three natural de nitions of plan value. We show that probl...

The notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  Probabilistic Metric space was  introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of  probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are  topological vector spaces and the open mapping an...

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we p...

We extend Lutz's measure to probabilistic classes, and obtain notions of measure on probabilistic complexity classes C such as BPP, BPE and BPEXP. Unlike former attempts, all our measure notions satisfy all three Lutz's measure axioms, that is every singleton fLg has measure zero in C, the whole space C has measure one in C, and "easy innnite unions" of measure zero sets have measure zero. Fina...

Methods of simulated annealing and genetic programming over probabilistic program traces are developed firstly. These methods combine expressiveness of Turing-complete probabilistic languages, in which arbitrary generative models can be defined, and search effectiveness of meta-heuristic methods. To use these methods, one should only specify a generative model of objects of interest and a fitne...

This paper extends the concept of “probabilistic completeness” defined for the motion planners in the state space (or configuration space) to the concept of “probabilistic completeness under uncertainty” for the motion planners in the belief space. Accordingly, an approach is proposed to verify the probabilistic completeness of the sampling-based planners in the belief space. Finally, through t...