As probabilistic computations play an increasing role in solving various problems, researchers have designed probabilistic languages which treat probability distributions as primitive datatypes. Most probabilistic languages, however, focus only on discrete distributions and have limited expressive power. This paper presents a probabilistic language, called λ○, whose expressive power is beyond discrete distributions. Rich expressiveness of λ ○ is due to its use of sampling functions, i.e., mappings from the unit interval (0.0, 1.0] to probability domains, in specifying probability distributions. As such, λ ○ enables programmers to formally express and reason about sampling methods developed in simulation theory. The use of λ ○ is demonstrated with three applications in robotics: robot localization, people tracking, and robotic mapping. All experiments have been carried out with real robots.

Motivated by many practical applications that have to compute in the presence of uncertainty, we propose a monadic probabilistic language based upon the mathematical notion of sampling function. Our language provides a unified representation scheme for probability distributions, enjoys rich expressiveness, and o#ers high versatility in encoding probability distributions. We also develop a novel style of operational semantics called a horizontal operational semantics, under which an evaluation returns not a single outcome but multiple outcomes. We have preliminary evidence that the horizontal operational semantics improves the ordinary operational semantics with respect to both execution time and accuracy in representing probability distributions.

As probabilistic computations play an increasing role in solving various problems, researchers have designed probabilistic languages which treat probability distributions as primitive datatypes. Most probabilistic languages, however, focus only on discrete distributions and have limited expressive power. This article presents a probabilistic language, called λ○, whose expressive power is beyond discrete distributions. Rich expressiveness of λ ○ is due to its use of sampling functions, that is, mappings from the unit interval (0.0, 1.0] to probability domains, in specifying probability distributions. As such, λ ○ enables programmers to formally express and reason about sampling methods developed in simulation theory. The use of λ ○ is demonstrated with three applications in robotics: robot localization, people tracking, and robotic mapping. All experiments have been carried out with real robots.

In a rational programming language, a program specifes a situation encountered by an agent; evaluating the program amounts to computing what a rational agent would believe or do in the situation. Rational programming combines the advantages of declarative representations with features of programming languages such

We have created a logic-based, first-order, and Turingcomplete set of software tools for stochastic modeling. Because the inference scheme for this language is based on a variant of Pearl's loopy belief propagation algorithm, we call it Loopy Logic. Traditional Bayesian belief networks have limited expressive power, basically constrained to that of atomic elements as in the propositional calculus. Our language contains variables that can capture general classes of situations, events, and relationships. A Turing-complete language is able to reason about potentially infinite classes and situations, with a Dynamic Bayesian Network. Since the inference algorithm for Loopy Logic is based on a variant of loopy belief propagation, the language includes an Expectation Maximization-type learning of parameters in the modeling domain. In this paper we briefly present the theoretical foundations for our loopy-logic language and then demonstrate several examples of stochastic modeling and diagnosis.

As probabilistic computations play an increasing role in solving various problems, researchers have designed probabilistic languages to facilitate their modeling. Most of the existing probabilistic languages, however, focus only on discrete distributions, and there has been little effort to develop probabilistic languages whose expressive power is beyond discrete distributions. This dissertation presents a probabilistic language, called PTP (ProbabilisTic Programming), which supports all kinds of probability distributions.

We have created a logic-based, first-order, and Turing-complete set of software tools for stochastic modeling. Because the inference scheme for this language is based on a variant of Pearl’s loopy belief propagation algorithm, we call it Loopy Logic. Traditional Bayesian belief networks have limited expressive power, basically constrained to that of atomic elements as in the propositional calculus. A first-order language contains variables that can capture general classes of situations, events, and relationships. A Turing-complete language is able to reason about potentially infinite classes and situations. Since the inference algorithm for Loopy Logic is based on a variant of loopy belief propagation, the language includes an Expectation Maximization-type learning of parameters in the modeling domain. In this paper we present the theoretical foundations for our loopy-logic language and then demonstrate several examples using the Loopy Logic system for stochastic modeling and diagnosis. 1