RankPL: A Qualitative Probabilistic Programming Language

In this paper we introduce RankPL, a modeling language that can be thought of as a qualitative variant of a probabilistic programming language with a semantics based on Spohn's ranking theory. Broadly speaking, RankPL can be used to represent and reason about processes that exhibit uncertainty expressible by distinguishing "normal" from" surprising" events. RankPL allows (iterated) revision of rankings over alternative program states and supports various types of reasoning, including abduction and causal inference. We present the language, its denotational semantics, and a number of practical examples. We also discuss an implementation of RankPL that is available for download

Ranking Theory

Ranking theory is one of the salient formal representations of doxastic states. It differs from others in being able to represent belief in a proposition (= taking it to be true), to also represent degrees of belief (i.e. beliefs as more or less firm), and thus to generally account for the dynamics of these beliefs. It does so on the basis of fundamental and compelling rationality postulates and is hence one way of explicating the rational structure of doxastic states. Thereby it provides foundations for accounts of defeasible or nonmonotonic reasoning. It has widespread applications in philosophy, it proves to be most useful in Artificial Intelligence, and it has started to find applications as a model of reasoning in psychology

Qualitative probabilistic inference under varied entropy levels

In previous work, we studied four well known systems of qualitative probabilistic inference, and presented data from computer simulations in an attempt to illustrate the performance of the systems. These simulations evaluated the four systems in terms of their tendency to license inference to accurate and informative conclusions, given incomplete information about a randomly selected probability distribution. In our earlier work, the procedure used in generating the unknown probability distribution (representing the true stochastic state of the world) tended to yield probability distributions with moderately high entropy levels. In the present article, we present data charting the performance of the four systems when reasoning in environments of various entropy levels. The results illustrate variations in the performance of the respective reasoning systems that derive from the entropy of the environment, and allow for a more inclusive assessment of the reliability and robustness of the four systems