We represent knowledge as integrity constraints in a formalization of probabilistic spatiotemporal knowledge bases. We start by defining the syntax and semantics of a formalization called PST knowledge bases. This definition generalizes an earlier version, called SPOT, which is a declarative framework for the representation and processing of probabilistic spatio-temporal data where probability ...

Our goal is to develop general-purpose techniques for probabilistic reasoning and learning in structured spaces. These spaces are characterized by complex logical constraints on what constitutes a possible world. We propose a tractable formalism, called probabilistic sentential decision diagrams, and show it effectively learns structured probability distributions in two applications: product co...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

Probabilistic logic models are used ever more often to deal with the uncertain relations typical of the real world. However, these models usually require expensive inference procedures. Very recently the problem of identifying tractable languages has come to the fore. In this paper we consider the models used by the learning from interpretations ILP setting, namely sets of integrity constraints...

In this paper, we consider optimization problems under probabilistic constraints which are defined by two-sided inequalities for the underlying normally distributed random vector. As a main step for an algorithmic solution of such problems, we derive a derivative formula for (normal) probabilities of rectangles as functions of their lower or upper bounds. This formula allows to reduce the calcu...

We present probabilistic logic programming under inheritance with overriding. This approach is based on new notions of entailment for reasoning with conditional constraints, which are obtained from the classical notion of logical entailment by adding inheritance with overriding. This is done by using recent approaches to probabilistic default reasoning with conditional constraints. We analyze t...

We present probabilistic logic programming under inheritance with overriding. This approach is based on new notions of entailment for reasoning with conditional constraints, which are obtained from the classical notion of logical entailment by adding inheritance with overriding. This is done by using recent approaches to probabilistic default reasoning with conditional constraints. We analyze t...

Probabilistic constrained stochastic programming problems are considered with discrete random variables on the r.h.s. in the stochastic constraints. It is assumed that the random vector has multivariate Poisson, binomial or geometric distribution. We prove a general theorem that implies that in each of the above cases the c.d.f. majorizes the product of the univariate marginal c.d.f’s and then ...

We consider concurrent probabilistic systems, based on probabilistic automata of Segala & Lynch 55], which allow non-deterministic choice between probability distributions. These systems can be decomposed into a collection of \computation trees" which arise by resolving the non-deterministic, but not probabilistic, choices. The presence of non-determinism means that certain liveness properties ...