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

Probabilistic Default Reasoning with Conditional Constraints

We propose a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. In detail, we generalize the notions of Pearl's entailment in system Z, Lehmann's lexicographic entailment, and Geffner's conditional entailment to conditional constraints. We give some examples that show that the new notions of z-, lexicographic, and conditional entailment have similar properties like their classical counterparts. Moreover, we show that the new notions of z-, lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints.Comment: 8 pages; to appear in Proceedings of the Eighth International Workshop on Nonmonotonic Reasoning, Special Session on Uncertainty Frameworks in Nonmonotonic Reasoning, Breckenridge, Colorado, USA, 9-11 April 200

Confluence versus Ample Sets in Probabilistic Branching Time

To improve the efficiency of model checking in general, and probabilistic model checking in particular, several reduction techniques have been introduced. Two of these, confluence reduction and partial-order reduction by means of ample sets, are based on similar principles, and both preserve branching-time properties for probabilistic models. Confluence reduction has been introduced for probabilistic automata, whereas ample set reduction has been introduced for Markov decision processes. In this presentation we will explore the relationship between confluence and ample sets. To this end, we redefine confluence reduction to handle MDPs. We show that all non-trivial ample sets consist of confluent transitions, but that the converse is not true. We also show that the two notions coincide if the definition of confluence is restricted, and point out the relevant parts where the two theories differ. The results we present also hold for non-probabilistic models, as our theorems can just as well be applied in a context where all transitions are non-probabilistic. To show a practical application of our results, we adapt a state space generation technique based on representative states, already known in combination with confluence reduction, so that it can also be applied with partial-order reduction

A probabilistic analysis of argument cogency

This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align